diff options
| author | Erik Schnetter <eschnett@10-4-36-54.lsu.edu> | 2007-11-05 11:21:08 -0600 |
|---|---|---|
| committer | Erik Schnetter <eschnett@10-4-36-54.lsu.edu> | 2007-11-05 11:21:08 -0600 |
| commit | 3cb4af668f8aae3585fad040ee5afcb7254f5fb5 (patch) | |
| tree | b09b1ced63cff895dc51ac766eefbe5d9b856e98 | |
| parent | 0ce4347e570531db0b35480a8f1272f7de555550 (diff) | |
Internal changes, add debug statements
Reverse order of canonical indices of symmetric tensors.
Add debug statements for BSSN constraints.
26 files changed, 2717 insertions, 2590 deletions
diff --git a/ML_ADM/interface.ccl b/ML_ADM/interface.ccl index c3fae86..7137187 100644 --- a/ML_ADM/interface.ccl +++ b/ML_ADM/interface.ccl @@ -48,10 +48,10 @@ public: CCTK_REAL curvrhs type=GF timelevels=1 tags='tensortypealias="DD_sym" tensorweight=1.0000000000000000000' { K11rhs, - K21rhs, - K31rhs, + K12rhs, + K13rhs, K22rhs, - K32rhs, + K23rhs, K33rhs } "curvrhs" @@ -65,10 +65,10 @@ public: CCTK_REAL metricrhs type=GF timelevels=1 tags='tensortypealias="DD_sym" tensorweight=1.0000000000000000000' { g11rhs, - g21rhs, - g31rhs, + g12rhs, + g13rhs, g22rhs, - g32rhs, + g23rhs, g33rhs } "metricrhs" @@ -84,10 +84,10 @@ public: CCTK_REAL curv type=GF timelevels=3 tags='tensortypealias="DD_sym" tensorweight=1.0000000000000000000' { K11, - K21, - K31, + K12, + K13, K22, - K32, + K23, K33 } "curv" @@ -101,10 +101,10 @@ public: CCTK_REAL metric type=GF timelevels=3 tags='tensortypealias="DD_sym" tensorweight=1.0000000000000000000' { g11, - g21, - g31, + g12, + g13, g22, - g32, + g23, g33 } "metric" diff --git a/ML_ADM/param.ccl b/ML_ADM/param.ccl index 71c2edb..adba59f 100644 --- a/ML_ADM/param.ccl +++ b/ML_ADM/param.ccl @@ -121,7 +121,7 @@ KEYWORD K11_bound "Boundary condition to implement" } "skip" private: -KEYWORD K21_bound "Boundary condition to implement" +KEYWORD K12_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -133,7 +133,7 @@ KEYWORD K21_bound "Boundary condition to implement" } "skip" private: -KEYWORD K31_bound "Boundary condition to implement" +KEYWORD K13_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -157,7 +157,7 @@ KEYWORD K22_bound "Boundary condition to implement" } "skip" private: -KEYWORD K32_bound "Boundary condition to implement" +KEYWORD K23_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -205,7 +205,7 @@ KEYWORD g11_bound "Boundary condition to implement" } "skip" private: -KEYWORD g21_bound "Boundary condition to implement" +KEYWORD g12_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -217,7 +217,7 @@ KEYWORD g21_bound "Boundary condition to implement" } "skip" private: -KEYWORD g31_bound "Boundary condition to implement" +KEYWORD g13_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -241,7 +241,7 @@ KEYWORD g22_bound "Boundary condition to implement" } "skip" private: -KEYWORD g32_bound "Boundary condition to implement" +KEYWORD g23_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -355,13 +355,13 @@ CCTK_REAL K11_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL K21_bound_speed "characteristic speed at boundary" +CCTK_REAL K12_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. private: -CCTK_REAL K31_bound_speed "characteristic speed at boundary" +CCTK_REAL K13_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -373,7 +373,7 @@ CCTK_REAL K22_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL K32_bound_speed "characteristic speed at boundary" +CCTK_REAL K23_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -397,13 +397,13 @@ CCTK_REAL g11_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL g21_bound_speed "characteristic speed at boundary" +CCTK_REAL g12_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. private: -CCTK_REAL g31_bound_speed "characteristic speed at boundary" +CCTK_REAL g13_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -415,7 +415,7 @@ CCTK_REAL g22_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL g32_bound_speed "characteristic speed at boundary" +CCTK_REAL g23_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -475,13 +475,13 @@ CCTK_REAL K11_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL K21_bound_limit "limit value for r -> infinity" +CCTK_REAL K12_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. private: -CCTK_REAL K31_bound_limit "limit value for r -> infinity" +CCTK_REAL K13_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -493,7 +493,7 @@ CCTK_REAL K22_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL K32_bound_limit "limit value for r -> infinity" +CCTK_REAL K23_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -517,13 +517,13 @@ CCTK_REAL g11_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL g21_bound_limit "limit value for r -> infinity" +CCTK_REAL g12_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. private: -CCTK_REAL g31_bound_limit "limit value for r -> infinity" +CCTK_REAL g13_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -535,7 +535,7 @@ CCTK_REAL g22_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL g32_bound_limit "limit value for r -> infinity" +CCTK_REAL g23_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -595,13 +595,13 @@ CCTK_REAL K11_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL K21_bound_scalar "Dirichlet boundary value" +CCTK_REAL K12_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. private: -CCTK_REAL K31_bound_scalar "Dirichlet boundary value" +CCTK_REAL K13_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -613,7 +613,7 @@ CCTK_REAL K22_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL K32_bound_scalar "Dirichlet boundary value" +CCTK_REAL K23_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -637,13 +637,13 @@ CCTK_REAL g11_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL g21_bound_scalar "Dirichlet boundary value" +CCTK_REAL g12_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. private: -CCTK_REAL g31_bound_scalar "Dirichlet boundary value" +CCTK_REAL g13_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -655,7 +655,7 @@ CCTK_REAL g22_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL g32_bound_scalar "Dirichlet boundary value" +CCTK_REAL g23_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. diff --git a/ML_ADM/src/Boundaries.c b/ML_ADM/src/Boundaries.c index a79a204..6d66707 100644 --- a/ML_ADM/src/Boundaries.c +++ b/ML_ADM/src/Boundaries.c @@ -90,26 +90,26 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register K11_bound BC for ML_ADM::K11!"); } - if (CCTK_EQUALS(K21_bound, "none" ) || - CCTK_EQUALS(K21_bound, "static") || - CCTK_EQUALS(K21_bound, "flat" ) || - CCTK_EQUALS(K21_bound, "zero" ) ) + if (CCTK_EQUALS(K12_bound, "none" ) || + CCTK_EQUALS(K12_bound, "static") || + CCTK_EQUALS(K12_bound, "flat" ) || + CCTK_EQUALS(K12_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::K21", K21_bound); + "ML_ADM::K12", K12_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register K21_bound BC for ML_ADM::K21!"); + CCTK_WARN(-1, "Failed to register K12_bound BC for ML_ADM::K12!"); } - if (CCTK_EQUALS(K31_bound, "none" ) || - CCTK_EQUALS(K31_bound, "static") || - CCTK_EQUALS(K31_bound, "flat" ) || - CCTK_EQUALS(K31_bound, "zero" ) ) + if (CCTK_EQUALS(K13_bound, "none" ) || + CCTK_EQUALS(K13_bound, "static") || + CCTK_EQUALS(K13_bound, "flat" ) || + CCTK_EQUALS(K13_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::K31", K31_bound); + "ML_ADM::K13", K13_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register K31_bound BC for ML_ADM::K31!"); + CCTK_WARN(-1, "Failed to register K13_bound BC for ML_ADM::K13!"); } if (CCTK_EQUALS(K22_bound, "none" ) || @@ -123,15 +123,15 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register K22_bound BC for ML_ADM::K22!"); } - if (CCTK_EQUALS(K32_bound, "none" ) || - CCTK_EQUALS(K32_bound, "static") || - CCTK_EQUALS(K32_bound, "flat" ) || - CCTK_EQUALS(K32_bound, "zero" ) ) + if (CCTK_EQUALS(K23_bound, "none" ) || + CCTK_EQUALS(K23_bound, "static") || + CCTK_EQUALS(K23_bound, "flat" ) || + CCTK_EQUALS(K23_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::K32", K32_bound); + "ML_ADM::K23", K23_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register K32_bound BC for ML_ADM::K32!"); + CCTK_WARN(-1, "Failed to register K23_bound BC for ML_ADM::K23!"); } if (CCTK_EQUALS(K33_bound, "none" ) || @@ -167,26 +167,26 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register g11_bound BC for ML_ADM::g11!"); } - if (CCTK_EQUALS(g21_bound, "none" ) || - CCTK_EQUALS(g21_bound, "static") || - CCTK_EQUALS(g21_bound, "flat" ) || - CCTK_EQUALS(g21_bound, "zero" ) ) + if (CCTK_EQUALS(g12_bound, "none" ) || + CCTK_EQUALS(g12_bound, "static") || + CCTK_EQUALS(g12_bound, "flat" ) || + CCTK_EQUALS(g12_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::g21", g21_bound); + "ML_ADM::g12", g12_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register g21_bound BC for ML_ADM::g21!"); + CCTK_WARN(-1, "Failed to register g12_bound BC for ML_ADM::g12!"); } - if (CCTK_EQUALS(g31_bound, "none" ) || - CCTK_EQUALS(g31_bound, "static") || - CCTK_EQUALS(g31_bound, "flat" ) || - CCTK_EQUALS(g31_bound, "zero" ) ) + if (CCTK_EQUALS(g13_bound, "none" ) || + CCTK_EQUALS(g13_bound, "static") || + CCTK_EQUALS(g13_bound, "flat" ) || + CCTK_EQUALS(g13_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::g31", g31_bound); + "ML_ADM::g13", g13_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register g31_bound BC for ML_ADM::g31!"); + CCTK_WARN(-1, "Failed to register g13_bound BC for ML_ADM::g13!"); } if (CCTK_EQUALS(g22_bound, "none" ) || @@ -200,15 +200,15 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register g22_bound BC for ML_ADM::g22!"); } - if (CCTK_EQUALS(g32_bound, "none" ) || - CCTK_EQUALS(g32_bound, "static") || - CCTK_EQUALS(g32_bound, "flat" ) || - CCTK_EQUALS(g32_bound, "zero" ) ) + if (CCTK_EQUALS(g23_bound, "none" ) || + CCTK_EQUALS(g23_bound, "static") || + CCTK_EQUALS(g23_bound, "flat" ) || + CCTK_EQUALS(g23_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_ADM::g32", g32_bound); + "ML_ADM::g23", g23_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register g32_bound BC for ML_ADM::g32!"); + CCTK_WARN(-1, "Failed to register g23_bound BC for ML_ADM::g23!"); } if (CCTK_EQUALS(g33_bound, "none" ) || @@ -345,39 +345,39 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(K21_bound, "radiative")) + if (CCTK_EQUALS(K12_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_K21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K21_bound , K21_bound_limit, "LIMIT") < 0) + CCTK_INT handle_K12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K12_bound , K12_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_K21_bound ,K21_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_K12_bound ,K12_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K21_bound, - "ML_ADM::K21", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K12_bound, + "ML_ADM::K12", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K21!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K12!"); } - if (CCTK_EQUALS(K31_bound, "radiative")) + if (CCTK_EQUALS(K13_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_K31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K31_bound , K31_bound_limit, "LIMIT") < 0) + CCTK_INT handle_K13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K13_bound , K13_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_K31_bound ,K31_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_K13_bound ,K13_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K31_bound, - "ML_ADM::K31", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K13_bound, + "ML_ADM::K13", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K31!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K13!"); } @@ -399,21 +399,21 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(K32_bound, "radiative")) + if (CCTK_EQUALS(K23_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_K32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K32_bound , K32_bound_limit, "LIMIT") < 0) + CCTK_INT handle_K23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K23_bound , K23_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_K32_bound ,K32_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_K23_bound ,K23_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K32_bound, - "ML_ADM::K32", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K23_bound, + "ML_ADM::K23", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K32!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::K23!"); } @@ -471,39 +471,39 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(g21_bound, "radiative")) + if (CCTK_EQUALS(g12_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_g21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g21_bound , g21_bound_limit, "LIMIT") < 0) + CCTK_INT handle_g12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g12_bound , g12_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_g21_bound ,g21_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_g12_bound ,g12_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g21_bound, - "ML_ADM::g21", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g12_bound, + "ML_ADM::g12", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g21!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g12!"); } - if (CCTK_EQUALS(g31_bound, "radiative")) + if (CCTK_EQUALS(g13_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_g31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g31_bound , g31_bound_limit, "LIMIT") < 0) + CCTK_INT handle_g13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g13_bound , g13_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_g31_bound ,g31_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_g13_bound ,g13_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g31_bound, - "ML_ADM::g31", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g13_bound, + "ML_ADM::g13", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g31!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g13!"); } @@ -525,21 +525,21 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(g32_bound, "radiative")) + if (CCTK_EQUALS(g23_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_g32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g32_bound , g32_bound_limit, "LIMIT") < 0) + CCTK_INT handle_g23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g23_bound , g23_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_g32_bound ,g32_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_g23_bound ,g23_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g32_bound, - "ML_ADM::g32", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g23_bound, + "ML_ADM::g23", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g32!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_ADM::g23!"); } @@ -695,35 +695,35 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(K21_bound, "scalar")) + if (CCTK_EQUALS(K12_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_K21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K21_bound ,K21_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_K12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K12_bound ,K12_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K21_bound, - "ML_ADM::K21", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K12_bound, + "ML_ADM::K12", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K21!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K12!"); } - if (CCTK_EQUALS(K31_bound, "scalar")) + if (CCTK_EQUALS(K13_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_K31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K31_bound ,K31_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_K13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K13_bound ,K13_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K31_bound, - "ML_ADM::K31", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K13_bound, + "ML_ADM::K13", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K31!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K13!"); } @@ -743,19 +743,19 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(K32_bound, "scalar")) + if (CCTK_EQUALS(K23_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_K32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_K32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_K32_bound ,K32_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_K23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_K23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_K23_bound ,K23_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K32_bound, - "ML_ADM::K32", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_K23_bound, + "ML_ADM::K23", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K32!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::K23!"); } @@ -807,35 +807,35 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(g21_bound, "scalar")) + if (CCTK_EQUALS(g12_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_g21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g21_bound ,g21_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_g12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g12_bound ,g12_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g21_bound, - "ML_ADM::g21", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g12_bound, + "ML_ADM::g12", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g21!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g12!"); } - if (CCTK_EQUALS(g31_bound, "scalar")) + if (CCTK_EQUALS(g13_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_g31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g31_bound ,g31_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_g13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g13_bound ,g13_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g31_bound, - "ML_ADM::g31", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g13_bound, + "ML_ADM::g13", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g31!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g13!"); } @@ -855,19 +855,19 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(g32_bound, "scalar")) + if (CCTK_EQUALS(g23_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_g32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_g32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_g32_bound ,g32_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_g23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_g23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_g23_bound ,g23_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g32_bound, - "ML_ADM::g32", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_g23_bound, + "ML_ADM::g23", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g32!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_ADM::g23!"); } @@ -965,25 +965,25 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) #$bound$#ML_ADM::K11_bound_limit = 0.0 #$bound$#ML_ADM::K11_bound_scalar = 0.0 -#$bound$#ML_ADM::K21_bound = "skip" -#$bound$#ML_ADM::K21_bound_speed = 1.0 -#$bound$#ML_ADM::K21_bound_limit = 0.0 -#$bound$#ML_ADM::K21_bound_scalar = 0.0 +#$bound$#ML_ADM::K12_bound = "skip" +#$bound$#ML_ADM::K12_bound_speed = 1.0 +#$bound$#ML_ADM::K12_bound_limit = 0.0 +#$bound$#ML_ADM::K12_bound_scalar = 0.0 -#$bound$#ML_ADM::K31_bound = "skip" -#$bound$#ML_ADM::K31_bound_speed = 1.0 -#$bound$#ML_ADM::K31_bound_limit = 0.0 -#$bound$#ML_ADM::K31_bound_scalar = 0.0 +#$bound$#ML_ADM::K13_bound = "skip" +#$bound$#ML_ADM::K13_bound_speed = 1.0 +#$bound$#ML_ADM::K13_bound_limit = 0.0 +#$bound$#ML_ADM::K13_bound_scalar = 0.0 #$bound$#ML_ADM::K22_bound = "skip" #$bound$#ML_ADM::K22_bound_speed = 1.0 #$bound$#ML_ADM::K22_bound_limit = 0.0 #$bound$#ML_ADM::K22_bound_scalar = 0.0 -#$bound$#ML_ADM::K32_bound = "skip" -#$bound$#ML_ADM::K32_bound_speed = 1.0 -#$bound$#ML_ADM::K32_bound_limit = 0.0 -#$bound$#ML_ADM::K32_bound_scalar = 0.0 +#$bound$#ML_ADM::K23_bound = "skip" +#$bound$#ML_ADM::K23_bound_speed = 1.0 +#$bound$#ML_ADM::K23_bound_limit = 0.0 +#$bound$#ML_ADM::K23_bound_scalar = 0.0 #$bound$#ML_ADM::K33_bound = "skip" #$bound$#ML_ADM::K33_bound_speed = 1.0 @@ -1000,25 +1000,25 @@ void ML_ADM_ApplyBoundConds(CCTK_ARGUMENTS) #$bound$#ML_ADM::g11_bound_limit = 0.0 #$bound$#ML_ADM::g11_bound_scalar = 0.0 -#$bound$#ML_ADM::g21_bound = "skip" -#$bound$#ML_ADM::g21_bound_speed = 1.0 -#$bound$#ML_ADM::g21_bound_limit = 0.0 -#$bound$#ML_ADM::g21_bound_scalar = 0.0 +#$bound$#ML_ADM::g12_bound = "skip" +#$bound$#ML_ADM::g12_bound_speed = 1.0 +#$bound$#ML_ADM::g12_bound_limit = 0.0 +#$bound$#ML_ADM::g12_bound_scalar = 0.0 -#$bound$#ML_ADM::g31_bound = "skip" -#$bound$#ML_ADM::g31_bound_speed = 1.0 -#$bound$#ML_ADM::g31_bound_limit = 0.0 -#$bound$#ML_ADM::g31_bound_scalar = 0.0 +#$bound$#ML_ADM::g13_bound = "skip" +#$bound$#ML_ADM::g13_bound_speed = 1.0 +#$bound$#ML_ADM::g13_bound_limit = 0.0 +#$bound$#ML_ADM::g13_bound_scalar = 0.0 #$bound$#ML_ADM::g22_bound = "skip" #$bound$#ML_ADM::g22_bound_speed = 1.0 #$bound$#ML_ADM::g22_bound_limit = 0.0 #$bound$#ML_ADM::g22_bound_scalar = 0.0 -#$bound$#ML_ADM::g32_bound = "skip" -#$bound$#ML_ADM::g32_bound_speed = 1.0 -#$bound$#ML_ADM::g32_bound_limit = 0.0 -#$bound$#ML_ADM::g32_bound_scalar = 0.0 +#$bound$#ML_ADM::g23_bound = "skip" +#$bound$#ML_ADM::g23_bound_speed = 1.0 +#$bound$#ML_ADM::g23_bound_limit = 0.0 +#$bound$#ML_ADM::g23_bound_scalar = 0.0 #$bound$#ML_ADM::g33_bound = "skip" #$bound$#ML_ADM::g33_bound_speed = 1.0 diff --git a/ML_ADM/src/ML_ADM_Minkowski.c b/ML_ADM/src/ML_ADM_Minkowski.c index 9319aea..8b4b7b6 100644 --- a/ML_ADM/src/ML_ADM_Minkowski.c +++ b/ML_ADM/src/ML_ADM_Minkowski.c @@ -98,8 +98,8 @@ void ML_ADM_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL n /* Declare local copies of grid functions */ CCTK_REAL alphaL = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta2L = INITVALUE, beta3L = INITVALUE; - CCTK_REAL g11L = INITVALUE, g21L = INITVALUE, g22L = INITVALUE, g31L = INITVALUE, g32L = INITVALUE, g33L = INITVALUE; - CCTK_REAL K11L = INITVALUE, K21L = INITVALUE, K22L = INITVALUE, K31L = INITVALUE, K32L = INITVALUE, K33L = INITVALUE; + CCTK_REAL g11L = INITVALUE, g12L = INITVALUE, g13L = INITVALUE, g22L = INITVALUE, g23L = INITVALUE, g33L = INITVALUE; + CCTK_REAL K11L = INITVALUE, K12L = INITVALUE, K13L = INITVALUE, K22L = INITVALUE, K23L = INITVALUE, K33L = INITVALUE; /* Declare precomputed derivatives*/ /* Declare derivatives */ @@ -117,25 +117,25 @@ void ML_ADM_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL n /* Calculate temporaries and grid functions */ g11L = 1; - g21L = 0; + g12L = 0; - g31L = 0; + g13L = 0; g22L = 1; - g32L = 0; + g23L = 0; g33L = 1; K11L = 0; - K21L = 0; + K12L = 0; - K31L = 0; + K13L = 0; K22L = 0; - K32L = 0; + K23L = 0; K33L = 0; @@ -154,16 +154,16 @@ void ML_ADM_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL n beta2[index] = beta2L; beta3[index] = beta3L; g11[index] = g11L; - g21[index] = g21L; + g12[index] = g12L; + g13[index] = g13L; g22[index] = g22L; - g31[index] = g31L; - g32[index] = g32L; + g23[index] = g23L; g33[index] = g33L; K11[index] = K11L; - K21[index] = K21L; + K12[index] = K12L; + K13[index] = K13L; K22[index] = K22L; - K31[index] = K31L; - K32[index] = K32L; + K23[index] = K23L; K33[index] = K33L; /* Copy local copies back to subblock grid functions */ diff --git a/ML_ADM/src/ML_ADM_RHS.c b/ML_ADM/src/ML_ADM_RHS.c index 718eedc..db9a713 100644 --- a/ML_ADM/src/ML_ADM_RHS.c +++ b/ML_ADM/src/ML_ADM_RHS.c @@ -95,22 +95,22 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ /* Declare shorthands */ CCTK_REAL detg = INITVALUE; - CCTK_REAL G111 = INITVALUE, G121 = INITVALUE, G122 = INITVALUE, G131 = INITVALUE, G132 = INITVALUE, G133 = INITVALUE; - CCTK_REAL G211 = INITVALUE, G221 = INITVALUE, G222 = INITVALUE, G231 = INITVALUE, G232 = INITVALUE, G233 = INITVALUE; - CCTK_REAL G311 = INITVALUE, G321 = INITVALUE, G322 = INITVALUE, G331 = INITVALUE, G332 = INITVALUE, G333 = INITVALUE; - CCTK_REAL gu11 = INITVALUE, gu12 = INITVALUE, gu13 = INITVALUE, gu22 = INITVALUE, gu23 = INITVALUE, gu33 = INITVALUE; + CCTK_REAL G111 = INITVALUE, G112 = INITVALUE, G113 = INITVALUE, G122 = INITVALUE, G123 = INITVALUE, G133 = INITVALUE; + CCTK_REAL G211 = INITVALUE, G212 = INITVALUE, G213 = INITVALUE, G222 = INITVALUE, G223 = INITVALUE, G233 = INITVALUE; + CCTK_REAL G311 = INITVALUE, G312 = INITVALUE, G313 = INITVALUE, G322 = INITVALUE, G323 = INITVALUE, G333 = INITVALUE; + CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE; CCTK_REAL Km11 = INITVALUE, Km12 = INITVALUE, Km13 = INITVALUE, Km21 = INITVALUE, Km22 = INITVALUE, Km23 = INITVALUE; CCTK_REAL Km31 = INITVALUE, Km32 = INITVALUE, Km33 = INITVALUE; - CCTK_REAL R11 = INITVALUE, R21 = INITVALUE, R22 = INITVALUE, R31 = INITVALUE, R32 = INITVALUE, R33 = INITVALUE; + CCTK_REAL R11 = INITVALUE, R12 = INITVALUE, R13 = INITVALUE, R22 = INITVALUE, R23 = INITVALUE, R33 = INITVALUE; CCTK_REAL trK = INITVALUE; /* Declare local copies of grid functions */ CCTK_REAL alphaL = INITVALUE, alpharhsL = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta1rhsL = INITVALUE, beta2L = INITVALUE, beta2rhsL = INITVALUE, beta3L = INITVALUE, beta3rhsL = INITVALUE; - CCTK_REAL g11L = INITVALUE, g11rhsL = INITVALUE, g21L = INITVALUE, g21rhsL = INITVALUE, g22L = INITVALUE, g22rhsL = INITVALUE; - CCTK_REAL g31L = INITVALUE, g31rhsL = INITVALUE, g32L = INITVALUE, g32rhsL = INITVALUE, g33L = INITVALUE, g33rhsL = INITVALUE; - CCTK_REAL K11L = INITVALUE, K11rhsL = INITVALUE, K21L = INITVALUE, K21rhsL = INITVALUE, K22L = INITVALUE, K22rhsL = INITVALUE; - CCTK_REAL K31L = INITVALUE, K31rhsL = INITVALUE, K32L = INITVALUE, K32rhsL = INITVALUE, K33L = INITVALUE, K33rhsL = INITVALUE; + CCTK_REAL g11L = INITVALUE, g11rhsL = INITVALUE, g12L = INITVALUE, g12rhsL = INITVALUE, g13L = INITVALUE, g13rhsL = INITVALUE; + CCTK_REAL g22L = INITVALUE, g22rhsL = INITVALUE, g23L = INITVALUE, g23rhsL = INITVALUE, g33L = INITVALUE, g33rhsL = INITVALUE; + CCTK_REAL K11L = INITVALUE, K11rhsL = INITVALUE, K12L = INITVALUE, K12rhsL = INITVALUE, K13L = INITVALUE, K13rhsL = INITVALUE; + CCTK_REAL K22L = INITVALUE, K22rhsL = INITVALUE, K23L = INITVALUE, K23rhsL = INITVALUE, K33L = INITVALUE, K33rhsL = INITVALUE; /* Declare precomputed derivatives*/ /* Declare derivatives */ @@ -143,16 +143,26 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ CCTK_REAL PDstandard4th23g11 = INITVALUE; CCTK_REAL PDstandard4th31g11 = INITVALUE; CCTK_REAL PDstandard4th32g11 = INITVALUE; - CCTK_REAL PDstandard4th1g21 = INITVALUE; - CCTK_REAL PDstandard4th2g21 = INITVALUE; - CCTK_REAL PDstandard4th3g21 = INITVALUE; - CCTK_REAL PDstandard4th33g21 = INITVALUE; - CCTK_REAL PDstandard4th12g21 = INITVALUE; - CCTK_REAL PDstandard4th13g21 = INITVALUE; - CCTK_REAL PDstandard4th21g21 = INITVALUE; - CCTK_REAL PDstandard4th23g21 = INITVALUE; - CCTK_REAL PDstandard4th31g21 = INITVALUE; - CCTK_REAL PDstandard4th32g21 = INITVALUE; + CCTK_REAL PDstandard4th1g12 = INITVALUE; + CCTK_REAL PDstandard4th2g12 = INITVALUE; + CCTK_REAL PDstandard4th3g12 = INITVALUE; + CCTK_REAL PDstandard4th33g12 = INITVALUE; + CCTK_REAL PDstandard4th12g12 = INITVALUE; + CCTK_REAL PDstandard4th13g12 = INITVALUE; + CCTK_REAL PDstandard4th21g12 = INITVALUE; + CCTK_REAL PDstandard4th23g12 = INITVALUE; + CCTK_REAL PDstandard4th31g12 = INITVALUE; + CCTK_REAL PDstandard4th32g12 = INITVALUE; + CCTK_REAL PDstandard4th1g13 = INITVALUE; + CCTK_REAL PDstandard4th2g13 = INITVALUE; + CCTK_REAL PDstandard4th3g13 = INITVALUE; + CCTK_REAL PDstandard4th22g13 = INITVALUE; + CCTK_REAL PDstandard4th12g13 = INITVALUE; + CCTK_REAL PDstandard4th13g13 = INITVALUE; + CCTK_REAL PDstandard4th21g13 = INITVALUE; + CCTK_REAL PDstandard4th23g13 = INITVALUE; + CCTK_REAL PDstandard4th31g13 = INITVALUE; + CCTK_REAL PDstandard4th32g13 = INITVALUE; CCTK_REAL PDstandard4th1g22 = INITVALUE; CCTK_REAL PDstandard4th2g22 = INITVALUE; CCTK_REAL PDstandard4th3g22 = INITVALUE; @@ -164,26 +174,16 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ CCTK_REAL PDstandard4th23g22 = INITVALUE; CCTK_REAL PDstandard4th31g22 = INITVALUE; CCTK_REAL PDstandard4th32g22 = INITVALUE; - CCTK_REAL PDstandard4th1g31 = INITVALUE; - CCTK_REAL PDstandard4th2g31 = INITVALUE; - CCTK_REAL PDstandard4th3g31 = INITVALUE; - CCTK_REAL PDstandard4th22g31 = INITVALUE; - CCTK_REAL PDstandard4th12g31 = INITVALUE; - CCTK_REAL PDstandard4th13g31 = INITVALUE; - CCTK_REAL PDstandard4th21g31 = INITVALUE; - CCTK_REAL PDstandard4th23g31 = INITVALUE; - CCTK_REAL PDstandard4th31g31 = INITVALUE; - CCTK_REAL PDstandard4th32g31 = INITVALUE; - CCTK_REAL PDstandard4th1g32 = INITVALUE; - CCTK_REAL PDstandard4th2g32 = INITVALUE; - CCTK_REAL PDstandard4th3g32 = INITVALUE; - CCTK_REAL PDstandard4th11g32 = INITVALUE; - CCTK_REAL PDstandard4th12g32 = INITVALUE; - CCTK_REAL PDstandard4th13g32 = INITVALUE; - CCTK_REAL PDstandard4th21g32 = INITVALUE; - CCTK_REAL PDstandard4th23g32 = INITVALUE; - CCTK_REAL PDstandard4th31g32 = INITVALUE; - CCTK_REAL PDstandard4th32g32 = INITVALUE; + CCTK_REAL PDstandard4th1g23 = INITVALUE; + CCTK_REAL PDstandard4th2g23 = INITVALUE; + CCTK_REAL PDstandard4th3g23 = INITVALUE; + CCTK_REAL PDstandard4th11g23 = INITVALUE; + CCTK_REAL PDstandard4th12g23 = INITVALUE; + CCTK_REAL PDstandard4th13g23 = INITVALUE; + CCTK_REAL PDstandard4th21g23 = INITVALUE; + CCTK_REAL PDstandard4th23g23 = INITVALUE; + CCTK_REAL PDstandard4th31g23 = INITVALUE; + CCTK_REAL PDstandard4th32g23 = INITVALUE; CCTK_REAL PDstandard4th1g33 = INITVALUE; CCTK_REAL PDstandard4th2g33 = INITVALUE; CCTK_REAL PDstandard4th3g33 = INITVALUE; @@ -198,18 +198,18 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ CCTK_REAL PDstandard4th1K11 = INITVALUE; CCTK_REAL PDstandard4th2K11 = INITVALUE; CCTK_REAL PDstandard4th3K11 = INITVALUE; - CCTK_REAL PDstandard4th1K21 = INITVALUE; - CCTK_REAL PDstandard4th2K21 = INITVALUE; - CCTK_REAL PDstandard4th3K21 = INITVALUE; + CCTK_REAL PDstandard4th1K12 = INITVALUE; + CCTK_REAL PDstandard4th2K12 = INITVALUE; + CCTK_REAL PDstandard4th3K12 = INITVALUE; + CCTK_REAL PDstandard4th1K13 = INITVALUE; + CCTK_REAL PDstandard4th2K13 = INITVALUE; + CCTK_REAL PDstandard4th3K13 = INITVALUE; CCTK_REAL PDstandard4th1K22 = INITVALUE; CCTK_REAL PDstandard4th2K22 = INITVALUE; CCTK_REAL PDstandard4th3K22 = INITVALUE; - CCTK_REAL PDstandard4th1K31 = INITVALUE; - CCTK_REAL PDstandard4th2K31 = INITVALUE; - CCTK_REAL PDstandard4th3K31 = INITVALUE; - CCTK_REAL PDstandard4th1K32 = INITVALUE; - CCTK_REAL PDstandard4th2K32 = INITVALUE; - CCTK_REAL PDstandard4th3K32 = INITVALUE; + CCTK_REAL PDstandard4th1K23 = INITVALUE; + CCTK_REAL PDstandard4th2K23 = INITVALUE; + CCTK_REAL PDstandard4th3K23 = INITVALUE; CCTK_REAL PDstandard4th1K33 = INITVALUE; CCTK_REAL PDstandard4th2K33 = INITVALUE; CCTK_REAL PDstandard4th3K33 = INITVALUE; @@ -220,16 +220,16 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ beta2L = beta2[index]; beta3L = beta3[index]; g11L = g11[index]; - g21L = g21[index]; + g12L = g12[index]; + g13L = g13[index]; g22L = g22[index]; - g31L = g31[index]; - g32L = g32[index]; + g23L = g23[index]; g33L = g33[index]; K11L = K11[index]; - K21L = K21[index]; + K12L = K12[index]; + K13L = K13[index]; K22L = K22[index]; - K31L = K31[index]; - K32L = K32[index]; + K23L = K23[index]; K33L = K33[index]; /* Assign local copies of subblock grid functions */ @@ -261,33 +261,33 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ PDstandard4th22g11 = PDstandard4th22(g11, i, j, k); PDstandard4th33g11 = PDstandard4th33(g11, i, j, k); PDstandard4th23g11 = PDstandard4th23(g11, i, j, k); - PDstandard4th1g21 = PDstandard4th1(g21, i, j, k); - PDstandard4th2g21 = PDstandard4th2(g21, i, j, k); - PDstandard4th3g21 = PDstandard4th3(g21, i, j, k); - PDstandard4th33g21 = PDstandard4th33(g21, i, j, k); - PDstandard4th12g21 = PDstandard4th12(g21, i, j, k); - PDstandard4th13g21 = PDstandard4th13(g21, i, j, k); - PDstandard4th23g21 = PDstandard4th23(g21, i, j, k); + PDstandard4th1g12 = PDstandard4th1(g12, i, j, k); + PDstandard4th2g12 = PDstandard4th2(g12, i, j, k); + PDstandard4th3g12 = PDstandard4th3(g12, i, j, k); + PDstandard4th33g12 = PDstandard4th33(g12, i, j, k); + PDstandard4th12g12 = PDstandard4th12(g12, i, j, k); + PDstandard4th13g12 = PDstandard4th13(g12, i, j, k); + PDstandard4th23g12 = PDstandard4th23(g12, i, j, k); + PDstandard4th1g13 = PDstandard4th1(g13, i, j, k); + PDstandard4th2g13 = PDstandard4th2(g13, i, j, k); + PDstandard4th3g13 = PDstandard4th3(g13, i, j, k); + PDstandard4th22g13 = PDstandard4th22(g13, i, j, k); + PDstandard4th12g13 = PDstandard4th12(g13, i, j, k); + PDstandard4th13g13 = PDstandard4th13(g13, i, j, k); + PDstandard4th23g13 = PDstandard4th23(g13, i, j, k); PDstandard4th1g22 = PDstandard4th1(g22, i, j, k); PDstandard4th2g22 = PDstandard4th2(g22, i, j, k); PDstandard4th3g22 = PDstandard4th3(g22, i, j, k); PDstandard4th11g22 = PDstandard4th11(g22, i, j, k); PDstandard4th33g22 = PDstandard4th33(g22, i, j, k); PDstandard4th13g22 = PDstandard4th13(g22, i, j, k); - PDstandard4th1g31 = PDstandard4th1(g31, i, j, k); - PDstandard4th2g31 = PDstandard4th2(g31, i, j, k); - PDstandard4th3g31 = PDstandard4th3(g31, i, j, k); - PDstandard4th22g31 = PDstandard4th22(g31, i, j, k); - PDstandard4th12g31 = PDstandard4th12(g31, i, j, k); - PDstandard4th13g31 = PDstandard4th13(g31, i, j, k); - PDstandard4th23g31 = PDstandard4th23(g31, i, j, k); - PDstandard4th1g32 = PDstandard4th1(g32, i, j, k); - PDstandard4th2g32 = PDstandard4th2(g32, i, j, k); - PDstandard4th3g32 = PDstandard4th3(g32, i, j, k); - PDstandard4th11g32 = PDstandard4th11(g32, i, j, k); - PDstandard4th12g32 = PDstandard4th12(g32, i, j, k); - PDstandard4th13g32 = PDstandard4th13(g32, i, j, k); - PDstandard4th23g32 = PDstandard4th23(g32, i, j, k); + PDstandard4th1g23 = PDstandard4th1(g23, i, j, k); + PDstandard4th2g23 = PDstandard4th2(g23, i, j, k); + PDstandard4th3g23 = PDstandard4th3(g23, i, j, k); + PDstandard4th11g23 = PDstandard4th11(g23, i, j, k); + PDstandard4th12g23 = PDstandard4th12(g23, i, j, k); + PDstandard4th13g23 = PDstandard4th13(g23, i, j, k); + PDstandard4th23g23 = PDstandard4th23(g23, i, j, k); PDstandard4th1g33 = PDstandard4th1(g33, i, j, k); PDstandard4th2g33 = PDstandard4th2(g33, i, j, k); PDstandard4th3g33 = PDstandard4th3(g33, i, j, k); @@ -297,18 +297,18 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ PDstandard4th1K11 = PDstandard4th1(K11, i, j, k); PDstandard4th2K11 = PDstandard4th2(K11, i, j, k); PDstandard4th3K11 = PDstandard4th3(K11, i, j, k); - PDstandard4th1K21 = PDstandard4th1(K21, i, j, k); - PDstandard4th2K21 = PDstandard4th2(K21, i, j, k); - PDstandard4th3K21 = PDstandard4th3(K21, i, j, k); + PDstandard4th1K12 = PDstandard4th1(K12, i, j, k); + PDstandard4th2K12 = PDstandard4th2(K12, i, j, k); + PDstandard4th3K12 = PDstandard4th3(K12, i, j, k); + PDstandard4th1K13 = PDstandard4th1(K13, i, j, k); + PDstandard4th2K13 = PDstandard4th2(K13, i, j, k); + PDstandard4th3K13 = PDstandard4th3(K13, i, j, k); PDstandard4th1K22 = PDstandard4th1(K22, i, j, k); PDstandard4th2K22 = PDstandard4th2(K22, i, j, k); PDstandard4th3K22 = PDstandard4th3(K22, i, j, k); - PDstandard4th1K31 = PDstandard4th1(K31, i, j, k); - PDstandard4th2K31 = PDstandard4th2(K31, i, j, k); - PDstandard4th3K31 = PDstandard4th3(K31, i, j, k); - PDstandard4th1K32 = PDstandard4th1(K32, i, j, k); - PDstandard4th2K32 = PDstandard4th2(K32, i, j, k); - PDstandard4th3K32 = PDstandard4th3(K32, i, j, k); + PDstandard4th1K23 = PDstandard4th1(K23, i, j, k); + PDstandard4th2K23 = PDstandard4th2(K23, i, j, k); + PDstandard4th3K23 = PDstandard4th3(K23, i, j, k); PDstandard4th1K33 = PDstandard4th1(K33, i, j, k); PDstandard4th2K33 = PDstandard4th2(K33, i, j, k); PDstandard4th3K33 = PDstandard4th3(K33, i, j, k); @@ -316,184 +316,184 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ /* Precompute derivatives (old style) */ /* Calculate temporaries and grid functions */ - detg = 2*g21L*g31L*g32L + g33L*(g11L*g22L - SQR(g21L)) - g22L*SQR(g31L) - g11L*SQR(g32L); + detg = 2*g12L*g13L*g23L + g33L*(g11L*g22L - SQR(g12L)) - g22L*SQR(g13L) - g11L*SQR(g23L); - gu11 = INV(detg)*(g22L*g33L - SQR(g32L)); + gu11 = INV(detg)*(g22L*g33L - SQR(g23L)); - gu12 = (g31L*g32L - g21L*g33L)*INV(detg); + gu21 = (g13L*g23L - g12L*g33L)*INV(detg); - gu13 = (-(g22L*g31L) + g21L*g32L)*INV(detg); + gu31 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - gu22 = INV(detg)*(g11L*g33L - SQR(g31L)); + gu22 = INV(detg)*(g11L*g33L - SQR(g13L)); - gu23 = (g21L*g31L - g11L*g32L)*INV(detg); + gu32 = (g12L*g13L - g11L*g23L)*INV(detg); - gu33 = INV(detg)*(g11L*g22L - SQR(g21L)); + gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu12*PDstandard4th1g21 + gu13*PDstandard4th1g31) - gu12*PDstandard4th2g11 - - gu13*PDstandard4th3g11); + G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu21*PDstandard4th1g12 + gu31*PDstandard4th1g13) - gu21*PDstandard4th2g11 - + gu31*PDstandard4th3g11); - G211 = khalf*(gu12*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g21 + gu23*PDstandard4th1g31) - gu22*PDstandard4th2g11 - - gu23*PDstandard4th3g11); + G211 = khalf*(gu21*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g12 + gu32*PDstandard4th1g13) - gu22*PDstandard4th2g11 - + gu32*PDstandard4th3g11); - G311 = khalf*(gu13*PDstandard4th1g11 + 2*(gu23*PDstandard4th1g21 + gu33*PDstandard4th1g31) - gu23*PDstandard4th2g11 - + G311 = khalf*(gu31*PDstandard4th1g11 + 2*(gu32*PDstandard4th1g12 + gu33*PDstandard4th1g13) - gu32*PDstandard4th2g11 - gu33*PDstandard4th3g11); - G121 = khalf*(gu12*PDstandard4th1g22 + gu11*PDstandard4th2g11 + - gu13*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G112 = khalf*(gu21*PDstandard4th1g22 + gu11*PDstandard4th2g11 + + gu31*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G221 = khalf*(gu22*PDstandard4th1g22 + gu12*PDstandard4th2g11 + - gu23*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G212 = khalf*(gu22*PDstandard4th1g22 + gu21*PDstandard4th2g11 + + gu32*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G321 = khalf*(gu23*PDstandard4th1g22 + gu13*PDstandard4th2g11 + - gu33*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G312 = khalf*(gu32*PDstandard4th1g22 + gu31*PDstandard4th2g11 + + gu33*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G131 = khalf*(gu13*PDstandard4th1g33 + gu11*PDstandard4th3g11 + - gu12*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G113 = khalf*(gu31*PDstandard4th1g33 + gu11*PDstandard4th3g11 + + gu21*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G231 = khalf*(gu23*PDstandard4th1g33 + gu12*PDstandard4th3g11 + - gu22*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G213 = khalf*(gu32*PDstandard4th1g33 + gu21*PDstandard4th3g11 + + gu22*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G331 = khalf*(gu33*PDstandard4th1g33 + gu13*PDstandard4th3g11 + - gu23*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G313 = khalf*(gu33*PDstandard4th1g33 + gu31*PDstandard4th3g11 + + gu32*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu12*PDstandard4th2g22 + - gu13*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu21*PDstandard4th2g22 + + gu31*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G222 = khalf*(gu12*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu22*PDstandard4th2g22 + - gu23*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G222 = khalf*(gu21*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu22*PDstandard4th2g22 + + gu32*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G322 = khalf*(gu13*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu23*PDstandard4th2g22 + - gu33*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G322 = khalf*(gu31*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu32*PDstandard4th2g22 + + gu33*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G132 = khalf*(gu13*PDstandard4th2g33 + gu11*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + - gu12*PDstandard4th3g22); + G123 = khalf*(gu31*PDstandard4th2g33 + gu11*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + + gu21*PDstandard4th3g22); - G232 = khalf*(gu23*PDstandard4th2g33 + gu12*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + + G223 = khalf*(gu32*PDstandard4th2g33 + gu21*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + gu22*PDstandard4th3g22); - G332 = khalf*(gu33*PDstandard4th2g33 + gu13*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + - gu23*PDstandard4th3g22); + G323 = khalf*(gu33*PDstandard4th2g33 + gu31*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + + gu32*PDstandard4th3g22); - G133 = khalf*(-(gu11*PDstandard4th1g33) - gu12*PDstandard4th2g33 + 2*gu11*PDstandard4th3g31 + - 2*gu12*PDstandard4th3g32 + gu13*PDstandard4th3g33); + G133 = khalf*(-(gu11*PDstandard4th1g33) - gu21*PDstandard4th2g33 + 2*gu11*PDstandard4th3g13 + + 2*gu21*PDstandard4th3g23 + gu31*PDstandard4th3g33); - G233 = khalf*(-(gu12*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu12*PDstandard4th3g31 + - 2*gu22*PDstandard4th3g32 + gu23*PDstandard4th3g33); + G233 = khalf*(-(gu21*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu21*PDstandard4th3g13 + + 2*gu22*PDstandard4th3g23 + gu32*PDstandard4th3g33); - G333 = khalf*(-(gu13*PDstandard4th1g33) - gu23*PDstandard4th2g33 + 2*gu13*PDstandard4th3g31 + - 2*gu23*PDstandard4th3g32 + gu33*PDstandard4th3g33); + G333 = khalf*(-(gu31*PDstandard4th1g33) - gu32*PDstandard4th2g33 + 2*gu31*PDstandard4th3g13 + + 2*gu32*PDstandard4th3g23 + gu33*PDstandard4th3g33); - R11 = khalf*(4*G231*G321 + G211*(2*G121 - 2*G222 - 2*G332) + G311*(2*G131 - 2*G333) - gu22*PDstandard4th11g22 - - 2*(G111*G221 + G232*G311 + G111*G331 + gu23*PDstandard4th11g32) - gu33*PDstandard4th11g33 + - 2*gu22*PDstandard4th12g21 + 2*gu23*PDstandard4th12g31 + 2*gu23*PDstandard4th13g21 + 2*gu33*PDstandard4th13g31 - - gu22*PDstandard4th22g11 - 2*gu23*PDstandard4th23g11 - gu33*PDstandard4th33g11 + 2*SQR(G221) + 2*SQR(G331)); + R11 = khalf*(4*G213*G312 + G211*(2*G112 - 2*G222 - 2*G323) + G311*(2*G113 - 2*G333) - gu22*PDstandard4th11g22 - + 2*(G111*G212 + G223*G311 + G111*G313 + gu32*PDstandard4th11g23) - gu33*PDstandard4th11g33 + + 2*gu22*PDstandard4th12g12 + 2*gu32*PDstandard4th12g13 + 2*gu32*PDstandard4th13g12 + 2*gu33*PDstandard4th13g13 - + gu22*PDstandard4th22g11 - 2*gu32*PDstandard4th23g11 - gu33*PDstandard4th33g11 + 2*SQR(G212) + 2*SQR(G313)); - R21 = khalf*(2*(G122*G211 + G132*G311 + G231*G322 + G331*G332) - - 2*(G121*G221 + G121*G331 + G221*G332 + G321*G333 + gu12*PDstandard4th12g21) - gu23*PDstandard4th12g32 - - gu33*PDstandard4th12g33 + gu13*(PDstandard4th11g32 - PDstandard4th12g31 - PDstandard4th13g21) + - gu23*PDstandard4th13g22 + gu33*PDstandard4th13g32 + gu12*(PDstandard4th11g22 + PDstandard4th22g11) + - gu23*PDstandard4th22g31 + gu13*PDstandard4th23g11 - gu23*PDstandard4th23g21 + gu33*PDstandard4th23g31 - - gu33*PDstandard4th33g21); + R12 = khalf*(2*(G122*G211 + G123*G311 + G213*G322 + G313*G323) - + 2*(G112*G212 + G112*G313 + G212*G323 + G312*G333 + gu21*PDstandard4th12g12) - gu32*PDstandard4th12g23 - + gu33*PDstandard4th12g33 + gu31*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12) + + gu32*PDstandard4th13g22 + gu33*PDstandard4th13g23 + gu21*(PDstandard4th11g22 + PDstandard4th22g11) + + gu32*PDstandard4th22g13 + gu31*PDstandard4th23g11 - gu32*PDstandard4th23g12 + gu33*PDstandard4th23g13 - + gu33*PDstandard4th33g12); - R31 = khalf*(2*(G132*G211 + G221*G232 + G133*G311 + G233*G321) - - 2*(G222*G231 + G232*G331 + G131*(G221 + G331) + gu13*PDstandard4th13g31) + - gu12*(PDstandard4th11g32 - PDstandard4th12g31 - PDstandard4th13g21 + PDstandard4th23g11) + - gu22*(PDstandard4th12g32 - PDstandard4th13g22 - PDstandard4th22g31 + PDstandard4th23g21) + - gu13*(PDstandard4th11g33 + PDstandard4th33g11) + - gu23*(PDstandard4th12g33 - PDstandard4th13g32 - PDstandard4th23g31 + PDstandard4th33g21)); + R13 = khalf*(2*(G123*G211 + G212*G223 + G133*G311 + G233*G312) - + 2*(G213*G222 + G223*G313 + G113*(G212 + G313) + gu31*PDstandard4th13g13) + + gu21*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12 + PDstandard4th23g11) + + gu22*(PDstandard4th12g23 - PDstandard4th13g22 - PDstandard4th22g13 + PDstandard4th23g12) + + gu31*(PDstandard4th11g33 + PDstandard4th33g11) + + gu32*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12)); - R22 = khalf*(4*G132*G321 + G122*(2*G221 - 2*(G111 + G331)) + G322*(2*G232 - 2*G333) - - 2*(G131*G322 + G222*(G121 + G332) + gu13*PDstandard4th13g22) + - gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g21 - PDstandard4th22g11) + - gu13*(-2*PDstandard4th22g31 + 2*(PDstandard4th12g32 + PDstandard4th23g21)) + - gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g32 - PDstandard4th33g22) + 2*(SQR(G121) + SQR(G332))); + R22 = khalf*(4*G123*G312 + G122*(2*G212 - 2*(G111 + G313)) + G322*(2*G223 - 2*G333) - + 2*(G113*G322 + G222*(G112 + G323) + gu31*PDstandard4th13g22) + + gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g12 - PDstandard4th22g11) + + gu31*(-2*PDstandard4th22g13 + 2*(PDstandard4th12g23 + PDstandard4th23g12)) + + gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + 2*(SQR(G112) + SQR(G323))); - R32 = khalf*(2*(G121*G131 + G122*G231 + G133*G321 + G233*G322) + - gu11*(-PDstandard4th11g32 + PDstandard4th12g31 + PDstandard4th13g21 - PDstandard4th23g11) + - gu12*(-PDstandard4th12g32 + PDstandard4th13g22 + PDstandard4th22g31 - PDstandard4th23g21) - - 2*(G111*G132 + G131*G332 + G232*(G121 + G332) + gu23*PDstandard4th23g32) + - gu13*(PDstandard4th12g33 - PDstandard4th13g32 - PDstandard4th23g31 + PDstandard4th33g21) + - gu23*(PDstandard4th22g33 + PDstandard4th33g22)); + R23 = khalf*(2*(G112*G113 + G122*G213 + G133*G312 + G233*G322) + + gu11*(-PDstandard4th11g23 + PDstandard4th12g13 + PDstandard4th13g12 - PDstandard4th23g11) + + gu21*(-PDstandard4th12g23 + PDstandard4th13g22 + PDstandard4th22g13 - PDstandard4th23g12) - + 2*(G111*G123 + G113*G323 + G223*(G112 + G323) + gu32*PDstandard4th23g23) + + gu31*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12) + + gu32*(PDstandard4th22g33 + PDstandard4th33g22)); - R33 = khalf*(4*G132*G231 - gu11*PDstandard4th11g33 - - 2*(G111*G133 + G133*G221 + G121*G233 + G222*G233 + G131*G333 + G232*G333 + gu12*PDstandard4th12g33) + - 2*(G133*G331 + G233*G332 + gu11*PDstandard4th13g31) + 2*gu12*PDstandard4th13g32 - gu22*PDstandard4th22g33 + - 2*gu12*PDstandard4th23g31 + 2*gu22*PDstandard4th23g32 - gu11*PDstandard4th33g11 - 2*gu12*PDstandard4th33g21 - - gu22*PDstandard4th33g22 + 2*SQR(G131) + 2*SQR(G232)); + R33 = khalf*(4*G123*G213 - gu11*PDstandard4th11g33 - + 2*(G111*G133 + G133*G212 + G112*G233 + G222*G233 + G113*G333 + G223*G333 + gu21*PDstandard4th12g33) + + 2*(G133*G313 + G233*G323 + gu11*PDstandard4th13g13) + 2*gu21*PDstandard4th13g23 - gu22*PDstandard4th22g33 + + 2*gu21*PDstandard4th23g13 + 2*gu22*PDstandard4th23g23 - gu11*PDstandard4th33g11 - 2*gu21*PDstandard4th33g12 - + gu22*PDstandard4th33g22 + 2*SQR(G113) + 2*SQR(G223)); - Km11 = gu11*K11L + gu12*K21L + gu13*K31L; + Km11 = gu11*K11L + gu21*K12L + gu31*K13L; - Km21 = gu12*K11L + gu22*K21L + gu23*K31L; + Km21 = gu21*K11L + gu22*K12L + gu32*K13L; - Km31 = gu13*K11L + gu23*K21L + gu33*K31L; + Km31 = gu31*K11L + gu32*K12L + gu33*K13L; - Km12 = gu11*K21L + gu12*K22L + gu13*K32L; + Km12 = gu11*K12L + gu21*K22L + gu31*K23L; - Km22 = gu12*K21L + gu22*K22L + gu23*K32L; + Km22 = gu21*K12L + gu22*K22L + gu32*K23L; - Km32 = gu13*K21L + gu23*K22L + gu33*K32L; + Km32 = gu31*K12L + gu32*K22L + gu33*K23L; - Km13 = gu11*K31L + gu12*K32L + gu13*K33L; + Km13 = gu11*K13L + gu21*K23L + gu31*K33L; - Km23 = gu12*K31L + gu22*K32L + gu23*K33L; + Km23 = gu21*K13L + gu22*K23L + gu32*K33L; - Km33 = gu13*K31L + gu23*K32L + gu33*K33L; + Km33 = gu31*K13L + gu32*K23L + gu33*K33L; trK = Km11 + Km22 + Km33; - g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandard4th1beta1 + g21L*PDstandard4th1beta2 + g31L*PDstandard4th1beta3) + + g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandard4th1beta1 + g12L*PDstandard4th1beta2 + g13L*PDstandard4th1beta3) + beta1L*PDstandard4th1g11 + beta2L*PDstandard4th2g11 + beta3L*PDstandard4th3g11; - g21rhsL = -2*alphaL*K21L + g22L*PDstandard4th1beta2 + g32L*PDstandard4th1beta3 + beta1L*PDstandard4th1g21 + - g11L*PDstandard4th2beta1 + g21L*(PDstandard4th1beta1 + PDstandard4th2beta2) + g31L*PDstandard4th2beta3 + - beta2L*PDstandard4th2g21 + beta3L*PDstandard4th3g21; + g12rhsL = -2*alphaL*K12L + g22L*PDstandard4th1beta2 + g23L*PDstandard4th1beta3 + beta1L*PDstandard4th1g12 + + g11L*PDstandard4th2beta1 + g12L*(PDstandard4th1beta1 + PDstandard4th2beta2) + g13L*PDstandard4th2beta3 + + beta2L*PDstandard4th2g12 + beta3L*PDstandard4th3g12; - g31rhsL = -2*alphaL*K31L + g32L*PDstandard4th1beta2 + g33L*PDstandard4th1beta3 + beta1L*PDstandard4th1g31 + - beta2L*PDstandard4th2g31 + g11L*PDstandard4th3beta1 + g21L*PDstandard4th3beta2 + - g31L*(PDstandard4th1beta1 + PDstandard4th3beta3) + beta3L*PDstandard4th3g31; + g13rhsL = -2*alphaL*K13L + g23L*PDstandard4th1beta2 + g33L*PDstandard4th1beta3 + beta1L*PDstandard4th1g13 + + beta2L*PDstandard4th2g13 + g11L*PDstandard4th3beta1 + g12L*PDstandard4th3beta2 + + g13L*(PDstandard4th1beta1 + PDstandard4th3beta3) + beta3L*PDstandard4th3g13; g22rhsL = -2*alphaL*K22L + beta1L*PDstandard4th1g22 + - 2*(g21L*PDstandard4th2beta1 + g22L*PDstandard4th2beta2 + g32L*PDstandard4th2beta3) + beta2L*PDstandard4th2g22 + + 2*(g12L*PDstandard4th2beta1 + g22L*PDstandard4th2beta2 + g23L*PDstandard4th2beta3) + beta2L*PDstandard4th2g22 + beta3L*PDstandard4th3g22; - g32rhsL = -2*alphaL*K32L + beta1L*PDstandard4th1g32 + g31L*PDstandard4th2beta1 + g33L*PDstandard4th2beta3 + - beta2L*PDstandard4th2g32 + g21L*PDstandard4th3beta1 + g22L*PDstandard4th3beta2 + - g32L*(PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3g32; + g23rhsL = -2*alphaL*K23L + beta1L*PDstandard4th1g23 + g13L*PDstandard4th2beta1 + g33L*PDstandard4th2beta3 + + beta2L*PDstandard4th2g23 + g12L*PDstandard4th3beta1 + g22L*PDstandard4th3beta2 + + g23L*(PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3g23; g33rhsL = -2*alphaL*K33L + beta1L*PDstandard4th1g33 + beta2L*PDstandard4th2g33 + - 2*(g31L*PDstandard4th3beta1 + g32L*PDstandard4th3beta2 + g33L*PDstandard4th3beta3) + beta3L*PDstandard4th3g33; + 2*(g13L*PDstandard4th3beta1 + g23L*PDstandard4th3beta2 + g33L*PDstandard4th3beta3) + beta3L*PDstandard4th3g33; K11rhsL = -PDstandard4th11alpha + G111*PDstandard4th1alpha + - 2*(K11L*PDstandard4th1beta1 + K21L*PDstandard4th1beta2 + K31L*PDstandard4th1beta3) + beta1L*PDstandard4th1K11 + + 2*(K11L*PDstandard4th1beta1 + K12L*PDstandard4th1beta2 + K13L*PDstandard4th1beta3) + beta1L*PDstandard4th1K11 + G211*PDstandard4th2alpha + beta2L*PDstandard4th2K11 + G311*PDstandard4th3alpha + beta3L*PDstandard4th3K11 + - alphaL*(-2*(K11L*Km11 + K21L*Km21 + K31L*Km31) + R11 + K11L*trK); + alphaL*(-2*(K11L*Km11 + K12L*Km21 + K13L*Km31) + R11 + K11L*trK); - K21rhsL = -PDstandard4th12alpha + G121*PDstandard4th1alpha + K22L*PDstandard4th1beta2 + K32L*PDstandard4th1beta3 + - beta1L*PDstandard4th1K21 + G221*PDstandard4th2alpha + K11L*PDstandard4th2beta1 + - K21L*(PDstandard4th1beta1 + PDstandard4th2beta2) + K31L*PDstandard4th2beta3 + beta2L*PDstandard4th2K21 + - G321*PDstandard4th3alpha + beta3L*PDstandard4th3K21 + - alphaL*(-2*(K11L*Km12 + K21L*Km22 + K31L*Km32) + R21 + K21L*trK); + K12rhsL = -PDstandard4th12alpha + G112*PDstandard4th1alpha + K22L*PDstandard4th1beta2 + K23L*PDstandard4th1beta3 + + beta1L*PDstandard4th1K12 + G212*PDstandard4th2alpha + K11L*PDstandard4th2beta1 + + K12L*(PDstandard4th1beta1 + PDstandard4th2beta2) + K13L*PDstandard4th2beta3 + beta2L*PDstandard4th2K12 + + G312*PDstandard4th3alpha + beta3L*PDstandard4th3K12 + + alphaL*(-2*(K11L*Km12 + K12L*Km22 + K13L*Km32) + R12 + K12L*trK); - K31rhsL = -PDstandard4th13alpha + G131*PDstandard4th1alpha + K32L*PDstandard4th1beta2 + K33L*PDstandard4th1beta3 + - beta1L*PDstandard4th1K31 + G231*PDstandard4th2alpha + beta2L*PDstandard4th2K31 + G331*PDstandard4th3alpha + - K11L*PDstandard4th3beta1 + K21L*PDstandard4th3beta2 + K31L*(PDstandard4th1beta1 + PDstandard4th3beta3) + - beta3L*PDstandard4th3K31 + alphaL*(-2*(K11L*Km13 + K21L*Km23 + K31L*Km33) + R31 + K31L*trK); + K13rhsL = -PDstandard4th13alpha + G113*PDstandard4th1alpha + K23L*PDstandard4th1beta2 + K33L*PDstandard4th1beta3 + + beta1L*PDstandard4th1K13 + G213*PDstandard4th2alpha + beta2L*PDstandard4th2K13 + G313*PDstandard4th3alpha + + K11L*PDstandard4th3beta1 + K12L*PDstandard4th3beta2 + K13L*(PDstandard4th1beta1 + PDstandard4th3beta3) + + beta3L*PDstandard4th3K13 + alphaL*(-2*(K11L*Km13 + K12L*Km23 + K13L*Km33) + R13 + K13L*trK); K22rhsL = G122*PDstandard4th1alpha + beta1L*PDstandard4th1K22 - PDstandard4th22alpha + G222*PDstandard4th2alpha + - 2*(K21L*PDstandard4th2beta1 + K22L*PDstandard4th2beta2 + K32L*PDstandard4th2beta3) + beta2L*PDstandard4th2K22 + + 2*(K12L*PDstandard4th2beta1 + K22L*PDstandard4th2beta2 + K23L*PDstandard4th2beta3) + beta2L*PDstandard4th2K22 + G322*PDstandard4th3alpha + beta3L*PDstandard4th3K22 + - alphaL*(-2*(K21L*Km12 + K22L*Km22 + K32L*Km32) + R22 + K22L*trK); + alphaL*(-2*(K12L*Km12 + K22L*Km22 + K23L*Km32) + R22 + K22L*trK); - K32rhsL = G132*PDstandard4th1alpha + beta1L*PDstandard4th1K32 - PDstandard4th23alpha + G232*PDstandard4th2alpha + - K31L*PDstandard4th2beta1 + K33L*PDstandard4th2beta3 + beta2L*PDstandard4th2K32 + G332*PDstandard4th3alpha + - K21L*PDstandard4th3beta1 + K22L*PDstandard4th3beta2 + K32L*(PDstandard4th2beta2 + PDstandard4th3beta3) + - beta3L*PDstandard4th3K32 + alphaL*(-2*(K21L*Km13 + K22L*Km23 + K32L*Km33) + R32 + K32L*trK); + K23rhsL = G123*PDstandard4th1alpha + beta1L*PDstandard4th1K23 - PDstandard4th23alpha + G223*PDstandard4th2alpha + + K13L*PDstandard4th2beta1 + K33L*PDstandard4th2beta3 + beta2L*PDstandard4th2K23 + G323*PDstandard4th3alpha + + K12L*PDstandard4th3beta1 + K22L*PDstandard4th3beta2 + K23L*(PDstandard4th2beta2 + PDstandard4th3beta3) + + beta3L*PDstandard4th3K23 + alphaL*(-2*(K12L*Km13 + K22L*Km23 + K23L*Km33) + R23 + K23L*trK); K33rhsL = G133*PDstandard4th1alpha + beta1L*PDstandard4th1K33 + G233*PDstandard4th2alpha + beta2L*PDstandard4th2K33 - PDstandard4th33alpha + G333*PDstandard4th3alpha + - 2*(K31L*PDstandard4th3beta1 + K32L*PDstandard4th3beta2 + K33L*PDstandard4th3beta3) + beta3L*PDstandard4th3K33 + - alphaL*(-2*(K31L*Km13 + K32L*Km23 + K33L*Km33) + R33 + K33L*trK); + 2*(K13L*PDstandard4th3beta1 + K23L*PDstandard4th3beta2 + K33L*PDstandard4th3beta3) + beta3L*PDstandard4th3K33 + + alphaL*(-2*(K13L*Km13 + K23L*Km23 + K33L*Km33) + R33 + K33L*trK); alpharhsL = 0; @@ -510,16 +510,16 @@ void ML_ADM_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal[ beta2rhs[index] = beta2rhsL; beta3rhs[index] = beta3rhsL; g11rhs[index] = g11rhsL; - g21rhs[index] = g21rhsL; + g12rhs[index] = g12rhsL; + g13rhs[index] = g13rhsL; g22rhs[index] = g22rhsL; - g31rhs[index] = g31rhsL; - g32rhs[index] = g32rhsL; + g23rhs[index] = g23rhsL; g33rhs[index] = g33rhsL; K11rhs[index] = K11rhsL; - K21rhs[index] = K21rhsL; + K12rhs[index] = K12rhsL; + K13rhs[index] = K13rhsL; K22rhs[index] = K22rhsL; - K31rhs[index] = K31rhsL; - K32rhs[index] = K32rhsL; + K23rhs[index] = K23rhsL; K33rhs[index] = K33rhsL; /* Copy local copies back to subblock grid functions */ diff --git a/ML_ADM/src/ML_ADM_constraints.c b/ML_ADM/src/ML_ADM_constraints.c index 420fbe7..8dd52b2 100644 --- a/ML_ADM/src/ML_ADM_constraints.c +++ b/ML_ADM/src/ML_ADM_constraints.c @@ -95,20 +95,20 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL /* Declare shorthands */ CCTK_REAL detg = INITVALUE; - CCTK_REAL G111 = INITVALUE, G121 = INITVALUE, G122 = INITVALUE, G131 = INITVALUE, G132 = INITVALUE, G133 = INITVALUE; - CCTK_REAL G211 = INITVALUE, G221 = INITVALUE, G222 = INITVALUE, G231 = INITVALUE, G232 = INITVALUE, G233 = INITVALUE; - CCTK_REAL G311 = INITVALUE, G321 = INITVALUE, G322 = INITVALUE, G331 = INITVALUE, G332 = INITVALUE, G333 = INITVALUE; - CCTK_REAL gu11 = INITVALUE, gu12 = INITVALUE, gu13 = INITVALUE, gu22 = INITVALUE, gu23 = INITVALUE, gu33 = INITVALUE; + CCTK_REAL G111 = INITVALUE, G112 = INITVALUE, G113 = INITVALUE, G122 = INITVALUE, G123 = INITVALUE, G133 = INITVALUE; + CCTK_REAL G211 = INITVALUE, G212 = INITVALUE, G213 = INITVALUE, G222 = INITVALUE, G223 = INITVALUE, G233 = INITVALUE; + CCTK_REAL G311 = INITVALUE, G312 = INITVALUE, G313 = INITVALUE, G322 = INITVALUE, G323 = INITVALUE, G333 = INITVALUE; + CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE; CCTK_REAL Km11 = INITVALUE, Km12 = INITVALUE, Km13 = INITVALUE, Km21 = INITVALUE, Km22 = INITVALUE, Km23 = INITVALUE; CCTK_REAL Km31 = INITVALUE, Km32 = INITVALUE, Km33 = INITVALUE; - CCTK_REAL R11 = INITVALUE, R21 = INITVALUE, R22 = INITVALUE, R31 = INITVALUE, R32 = INITVALUE, R33 = INITVALUE; + CCTK_REAL R11 = INITVALUE, R12 = INITVALUE, R13 = INITVALUE, R22 = INITVALUE, R23 = INITVALUE, R33 = INITVALUE; CCTK_REAL trK = INITVALUE; CCTK_REAL trR = INITVALUE; /* Declare local copies of grid functions */ - CCTK_REAL g11L = INITVALUE, g21L = INITVALUE, g22L = INITVALUE, g31L = INITVALUE, g32L = INITVALUE, g33L = INITVALUE; + CCTK_REAL g11L = INITVALUE, g12L = INITVALUE, g13L = INITVALUE, g22L = INITVALUE, g23L = INITVALUE, g33L = INITVALUE; CCTK_REAL HL = INITVALUE; - CCTK_REAL K11L = INITVALUE, K21L = INITVALUE, K22L = INITVALUE, K31L = INITVALUE, K32L = INITVALUE, K33L = INITVALUE; + CCTK_REAL K11L = INITVALUE, K12L = INITVALUE, K13L = INITVALUE, K22L = INITVALUE, K23L = INITVALUE, K33L = INITVALUE; CCTK_REAL M1L = INITVALUE, M2L = INITVALUE, M3L = INITVALUE; /* Declare precomputed derivatives*/ @@ -124,16 +124,26 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL CCTK_REAL PDstandard4th23g11 = INITVALUE; CCTK_REAL PDstandard4th31g11 = INITVALUE; CCTK_REAL PDstandard4th32g11 = INITVALUE; - CCTK_REAL PDstandard4th1g21 = INITVALUE; - CCTK_REAL PDstandard4th2g21 = INITVALUE; - CCTK_REAL PDstandard4th3g21 = INITVALUE; - CCTK_REAL PDstandard4th33g21 = INITVALUE; - CCTK_REAL PDstandard4th12g21 = INITVALUE; - CCTK_REAL PDstandard4th13g21 = INITVALUE; - CCTK_REAL PDstandard4th21g21 = INITVALUE; - CCTK_REAL PDstandard4th23g21 = INITVALUE; - CCTK_REAL PDstandard4th31g21 = INITVALUE; - CCTK_REAL PDstandard4th32g21 = INITVALUE; + CCTK_REAL PDstandard4th1g12 = INITVALUE; + CCTK_REAL PDstandard4th2g12 = INITVALUE; + CCTK_REAL PDstandard4th3g12 = INITVALUE; + CCTK_REAL PDstandard4th33g12 = INITVALUE; + CCTK_REAL PDstandard4th12g12 = INITVALUE; + CCTK_REAL PDstandard4th13g12 = INITVALUE; + CCTK_REAL PDstandard4th21g12 = INITVALUE; + CCTK_REAL PDstandard4th23g12 = INITVALUE; + CCTK_REAL PDstandard4th31g12 = INITVALUE; + CCTK_REAL PDstandard4th32g12 = INITVALUE; + CCTK_REAL PDstandard4th1g13 = INITVALUE; + CCTK_REAL PDstandard4th2g13 = INITVALUE; + CCTK_REAL PDstandard4th3g13 = INITVALUE; + CCTK_REAL PDstandard4th22g13 = INITVALUE; + CCTK_REAL PDstandard4th12g13 = INITVALUE; + CCTK_REAL PDstandard4th13g13 = INITVALUE; + CCTK_REAL PDstandard4th21g13 = INITVALUE; + CCTK_REAL PDstandard4th23g13 = INITVALUE; + CCTK_REAL PDstandard4th31g13 = INITVALUE; + CCTK_REAL PDstandard4th32g13 = INITVALUE; CCTK_REAL PDstandard4th1g22 = INITVALUE; CCTK_REAL PDstandard4th2g22 = INITVALUE; CCTK_REAL PDstandard4th3g22 = INITVALUE; @@ -145,26 +155,16 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL CCTK_REAL PDstandard4th23g22 = INITVALUE; CCTK_REAL PDstandard4th31g22 = INITVALUE; CCTK_REAL PDstandard4th32g22 = INITVALUE; - CCTK_REAL PDstandard4th1g31 = INITVALUE; - CCTK_REAL PDstandard4th2g31 = INITVALUE; - CCTK_REAL PDstandard4th3g31 = INITVALUE; - CCTK_REAL PDstandard4th22g31 = INITVALUE; - CCTK_REAL PDstandard4th12g31 = INITVALUE; - CCTK_REAL PDstandard4th13g31 = INITVALUE; - CCTK_REAL PDstandard4th21g31 = INITVALUE; - CCTK_REAL PDstandard4th23g31 = INITVALUE; - CCTK_REAL PDstandard4th31g31 = INITVALUE; - CCTK_REAL PDstandard4th32g31 = INITVALUE; - CCTK_REAL PDstandard4th1g32 = INITVALUE; - CCTK_REAL PDstandard4th2g32 = INITVALUE; - CCTK_REAL PDstandard4th3g32 = INITVALUE; - CCTK_REAL PDstandard4th11g32 = INITVALUE; - CCTK_REAL PDstandard4th12g32 = INITVALUE; - CCTK_REAL PDstandard4th13g32 = INITVALUE; - CCTK_REAL PDstandard4th21g32 = INITVALUE; - CCTK_REAL PDstandard4th23g32 = INITVALUE; - CCTK_REAL PDstandard4th31g32 = INITVALUE; - CCTK_REAL PDstandard4th32g32 = INITVALUE; + CCTK_REAL PDstandard4th1g23 = INITVALUE; + CCTK_REAL PDstandard4th2g23 = INITVALUE; + CCTK_REAL PDstandard4th3g23 = INITVALUE; + CCTK_REAL PDstandard4th11g23 = INITVALUE; + CCTK_REAL PDstandard4th12g23 = INITVALUE; + CCTK_REAL PDstandard4th13g23 = INITVALUE; + CCTK_REAL PDstandard4th21g23 = INITVALUE; + CCTK_REAL PDstandard4th23g23 = INITVALUE; + CCTK_REAL PDstandard4th31g23 = INITVALUE; + CCTK_REAL PDstandard4th32g23 = INITVALUE; CCTK_REAL PDstandard4th1g33 = INITVALUE; CCTK_REAL PDstandard4th2g33 = INITVALUE; CCTK_REAL PDstandard4th3g33 = INITVALUE; @@ -178,32 +178,32 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL CCTK_REAL PDstandard4th32g33 = INITVALUE; CCTK_REAL PDstandard4th2K11 = INITVALUE; CCTK_REAL PDstandard4th3K11 = INITVALUE; - CCTK_REAL PDstandard4th1K21 = INITVALUE; - CCTK_REAL PDstandard4th2K21 = INITVALUE; - CCTK_REAL PDstandard4th3K21 = INITVALUE; + CCTK_REAL PDstandard4th1K12 = INITVALUE; + CCTK_REAL PDstandard4th2K12 = INITVALUE; + CCTK_REAL PDstandard4th3K12 = INITVALUE; + CCTK_REAL PDstandard4th1K13 = INITVALUE; + CCTK_REAL PDstandard4th2K13 = INITVALUE; + CCTK_REAL PDstandard4th3K13 = INITVALUE; CCTK_REAL PDstandard4th1K22 = INITVALUE; CCTK_REAL PDstandard4th3K22 = INITVALUE; - CCTK_REAL PDstandard4th1K31 = INITVALUE; - CCTK_REAL PDstandard4th2K31 = INITVALUE; - CCTK_REAL PDstandard4th3K31 = INITVALUE; - CCTK_REAL PDstandard4th1K32 = INITVALUE; - CCTK_REAL PDstandard4th2K32 = INITVALUE; - CCTK_REAL PDstandard4th3K32 = INITVALUE; + CCTK_REAL PDstandard4th1K23 = INITVALUE; + CCTK_REAL PDstandard4th2K23 = INITVALUE; + CCTK_REAL PDstandard4th3K23 = INITVALUE; CCTK_REAL PDstandard4th1K33 = INITVALUE; CCTK_REAL PDstandard4th2K33 = INITVALUE; /* Assign local copies of grid functions */ g11L = g11[index]; - g21L = g21[index]; + g12L = g12[index]; + g13L = g13[index]; g22L = g22[index]; - g31L = g31[index]; - g32L = g32[index]; + g23L = g23[index]; g33L = g33[index]; K11L = K11[index]; - K21L = K21[index]; + K12L = K12[index]; + K13L = K13[index]; K22L = K22[index]; - K31L = K31[index]; - K32L = K32[index]; + K23L = K23[index]; K33L = K33[index]; /* Assign local copies of subblock grid functions */ @@ -217,33 +217,33 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL PDstandard4th22g11 = PDstandard4th22(g11, i, j, k); PDstandard4th33g11 = PDstandard4th33(g11, i, j, k); PDstandard4th23g11 = PDstandard4th23(g11, i, j, k); - PDstandard4th1g21 = PDstandard4th1(g21, i, j, k); - PDstandard4th2g21 = PDstandard4th2(g21, i, j, k); - PDstandard4th3g21 = PDstandard4th3(g21, i, j, k); - PDstandard4th33g21 = PDstandard4th33(g21, i, j, k); - PDstandard4th12g21 = PDstandard4th12(g21, i, j, k); - PDstandard4th13g21 = PDstandard4th13(g21, i, j, k); - PDstandard4th23g21 = PDstandard4th23(g21, i, j, k); + PDstandard4th1g12 = PDstandard4th1(g12, i, j, k); + PDstandard4th2g12 = PDstandard4th2(g12, i, j, k); + PDstandard4th3g12 = PDstandard4th3(g12, i, j, k); + PDstandard4th33g12 = PDstandard4th33(g12, i, j, k); + PDstandard4th12g12 = PDstandard4th12(g12, i, j, k); + PDstandard4th13g12 = PDstandard4th13(g12, i, j, k); + PDstandard4th23g12 = PDstandard4th23(g12, i, j, k); + PDstandard4th1g13 = PDstandard4th1(g13, i, j, k); + PDstandard4th2g13 = PDstandard4th2(g13, i, j, k); + PDstandard4th3g13 = PDstandard4th3(g13, i, j, k); + PDstandard4th22g13 = PDstandard4th22(g13, i, j, k); + PDstandard4th12g13 = PDstandard4th12(g13, i, j, k); + PDstandard4th13g13 = PDstandard4th13(g13, i, j, k); + PDstandard4th23g13 = PDstandard4th23(g13, i, j, k); PDstandard4th1g22 = PDstandard4th1(g22, i, j, k); PDstandard4th2g22 = PDstandard4th2(g22, i, j, k); PDstandard4th3g22 = PDstandard4th3(g22, i, j, k); PDstandard4th11g22 = PDstandard4th11(g22, i, j, k); PDstandard4th33g22 = PDstandard4th33(g22, i, j, k); PDstandard4th13g22 = PDstandard4th13(g22, i, j, k); - PDstandard4th1g31 = PDstandard4th1(g31, i, j, k); - PDstandard4th2g31 = PDstandard4th2(g31, i, j, k); - PDstandard4th3g31 = PDstandard4th3(g31, i, j, k); - PDstandard4th22g31 = PDstandard4th22(g31, i, j, k); - PDstandard4th12g31 = PDstandard4th12(g31, i, j, k); - PDstandard4th13g31 = PDstandard4th13(g31, i, j, k); - PDstandard4th23g31 = PDstandard4th23(g31, i, j, k); - PDstandard4th1g32 = PDstandard4th1(g32, i, j, k); - PDstandard4th2g32 = PDstandard4th2(g32, i, j, k); - PDstandard4th3g32 = PDstandard4th3(g32, i, j, k); - PDstandard4th11g32 = PDstandard4th11(g32, i, j, k); - PDstandard4th12g32 = PDstandard4th12(g32, i, j, k); - PDstandard4th13g32 = PDstandard4th13(g32, i, j, k); - PDstandard4th23g32 = PDstandard4th23(g32, i, j, k); + PDstandard4th1g23 = PDstandard4th1(g23, i, j, k); + PDstandard4th2g23 = PDstandard4th2(g23, i, j, k); + PDstandard4th3g23 = PDstandard4th3(g23, i, j, k); + PDstandard4th11g23 = PDstandard4th11(g23, i, j, k); + PDstandard4th12g23 = PDstandard4th12(g23, i, j, k); + PDstandard4th13g23 = PDstandard4th13(g23, i, j, k); + PDstandard4th23g23 = PDstandard4th23(g23, i, j, k); PDstandard4th1g33 = PDstandard4th1(g33, i, j, k); PDstandard4th2g33 = PDstandard4th2(g33, i, j, k); PDstandard4th3g33 = PDstandard4th3(g33, i, j, k); @@ -252,177 +252,177 @@ void ML_ADM_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL PDstandard4th12g33 = PDstandard4th12(g33, i, j, k); PDstandard4th2K11 = PDstandard4th2(K11, i, j, k); PDstandard4th3K11 = PDstandard4th3(K11, i, j, k); - PDstandard4th1K21 = PDstandard4th1(K21, i, j, k); - PDstandard4th2K21 = PDstandard4th2(K21, i, j, k); - PDstandard4th3K21 = PDstandard4th3(K21, i, j, k); + PDstandard4th1K12 = PDstandard4th1(K12, i, j, k); + PDstandard4th2K12 = PDstandard4th2(K12, i, j, k); + PDstandard4th3K12 = PDstandard4th3(K12, i, j, k); + PDstandard4th1K13 = PDstandard4th1(K13, i, j, k); + PDstandard4th2K13 = PDstandard4th2(K13, i, j, k); + PDstandard4th3K13 = PDstandard4th3(K13, i, j, k); PDstandard4th1K22 = PDstandard4th1(K22, i, j, k); PDstandard4th3K22 = PDstandard4th3(K22, i, j, k); - PDstandard4th1K31 = PDstandard4th1(K31, i, j, k); - PDstandard4th2K31 = PDstandard4th2(K31, i, j, k); - PDstandard4th3K31 = PDstandard4th3(K31, i, j, k); - PDstandard4th1K32 = PDstandard4th1(K32, i, j, k); - PDstandard4th2K32 = PDstandard4th2(K32, i, j, k); - PDstandard4th3K32 = PDstandard4th3(K32, i, j, k); + PDstandard4th1K23 = PDstandard4th1(K23, i, j, k); + PDstandard4th2K23 = PDstandard4th2(K23, i, j, k); + PDstandard4th3K23 = PDstandard4th3(K23, i, j, k); PDstandard4th1K33 = PDstandard4th1(K33, i, j, k); PDstandard4th2K33 = PDstandard4th2(K33, i, j, k); /* Precompute derivatives (old style) */ /* Calculate temporaries and grid functions */ - detg = 2*g21L*g31L*g32L + g33L*(g11L*g22L - SQR(g21L)) - g22L*SQR(g31L) - g11L*SQR(g32L); + detg = 2*g12L*g13L*g23L + g33L*(g11L*g22L - SQR(g12L)) - g22L*SQR(g13L) - g11L*SQR(g23L); - gu11 = INV(detg)*(g22L*g33L - SQR(g32L)); + gu11 = INV(detg)*(g22L*g33L - SQR(g23L)); - gu12 = (g31L*g32L - g21L*g33L)*INV(detg); + gu21 = (g13L*g23L - g12L*g33L)*INV(detg); - gu13 = (-(g22L*g31L) + g21L*g32L)*INV(detg); + gu31 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - gu22 = INV(detg)*(g11L*g33L - SQR(g31L)); + gu22 = INV(detg)*(g11L*g33L - SQR(g13L)); - gu23 = (g21L*g31L - g11L*g32L)*INV(detg); + gu32 = (g12L*g13L - g11L*g23L)*INV(detg); - gu33 = INV(detg)*(g11L*g22L - SQR(g21L)); + gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu12*PDstandard4th1g21 + gu13*PDstandard4th1g31) - gu12*PDstandard4th2g11 - - gu13*PDstandard4th3g11); + G111 = khalf*(gu11*PDstandard4th1g11 + 2*(gu21*PDstandard4th1g12 + gu31*PDstandard4th1g13) - gu21*PDstandard4th2g11 - + gu31*PDstandard4th3g11); - G211 = khalf*(gu12*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g21 + gu23*PDstandard4th1g31) - gu22*PDstandard4th2g11 - - gu23*PDstandard4th3g11); + G211 = khalf*(gu21*PDstandard4th1g11 + 2*(gu22*PDstandard4th1g12 + gu32*PDstandard4th1g13) - gu22*PDstandard4th2g11 - + gu32*PDstandard4th3g11); - G311 = khalf*(gu13*PDstandard4th1g11 + 2*(gu23*PDstandard4th1g21 + gu33*PDstandard4th1g31) - gu23*PDstandard4th2g11 - + G311 = khalf*(gu31*PDstandard4th1g11 + 2*(gu32*PDstandard4th1g12 + gu33*PDstandard4th1g13) - gu32*PDstandard4th2g11 - gu33*PDstandard4th3g11); - G121 = khalf*(gu12*PDstandard4th1g22 + gu11*PDstandard4th2g11 + - gu13*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G112 = khalf*(gu21*PDstandard4th1g22 + gu11*PDstandard4th2g11 + + gu31*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G221 = khalf*(gu22*PDstandard4th1g22 + gu12*PDstandard4th2g11 + - gu23*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G212 = khalf*(gu22*PDstandard4th1g22 + gu21*PDstandard4th2g11 + + gu32*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G321 = khalf*(gu23*PDstandard4th1g22 + gu13*PDstandard4th2g11 + - gu33*(PDstandard4th1g32 + PDstandard4th2g31 - PDstandard4th3g21)); + G312 = khalf*(gu32*PDstandard4th1g22 + gu31*PDstandard4th2g11 + + gu33*(PDstandard4th1g23 + PDstandard4th2g13 - PDstandard4th3g12)); - G131 = khalf*(gu13*PDstandard4th1g33 + gu11*PDstandard4th3g11 + - gu12*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G113 = khalf*(gu31*PDstandard4th1g33 + gu11*PDstandard4th3g11 + + gu21*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G231 = khalf*(gu23*PDstandard4th1g33 + gu12*PDstandard4th3g11 + - gu22*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G213 = khalf*(gu32*PDstandard4th1g33 + gu21*PDstandard4th3g11 + + gu22*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G331 = khalf*(gu33*PDstandard4th1g33 + gu13*PDstandard4th3g11 + - gu23*(PDstandard4th1g32 - PDstandard4th2g31 + PDstandard4th3g21)); + G313 = khalf*(gu33*PDstandard4th1g33 + gu31*PDstandard4th3g11 + + gu32*(PDstandard4th1g23 - PDstandard4th2g13 + PDstandard4th3g12)); - G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu12*PDstandard4th2g22 + - gu13*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G122 = khalf*(gu11*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu21*PDstandard4th2g22 + + gu31*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G222 = khalf*(gu12*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu22*PDstandard4th2g22 + - gu23*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G222 = khalf*(gu21*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu22*PDstandard4th2g22 + + gu32*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G322 = khalf*(gu13*(-PDstandard4th1g22 + 2*PDstandard4th2g21) + gu23*PDstandard4th2g22 + - gu33*(2*PDstandard4th2g32 - PDstandard4th3g22)); + G322 = khalf*(gu31*(-PDstandard4th1g22 + 2*PDstandard4th2g12) + gu32*PDstandard4th2g22 + + gu33*(2*PDstandard4th2g23 - PDstandard4th3g22)); - G132 = khalf*(gu13*PDstandard4th2g33 + gu11*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + - gu12*PDstandard4th3g22); + G123 = khalf*(gu31*PDstandard4th2g33 + gu11*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + + gu21*PDstandard4th3g22); - G232 = khalf*(gu23*PDstandard4th2g33 + gu12*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + + G223 = khalf*(gu32*PDstandard4th2g33 + gu21*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + gu22*PDstandard4th3g22); - G332 = khalf*(gu33*PDstandard4th2g33 + gu13*(-PDstandard4th1g32 + PDstandard4th2g31 + PDstandard4th3g21) + - gu23*PDstandard4th3g22); + G323 = khalf*(gu33*PDstandard4th2g33 + gu31*(-PDstandard4th1g23 + PDstandard4th2g13 + PDstandard4th3g12) + + gu32*PDstandard4th3g22); - G133 = khalf*(-(gu11*PDstandard4th1g33) - gu12*PDstandard4th2g33 + 2*gu11*PDstandard4th3g31 + - 2*gu12*PDstandard4th3g32 + gu13*PDstandard4th3g33); + G133 = khalf*(-(gu11*PDstandard4th1g33) - gu21*PDstandard4th2g33 + 2*gu11*PDstandard4th3g13 + + 2*gu21*PDstandard4th3g23 + gu31*PDstandard4th3g33); - G233 = khalf*(-(gu12*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu12*PDstandard4th3g31 + - 2*gu22*PDstandard4th3g32 + gu23*PDstandard4th3g33); + G233 = khalf*(-(gu21*PDstandard4th1g33) - gu22*PDstandard4th2g33 + 2*gu21*PDstandard4th3g13 + + 2*gu22*PDstandard4th3g23 + gu32*PDstandard4th3g33); - G333 = khalf*(-(gu13*PDstandard4th1g33) - gu23*PDstandard4th2g33 + 2*gu13*PDstandard4th3g31 + - 2*gu23*PDstandard4th3g32 + gu33*PDstandard4th3g33); + G333 = khalf*(-(gu31*PDstandard4th1g33) - gu32*PDstandard4th2g33 + 2*gu31*PDstandard4th3g13 + + 2*gu32*PDstandard4th3g23 + gu33*PDstandard4th3g33); R11 = khalf*(-(gu22*PDstandard4th11g22) - 2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 + G311*G322 + G311*G333 + - gu23*PDstandard4th11g32) - gu33*PDstandard4th11g33 + 2*gu22*PDstandard4th12g21 + 2*gu23*PDstandard4th12g31 + - 2*gu23*PDstandard4th13g21 + 2*gu33*PDstandard4th13g31 - gu22*PDstandard4th22g11 - 2*gu23*PDstandard4th23g11 - - gu33*PDstandard4th33g11 + 2*SQR(G121) + 2*SQR(G131) + 2*SQR(G221) + 2*SQR(G231) + 2*SQR(G321) + 2*SQR(G331)); - - R21 = khalf*(2*(G131*G132 + G231*G232 + G331*G332) - 2*(G121*G133 + G221*G233 + G321*G333 + gu12*PDstandard4th12g21) - - gu23*PDstandard4th12g32 - gu33*PDstandard4th12g33 + - gu13*(PDstandard4th11g32 - PDstandard4th12g31 - PDstandard4th13g21) + gu23*PDstandard4th13g22 + - gu33*PDstandard4th13g32 + gu12*(PDstandard4th11g22 + PDstandard4th22g11) + gu23*PDstandard4th22g31 + - gu13*PDstandard4th23g11 - gu23*PDstandard4th23g21 + gu33*PDstandard4th23g31 - gu33*PDstandard4th33g21); - - R31 = khalf*(2*(G121*G132 + G221*G232 + G321*G332) - 2*(G122*G131 + G222*G231 + G322*G331 + gu13*PDstandard4th13g31) + - gu12*(PDstandard4th11g32 - PDstandard4th12g31 - PDstandard4th13g21 + PDstandard4th23g11) + - gu22*(PDstandard4th12g32 - PDstandard4th13g22 - PDstandard4th22g31 + PDstandard4th23g21) + - gu13*(PDstandard4th11g33 + PDstandard4th33g11) + - gu23*(PDstandard4th12g33 - PDstandard4th13g32 - PDstandard4th23g31 + PDstandard4th33g21)); - - R22 = khalf*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + G322*(G311 + G333) + gu13*PDstandard4th13g22) + - gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g21 - PDstandard4th22g11) + - gu13*(-2*PDstandard4th22g31 + 2*(PDstandard4th12g32 + PDstandard4th23g21)) + - gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g32 - PDstandard4th33g22) + - 2*(SQR(G121) + SQR(G132) + SQR(G221) + SQR(G232) + SQR(G321) + SQR(G332))); - - R32 = khalf*(2*(G121*G131 + G221*G231 + G321*G331) + - gu11*(-PDstandard4th11g32 + PDstandard4th12g31 + PDstandard4th13g21 - PDstandard4th23g11) + - gu12*(-PDstandard4th12g32 + PDstandard4th13g22 + PDstandard4th22g31 - PDstandard4th23g21) - - 2*(G111*G132 + G211*G232 + G311*G332 + gu23*PDstandard4th23g32) + - gu13*(PDstandard4th12g33 - PDstandard4th13g32 - PDstandard4th23g31 + PDstandard4th33g21) + - gu23*(PDstandard4th22g33 + PDstandard4th33g22)); - - R33 = khalf*(gu11*(-PDstandard4th11g33 + 2*PDstandard4th13g31 - PDstandard4th33g11) - + gu32*PDstandard4th11g23) - gu33*PDstandard4th11g33 + 2*gu22*PDstandard4th12g12 + 2*gu32*PDstandard4th12g13 + + 2*gu32*PDstandard4th13g12 + 2*gu33*PDstandard4th13g13 - gu22*PDstandard4th22g11 - 2*gu32*PDstandard4th23g11 - + gu33*PDstandard4th33g11 + 2*SQR(G112) + 2*SQR(G113) + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); + + R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*PDstandard4th12g12) - + gu32*PDstandard4th12g23 - gu33*PDstandard4th12g33 + + gu31*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12) + gu32*PDstandard4th13g22 + + gu33*PDstandard4th13g23 + gu21*(PDstandard4th11g22 + PDstandard4th22g11) + gu32*PDstandard4th22g13 + + gu31*PDstandard4th23g11 - gu32*PDstandard4th23g12 + gu33*PDstandard4th23g13 - gu33*PDstandard4th33g12); + + R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*PDstandard4th13g13) + + gu21*(PDstandard4th11g23 - PDstandard4th12g13 - PDstandard4th13g12 + PDstandard4th23g11) + + gu22*(PDstandard4th12g23 - PDstandard4th13g22 - PDstandard4th22g13 + PDstandard4th23g12) + + gu31*(PDstandard4th11g33 + PDstandard4th33g11) + + gu32*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12)); + + R22 = khalf*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + G322*(G311 + G333) + gu31*PDstandard4th13g22) + + gu11*(-PDstandard4th11g22 + 2*PDstandard4th12g12 - PDstandard4th22g11) + + gu31*(-2*PDstandard4th22g13 + 2*(PDstandard4th12g23 + PDstandard4th23g12)) + + gu33*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + + 2*(SQR(G112) + SQR(G123) + SQR(G212) + SQR(G223) + SQR(G312) + SQR(G323))); + + R23 = khalf*(2*(G112*G113 + G212*G213 + G312*G313) + + gu11*(-PDstandard4th11g23 + PDstandard4th12g13 + PDstandard4th13g12 - PDstandard4th23g11) + + gu21*(-PDstandard4th12g23 + PDstandard4th13g22 + PDstandard4th22g13 - PDstandard4th23g12) - + 2*(G111*G123 + G211*G223 + G311*G323 + gu32*PDstandard4th23g23) + + gu31*(PDstandard4th12g33 - PDstandard4th13g23 - PDstandard4th23g13 + PDstandard4th33g12) + + gu32*(PDstandard4th22g33 + PDstandard4th33g22)); + + R33 = khalf*(gu11*(-PDstandard4th11g33 + 2*PDstandard4th13g13 - PDstandard4th33g11) - 2*((G111 + G122)*G133 + (G211 + G222)*G233 + (G311 + G322)*G333 + - gu12*(PDstandard4th12g33 + PDstandard4th33g21)) + - gu22*(-PDstandard4th22g33 + 2*PDstandard4th23g32 - PDstandard4th33g22) + - 2*(gu12*(PDstandard4th13g32 + PDstandard4th23g31) + SQR(G131) + SQR(G132) + SQR(G231) + SQR(G232) + SQR(G331) + - SQR(G332))); + gu21*(PDstandard4th12g33 + PDstandard4th33g12)) + + gu22*(-PDstandard4th22g33 + 2*PDstandard4th23g23 - PDstandard4th33g22) + + 2*(gu21*(PDstandard4th13g23 + PDstandard4th23g13) + SQR(G113) + SQR(G123) + SQR(G213) + SQR(G223) + SQR(G313) + + SQR(G323))); - trR = gu11*R11 + gu22*R22 + 2*(gu12*R21 + gu13*R31 + gu23*R32) + gu33*R33; + trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; - Km11 = gu11*K11L + gu12*K21L + gu13*K31L; + Km11 = gu11*K11L + gu21*K12L + gu31*K13L; - Km21 = gu12*K11L + gu22*K21L + gu23*K31L; + Km21 = gu21*K11L + gu22*K12L + gu32*K13L; - Km31 = gu13*K11L + gu23*K21L + gu33*K31L; + Km31 = gu31*K11L + gu32*K12L + gu33*K13L; - Km12 = gu11*K21L + gu12*K22L + gu13*K32L; + Km12 = gu11*K12L + gu21*K22L + gu31*K23L; - Km22 = gu12*K21L + gu22*K22L + gu23*K32L; + Km22 = gu21*K12L + gu22*K22L + gu32*K23L; - Km32 = gu13*K21L + gu23*K22L + gu33*K32L; + Km32 = gu31*K12L + gu32*K22L + gu33*K23L; - Km13 = gu11*K31L + gu12*K32L + gu13*K33L; + Km13 = gu11*K13L + gu21*K23L + gu31*K33L; - Km23 = gu12*K31L + gu22*K32L + gu23*K33L; + Km23 = gu21*K13L + gu22*K23L + gu32*K33L; - Km33 = gu13*K31L + gu23*K32L + gu33*K33L; + Km33 = gu31*K13L + gu32*K23L + gu33*K33L; trK = Km11 + Km22 + Km33; HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR - SQR(Km11) - SQR(Km22) - SQR(Km33) + SQR(trK); - M1L = gu12*(-(G121*K11L) + G111*K21L - G221*K21L + G211*K22L - G321*K31L + G311*K32L - PDstandard4th1K21 + - PDstandard4th2K11) + gu22*(-(G122*K11L) + G121*K21L - G222*K21L + G221*K22L - G322*K31L + G321*K32L - - PDstandard4th1K22 + PDstandard4th2K21) + gu13* - (-(G131*K11L) - G231*K21L + G111*K31L - G331*K31L + G211*K32L + G311*K33L - PDstandard4th1K31 + PDstandard4th3K11)\ - + gu23*(G131*K21L + G231*K22L + G121*K31L + (G221 + G331)*K32L + G321*K33L - - 2*(G132*K11L + G232*K21L + G332*K31L + PDstandard4th1K32) + PDstandard4th2K31 + PDstandard4th3K21) + - gu33*(-(G133*K11L) - G233*K21L + G131*K31L - G333*K31L + G231*K32L + G331*K33L - PDstandard4th1K33 + - PDstandard4th3K31); - - M2L = gu11*(G121*K11L + (-G111 + G221)*K21L - G211*K22L + G321*K31L - G311*K32L + PDstandard4th1K21 - - PDstandard4th2K11) + gu12*(G122*K11L + (-G121 + G222)*K21L - G221*K22L + G322*K31L - G321*K32L + - PDstandard4th1K22 - PDstandard4th2K21) + gu13* - (G132*K11L + (-2*G131 + G232)*K21L + (G121 + G332)*K31L + G221*K32L + G321*K33L + PDstandard4th1K32 - - 2*(G231*K22L + G331*K32L + PDstandard4th2K31) + PDstandard4th3K21) + - gu23*(-(G132*K21L) - G232*K22L + G122*K31L + G222*K32L - G332*K32L + G322*K33L - PDstandard4th2K32 + - PDstandard4th3K22) + gu33*(-(G133*K21L) - G233*K22L + G132*K31L + G232*K32L - G333*K32L + G332*K33L - - PDstandard4th2K33 + PDstandard4th3K32); - - M3L = gu11*(G131*K11L + G231*K21L + (-G111 + G331)*K31L - G211*K32L - G311*K33L + PDstandard4th1K31 - - PDstandard4th3K11) + gu12*(G132*K11L + (G131 + G232)*K21L + G231*K22L + (-2*G121 + G332)*K31L + - (-2*G221 + G331)*K32L + PDstandard4th1K32 + PDstandard4th2K31 - 2*(G321*K33L + PDstandard4th3K21)) + - gu22*(G132*K21L + G232*K22L - G122*K31L - G222*K32L + G332*K32L - G322*K33L + PDstandard4th2K32 - - PDstandard4th3K22) + gu13*(G133*K11L + G233*K21L + (-G131 + G333)*K31L - G231*K32L - G331*K33L + - PDstandard4th1K33 - PDstandard4th3K31) + gu23* - (G133*K21L + G233*K22L - G132*K31L - G232*K32L + G333*K32L - G332*K33L + PDstandard4th2K33 - PDstandard4th3K32); + M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L + G211*K22L + G311*K23L - PDstandard4th1K12 + + PDstandard4th2K11) + gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L + G312*K23L - + PDstandard4th1K22 + PDstandard4th2K12) + gu31* + (-(G113*K11L) - G213*K12L + G111*K13L - G313*K13L + G211*K23L + G311*K33L - PDstandard4th1K13 + PDstandard4th3K11)\ + + gu32*(G113*K12L + G112*K13L + G213*K22L + (G212 + G313)*K23L + G312*K33L - + 2*(G123*K11L + G223*K12L + G323*K13L + PDstandard4th1K23) + PDstandard4th2K13 + PDstandard4th3K12) + + gu33*(-(G133*K11L) - G233*K12L + G113*K13L - G333*K13L + G213*K23L + G313*K33L - PDstandard4th1K33 + + PDstandard4th3K13); + + M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L - G211*K22L - G311*K23L + PDstandard4th1K12 - + PDstandard4th2K11) + gu21*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L - G312*K23L + + PDstandard4th1K22 - PDstandard4th2K12) + gu31* + (G123*K11L + (-2*G113 + G223)*K12L + (G112 + G323)*K13L + G212*K23L + G312*K33L + PDstandard4th1K23 - + 2*(G213*K22L + G313*K23L + PDstandard4th2K13) + PDstandard4th3K12) + + gu32*(-(G123*K12L) + G122*K13L - G223*K22L + G222*K23L - G323*K23L + G322*K33L - PDstandard4th2K23 + + PDstandard4th3K22) + gu33*(-(G133*K12L) + G123*K13L - G233*K22L + G223*K23L - G333*K23L + G323*K33L - + PDstandard4th2K33 + PDstandard4th3K23); + + M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L - G211*K23L - G311*K33L + PDstandard4th1K13 - + PDstandard4th3K11) + gu21*(G123*K11L + (G113 + G223)*K12L + (-2*G112 + G323)*K13L + G213*K22L + + (-2*G212 + G313)*K23L + PDstandard4th1K23 + PDstandard4th2K13 - 2*(G312*K33L + PDstandard4th3K12)) + + gu31*(G133*K11L + G233*K12L + (-G113 + G333)*K13L - G213*K23L - G313*K33L + PDstandard4th1K33 - + PDstandard4th3K13) + gu22*(G123*K12L - G122*K13L + G223*K22L - G222*K23L + G323*K23L - G322*K33L + + PDstandard4th2K23 - PDstandard4th3K22) + gu32* + (G133*K12L - G123*K13L + G233*K22L - G223*K23L + G333*K23L - G323*K33L + PDstandard4th2K33 - PDstandard4th3K23); /* Copy local copies back to grid functions */ diff --git a/ML_ADM/src/ML_ADM_convertFromADMBase.c b/ML_ADM/src/ML_ADM_convertFromADMBase.c index a634aeb..1288d06 100644 --- a/ML_ADM/src/ML_ADM_convertFromADMBase.c +++ b/ML_ADM/src/ML_ADM_convertFromADMBase.c @@ -102,14 +102,14 @@ void ML_ADM_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CC CCTK_REAL betaxL = INITVALUE; CCTK_REAL betayL = INITVALUE; CCTK_REAL betazL = INITVALUE; - CCTK_REAL g11L = INITVALUE, g21L = INITVALUE, g22L = INITVALUE, g31L = INITVALUE, g32L = INITVALUE, g33L = INITVALUE; + CCTK_REAL g11L = INITVALUE, g12L = INITVALUE, g13L = INITVALUE, g22L = INITVALUE, g23L = INITVALUE, g33L = INITVALUE; CCTK_REAL gxxL = INITVALUE; CCTK_REAL gxyL = INITVALUE; CCTK_REAL gxzL = INITVALUE; CCTK_REAL gyyL = INITVALUE; CCTK_REAL gyzL = INITVALUE; CCTK_REAL gzzL = INITVALUE; - CCTK_REAL K11L = INITVALUE, K21L = INITVALUE, K22L = INITVALUE, K31L = INITVALUE, K32L = INITVALUE, K33L = INITVALUE; + CCTK_REAL K11L = INITVALUE, K12L = INITVALUE, K13L = INITVALUE, K22L = INITVALUE, K23L = INITVALUE, K33L = INITVALUE; CCTK_REAL kxxL = INITVALUE; CCTK_REAL kxyL = INITVALUE; CCTK_REAL kxzL = INITVALUE; @@ -149,25 +149,25 @@ void ML_ADM_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CC /* Calculate temporaries and grid functions */ g11L = gxxL; - g21L = gxyL; + g12L = gxyL; - g31L = gxzL; + g13L = gxzL; g22L = gyyL; - g32L = gyzL; + g23L = gyzL; g33L = gzzL; K11L = kxxL; - K21L = kxyL; + K12L = kxyL; - K31L = kxzL; + K13L = kxzL; K22L = kyyL; - K32L = kyzL; + K23L = kyzL; K33L = kzzL; @@ -186,16 +186,16 @@ void ML_ADM_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CC beta2[index] = beta2L; beta3[index] = beta3L; g11[index] = g11L; - g21[index] = g21L; + g12[index] = g12L; + g13[index] = g13L; g22[index] = g22L; - g31[index] = g31L; - g32[index] = g32L; + g23[index] = g23L; g33[index] = g33L; K11[index] = K11L; - K21[index] = K21L; + K12[index] = K12L; + K13[index] = K13L; K22[index] = K22L; - K31[index] = K31L; - K32[index] = K32L; + K23[index] = K23L; K33[index] = K33L; /* Copy local copies back to subblock grid functions */ diff --git a/ML_ADM/src/ML_ADM_convertToADMBase.c b/ML_ADM/src/ML_ADM_convertToADMBase.c index 5f010fb..87dc888 100644 --- a/ML_ADM/src/ML_ADM_convertToADMBase.c +++ b/ML_ADM/src/ML_ADM_convertToADMBase.c @@ -106,14 +106,14 @@ void ML_ADM_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK CCTK_REAL dtbetaxL = INITVALUE; CCTK_REAL dtbetayL = INITVALUE; CCTK_REAL dtbetazL = INITVALUE; - CCTK_REAL g11L = INITVALUE, g21L = INITVALUE, g22L = INITVALUE, g31L = INITVALUE, g32L = INITVALUE, g33L = INITVALUE; + CCTK_REAL g11L = INITVALUE, g12L = INITVALUE, g13L = INITVALUE, g22L = INITVALUE, g23L = INITVALUE, g33L = INITVALUE; CCTK_REAL gxxL = INITVALUE; CCTK_REAL gxyL = INITVALUE; CCTK_REAL gxzL = INITVALUE; CCTK_REAL gyyL = INITVALUE; CCTK_REAL gyzL = INITVALUE; CCTK_REAL gzzL = INITVALUE; - CCTK_REAL K11L = INITVALUE, K21L = INITVALUE, K22L = INITVALUE, K31L = INITVALUE, K32L = INITVALUE, K33L = INITVALUE; + CCTK_REAL K11L = INITVALUE, K12L = INITVALUE, K13L = INITVALUE, K22L = INITVALUE, K23L = INITVALUE, K33L = INITVALUE; CCTK_REAL kxxL = INITVALUE; CCTK_REAL kxyL = INITVALUE; CCTK_REAL kxzL = INITVALUE; @@ -130,16 +130,16 @@ void ML_ADM_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK beta2L = beta2[index]; beta3L = beta3[index]; g11L = g11[index]; - g21L = g21[index]; + g12L = g12[index]; + g13L = g13[index]; g22L = g22[index]; - g31L = g31[index]; - g32L = g32[index]; + g23L = g23[index]; g33L = g33[index]; K11L = K11[index]; - K21L = K21[index]; + K12L = K12[index]; + K13L = K13[index]; K22L = K22[index]; - K31L = K31[index]; - K32L = K32[index]; + K23L = K23[index]; K33L = K33[index]; /* Assign local copies of subblock grid functions */ @@ -153,25 +153,25 @@ void ML_ADM_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK /* Calculate temporaries and grid functions */ gxxL = g11L; - gxyL = g21L; + gxyL = g12L; - gxzL = g31L; + gxzL = g13L; gyyL = g22L; - gyzL = g32L; + gyzL = g23L; gzzL = g33L; kxxL = K11L; - kxyL = K21L; + kxyL = K12L; - kxzL = K31L; + kxzL = K13L; kyyL = K22L; - kyzL = K32L; + kyzL = K23L; kzzL = K33L; diff --git a/ML_ADM/src/RegisterMoL.c b/ML_ADM/src/RegisterMoL.c index a87e176..a22fb2d 100644 --- a/ML_ADM/src/RegisterMoL.c +++ b/ML_ADM/src/RegisterMoL.c @@ -16,17 +16,17 @@ void ML_ADM_RegisterVars(CCTK_ARGUMENTS) /* Register all the evolved grid functions with MoL */ ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K11"), CCTK_VarIndex("ML_ADM::K11rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K21"), CCTK_VarIndex("ML_ADM::K21rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K31"), CCTK_VarIndex("ML_ADM::K31rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K12"), CCTK_VarIndex("ML_ADM::K12rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K13"), CCTK_VarIndex("ML_ADM::K13rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K22"), CCTK_VarIndex("ML_ADM::K22rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K32"), CCTK_VarIndex("ML_ADM::K32rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K23"), CCTK_VarIndex("ML_ADM::K23rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::K33"), CCTK_VarIndex("ML_ADM::K33rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::alpha"), CCTK_VarIndex("ML_ADM::alpharhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g11"), CCTK_VarIndex("ML_ADM::g11rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g21"), CCTK_VarIndex("ML_ADM::g21rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g31"), CCTK_VarIndex("ML_ADM::g31rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g12"), CCTK_VarIndex("ML_ADM::g12rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g13"), CCTK_VarIndex("ML_ADM::g13rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g22"), CCTK_VarIndex("ML_ADM::g22rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g32"), CCTK_VarIndex("ML_ADM::g32rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g23"), CCTK_VarIndex("ML_ADM::g23rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::g33"), CCTK_VarIndex("ML_ADM::g33rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::beta1"), CCTK_VarIndex("ML_ADM::beta1rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_ADM::beta2"), CCTK_VarIndex("ML_ADM::beta2rhs")); diff --git a/ML_ADM/src/RegisterSymmetries.c b/ML_ADM/src/RegisterSymmetries.c index 9a2e722..b610f81 100644 --- a/ML_ADM/src/RegisterSymmetries.c +++ b/ML_ADM/src/RegisterSymmetries.c @@ -27,12 +27,12 @@ void ML_ADM_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = -1; sym[1] = -1; sym[2] = 1; - SetCartSymVN(cctkGH, sym, "ML_ADM::K21"); + SetCartSymVN(cctkGH, sym, "ML_ADM::K12"); sym[0] = -1; sym[1] = 1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_ADM::K31"); + SetCartSymVN(cctkGH, sym, "ML_ADM::K13"); sym[0] = 1; sym[1] = 1; @@ -42,7 +42,7 @@ void ML_ADM_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = 1; sym[1] = -1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_ADM::K32"); + SetCartSymVN(cctkGH, sym, "ML_ADM::K23"); sym[0] = 1; sym[1] = 1; @@ -62,12 +62,12 @@ void ML_ADM_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = -1; sym[1] = -1; sym[2] = 1; - SetCartSymVN(cctkGH, sym, "ML_ADM::g21"); + SetCartSymVN(cctkGH, sym, "ML_ADM::g12"); sym[0] = -1; sym[1] = 1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_ADM::g31"); + SetCartSymVN(cctkGH, sym, "ML_ADM::g13"); sym[0] = 1; sym[1] = 1; @@ -77,7 +77,7 @@ void ML_ADM_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = 1; sym[1] = -1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_ADM::g32"); + SetCartSymVN(cctkGH, sym, "ML_ADM::g23"); sym[0] = 1; sym[1] = 1; diff --git a/ML_BSSN/interface.ccl b/ML_BSSN/interface.ccl index 5dfcf8c..dd11e9f 100644 --- a/ML_BSSN/interface.ccl +++ b/ML_BSSN/interface.ccl @@ -68,10 +68,10 @@ public: CCTK_REAL curvrhs type=GF timelevels=1 tags='tensortypealias="DD_sym" tensorweight=-0.66666666666666666667' { At11rhs, - At21rhs, - At31rhs, + At12rhs, + At13rhs, At22rhs, - At32rhs, + At23rhs, At33rhs } "curvrhs" @@ -113,10 +113,10 @@ public: CCTK_REAL metricrhs type=GF timelevels=1 tags='tensortypealias="DD_sym" tensorweight=-0.66666666666666666667' { gt11rhs, - gt21rhs, - gt31rhs, + gt12rhs, + gt13rhs, gt22rhs, - gt32rhs, + gt23rhs, gt33rhs } "metricrhs" @@ -138,10 +138,10 @@ public: CCTK_REAL curv type=GF timelevels=3 tags='tensortypealias="DD_sym" tensorweight=-0.66666666666666666667' { At11, - At21, - At31, + At12, + At13, At22, - At32, + At23, At33 } "curv" @@ -183,10 +183,10 @@ public: CCTK_REAL metric type=GF timelevels=3 tags='tensortypealias="DD_sym" tensorweight=-0.66666666666666666667' { gt11, - gt21, - gt31, + gt12, + gt13, gt22, - gt32, + gt23, gt33 } "metric" diff --git a/ML_BSSN/param.ccl b/ML_BSSN/param.ccl index 1430b55..a7f2534 100644 --- a/ML_BSSN/param.ccl +++ b/ML_BSSN/param.ccl @@ -181,7 +181,7 @@ KEYWORD At11_bound "Boundary condition to implement" } "skip" private: -KEYWORD At21_bound "Boundary condition to implement" +KEYWORD At12_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -193,7 +193,7 @@ KEYWORD At21_bound "Boundary condition to implement" } "skip" private: -KEYWORD At31_bound "Boundary condition to implement" +KEYWORD At13_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -217,7 +217,7 @@ KEYWORD At22_bound "Boundary condition to implement" } "skip" private: -KEYWORD At32_bound "Boundary condition to implement" +KEYWORD At23_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -361,7 +361,7 @@ KEYWORD gt11_bound "Boundary condition to implement" } "skip" private: -KEYWORD gt21_bound "Boundary condition to implement" +KEYWORD gt12_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -373,7 +373,7 @@ KEYWORD gt21_bound "Boundary condition to implement" } "skip" private: -KEYWORD gt31_bound "Boundary condition to implement" +KEYWORD gt13_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -397,7 +397,7 @@ KEYWORD gt22_bound "Boundary condition to implement" } "skip" private: -KEYWORD gt32_bound "Boundary condition to implement" +KEYWORD gt23_bound "Boundary condition to implement" { "flat" :: "Flat boundary condition" "none" :: "No boundary condition" @@ -583,13 +583,13 @@ CCTK_REAL At11_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL At21_bound_speed "characteristic speed at boundary" +CCTK_REAL At12_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. private: -CCTK_REAL At31_bound_speed "characteristic speed at boundary" +CCTK_REAL At13_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -601,7 +601,7 @@ CCTK_REAL At22_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL At32_bound_speed "characteristic speed at boundary" +CCTK_REAL At23_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -673,13 +673,13 @@ CCTK_REAL gt11_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL gt21_bound_speed "characteristic speed at boundary" +CCTK_REAL gt12_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. private: -CCTK_REAL gt31_bound_speed "characteristic speed at boundary" +CCTK_REAL gt13_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -691,7 +691,7 @@ CCTK_REAL gt22_bound_speed "characteristic speed at boundary" } 1. private: -CCTK_REAL gt32_bound_speed "characteristic speed at boundary" +CCTK_REAL gt23_bound_speed "characteristic speed at boundary" { "0:*" :: "outgoing characteristic speed > 0" } 1. @@ -787,13 +787,13 @@ CCTK_REAL At11_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL At21_bound_limit "limit value for r -> infinity" +CCTK_REAL At12_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. private: -CCTK_REAL At31_bound_limit "limit value for r -> infinity" +CCTK_REAL At13_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -805,7 +805,7 @@ CCTK_REAL At22_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL At32_bound_limit "limit value for r -> infinity" +CCTK_REAL At23_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -877,13 +877,13 @@ CCTK_REAL gt11_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL gt21_bound_limit "limit value for r -> infinity" +CCTK_REAL gt12_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. private: -CCTK_REAL gt31_bound_limit "limit value for r -> infinity" +CCTK_REAL gt13_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -895,7 +895,7 @@ CCTK_REAL gt22_bound_limit "limit value for r -> infinity" } 0. private: -CCTK_REAL gt32_bound_limit "limit value for r -> infinity" +CCTK_REAL gt23_bound_limit "limit value for r -> infinity" { "*:*" :: "value of limit value is unrestricted" } 0. @@ -991,13 +991,13 @@ CCTK_REAL At11_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL At21_bound_scalar "Dirichlet boundary value" +CCTK_REAL At12_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. private: -CCTK_REAL At31_bound_scalar "Dirichlet boundary value" +CCTK_REAL At13_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -1009,7 +1009,7 @@ CCTK_REAL At22_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL At32_bound_scalar "Dirichlet boundary value" +CCTK_REAL At23_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -1081,13 +1081,13 @@ CCTK_REAL gt11_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL gt21_bound_scalar "Dirichlet boundary value" +CCTK_REAL gt12_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. private: -CCTK_REAL gt31_bound_scalar "Dirichlet boundary value" +CCTK_REAL gt13_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. @@ -1099,7 +1099,7 @@ CCTK_REAL gt22_bound_scalar "Dirichlet boundary value" } 0. private: -CCTK_REAL gt32_bound_scalar "Dirichlet boundary value" +CCTK_REAL gt23_bound_scalar "Dirichlet boundary value" { "*:*" :: "unrestricted" } 0. diff --git a/ML_BSSN/src/Boundaries.c b/ML_BSSN/src/Boundaries.c index a5456e9..03838fd 100644 --- a/ML_BSSN/src/Boundaries.c +++ b/ML_BSSN/src/Boundaries.c @@ -145,26 +145,26 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register At11_bound BC for ML_BSSN::At11!"); } - if (CCTK_EQUALS(At21_bound, "none" ) || - CCTK_EQUALS(At21_bound, "static") || - CCTK_EQUALS(At21_bound, "flat" ) || - CCTK_EQUALS(At21_bound, "zero" ) ) + if (CCTK_EQUALS(At12_bound, "none" ) || + CCTK_EQUALS(At12_bound, "static") || + CCTK_EQUALS(At12_bound, "flat" ) || + CCTK_EQUALS(At12_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::At21", At21_bound); + "ML_BSSN::At12", At12_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register At21_bound BC for ML_BSSN::At21!"); + CCTK_WARN(-1, "Failed to register At12_bound BC for ML_BSSN::At12!"); } - if (CCTK_EQUALS(At31_bound, "none" ) || - CCTK_EQUALS(At31_bound, "static") || - CCTK_EQUALS(At31_bound, "flat" ) || - CCTK_EQUALS(At31_bound, "zero" ) ) + if (CCTK_EQUALS(At13_bound, "none" ) || + CCTK_EQUALS(At13_bound, "static") || + CCTK_EQUALS(At13_bound, "flat" ) || + CCTK_EQUALS(At13_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::At31", At31_bound); + "ML_BSSN::At13", At13_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register At31_bound BC for ML_BSSN::At31!"); + CCTK_WARN(-1, "Failed to register At13_bound BC for ML_BSSN::At13!"); } if (CCTK_EQUALS(At22_bound, "none" ) || @@ -178,15 +178,15 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register At22_bound BC for ML_BSSN::At22!"); } - if (CCTK_EQUALS(At32_bound, "none" ) || - CCTK_EQUALS(At32_bound, "static") || - CCTK_EQUALS(At32_bound, "flat" ) || - CCTK_EQUALS(At32_bound, "zero" ) ) + if (CCTK_EQUALS(At23_bound, "none" ) || + CCTK_EQUALS(At23_bound, "static") || + CCTK_EQUALS(At23_bound, "flat" ) || + CCTK_EQUALS(At23_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::At32", At32_bound); + "ML_BSSN::At23", At23_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register At32_bound BC for ML_BSSN::At32!"); + CCTK_WARN(-1, "Failed to register At23_bound BC for ML_BSSN::At23!"); } if (CCTK_EQUALS(At33_bound, "none" ) || @@ -310,26 +310,26 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register gt11_bound BC for ML_BSSN::gt11!"); } - if (CCTK_EQUALS(gt21_bound, "none" ) || - CCTK_EQUALS(gt21_bound, "static") || - CCTK_EQUALS(gt21_bound, "flat" ) || - CCTK_EQUALS(gt21_bound, "zero" ) ) + if (CCTK_EQUALS(gt12_bound, "none" ) || + CCTK_EQUALS(gt12_bound, "static") || + CCTK_EQUALS(gt12_bound, "flat" ) || + CCTK_EQUALS(gt12_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::gt21", gt21_bound); + "ML_BSSN::gt12", gt12_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register gt21_bound BC for ML_BSSN::gt21!"); + CCTK_WARN(-1, "Failed to register gt12_bound BC for ML_BSSN::gt12!"); } - if (CCTK_EQUALS(gt31_bound, "none" ) || - CCTK_EQUALS(gt31_bound, "static") || - CCTK_EQUALS(gt31_bound, "flat" ) || - CCTK_EQUALS(gt31_bound, "zero" ) ) + if (CCTK_EQUALS(gt13_bound, "none" ) || + CCTK_EQUALS(gt13_bound, "static") || + CCTK_EQUALS(gt13_bound, "flat" ) || + CCTK_EQUALS(gt13_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::gt31", gt31_bound); + "ML_BSSN::gt13", gt13_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register gt31_bound BC for ML_BSSN::gt31!"); + CCTK_WARN(-1, "Failed to register gt13_bound BC for ML_BSSN::gt13!"); } if (CCTK_EQUALS(gt22_bound, "none" ) || @@ -343,15 +343,15 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) CCTK_WARN(-1, "Failed to register gt22_bound BC for ML_BSSN::gt22!"); } - if (CCTK_EQUALS(gt32_bound, "none" ) || - CCTK_EQUALS(gt32_bound, "static") || - CCTK_EQUALS(gt32_bound, "flat" ) || - CCTK_EQUALS(gt32_bound, "zero" ) ) + if (CCTK_EQUALS(gt23_bound, "none" ) || + CCTK_EQUALS(gt23_bound, "static") || + CCTK_EQUALS(gt23_bound, "flat" ) || + CCTK_EQUALS(gt23_bound, "zero" ) ) { ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, -1, - "ML_BSSN::gt32", gt32_bound); + "ML_BSSN::gt23", gt23_bound); if (ierr < 0) - CCTK_WARN(-1, "Failed to register gt32_bound BC for ML_BSSN::gt32!"); + CCTK_WARN(-1, "Failed to register gt23_bound BC for ML_BSSN::gt23!"); } if (CCTK_EQUALS(gt33_bound, "none" ) || @@ -589,39 +589,39 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(At21_bound, "radiative")) + if (CCTK_EQUALS(At12_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_At21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At21_bound , At21_bound_limit, "LIMIT") < 0) + CCTK_INT handle_At12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At12_bound , At12_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_At21_bound ,At21_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_At12_bound ,At12_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At21_bound, - "ML_BSSN::At21", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At12_bound, + "ML_BSSN::At12", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At21!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At12!"); } - if (CCTK_EQUALS(At31_bound, "radiative")) + if (CCTK_EQUALS(At13_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_At31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At31_bound , At31_bound_limit, "LIMIT") < 0) + CCTK_INT handle_At13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At13_bound , At13_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_At31_bound ,At31_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_At13_bound ,At13_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At31_bound, - "ML_BSSN::At31", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At13_bound, + "ML_BSSN::At13", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At31!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At13!"); } @@ -643,21 +643,21 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(At32_bound, "radiative")) + if (CCTK_EQUALS(At23_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_At32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At32_bound , At32_bound_limit, "LIMIT") < 0) + CCTK_INT handle_At23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At23_bound , At23_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_At32_bound ,At32_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_At23_bound ,At23_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At32_bound, - "ML_BSSN::At32", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At23_bound, + "ML_BSSN::At23", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At32!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::At23!"); } @@ -859,39 +859,39 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(gt21_bound, "radiative")) + if (CCTK_EQUALS(gt12_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_gt21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt21_bound , gt21_bound_limit, "LIMIT") < 0) + CCTK_INT handle_gt12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt12_bound , gt12_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_gt21_bound ,gt21_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_gt12_bound ,gt12_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt21_bound, - "ML_BSSN::gt21", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt12_bound, + "ML_BSSN::gt12", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt21!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt12!"); } - if (CCTK_EQUALS(gt31_bound, "radiative")) + if (CCTK_EQUALS(gt13_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_gt31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt31_bound , gt31_bound_limit, "LIMIT") < 0) + CCTK_INT handle_gt13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt13_bound , gt13_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_gt31_bound ,gt31_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_gt13_bound ,gt13_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt31_bound, - "ML_BSSN::gt31", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt13_bound, + "ML_BSSN::gt13", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt31!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt13!"); } @@ -913,21 +913,21 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(gt32_bound, "radiative")) + if (CCTK_EQUALS(gt23_bound, "radiative")) { /* apply radiation boundary condition */ - CCTK_INT handle_gt32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt32_bound , gt32_bound_limit, "LIMIT") < 0) + CCTK_INT handle_gt23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt23_bound , gt23_bound_limit, "LIMIT") < 0) CCTK_WARN(-1, "could not set LIMIT value in table!"); - if (Util_TableSetReal(handle_gt32_bound ,gt32_bound_speed, "SPEED") < 0) + if (Util_TableSetReal(handle_gt23_bound ,gt23_bound_speed, "SPEED") < 0) CCTK_WARN(-1, "could not set SPEED value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt32_bound, - "ML_BSSN::gt32", "Radiation"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt23_bound, + "ML_BSSN::gt23", "Radiation"); if (ierr < 0) - CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt32!"); + CCTK_WARN(-1, "Failed to register Radiation BC for ML_BSSN::gt23!"); } @@ -1181,35 +1181,35 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(At21_bound, "scalar")) + if (CCTK_EQUALS(At12_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_At21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At21_bound ,At21_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_At12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At12_bound ,At12_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At21_bound, - "ML_BSSN::At21", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At12_bound, + "ML_BSSN::At12", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At21!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At12!"); } - if (CCTK_EQUALS(At31_bound, "scalar")) + if (CCTK_EQUALS(At13_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_At31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At31_bound ,At31_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_At13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At13_bound ,At13_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At31_bound, - "ML_BSSN::At31", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At13_bound, + "ML_BSSN::At13", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At31!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At13!"); } @@ -1229,19 +1229,19 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(At32_bound, "scalar")) + if (CCTK_EQUALS(At23_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_At32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_At32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_At32_bound ,At32_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_At23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_At23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_At23_bound ,At23_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At32_bound, - "ML_BSSN::At32", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_At23_bound, + "ML_BSSN::At23", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At32!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::At23!"); } @@ -1421,35 +1421,35 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(gt21_bound, "scalar")) + if (CCTK_EQUALS(gt12_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_gt21_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt21_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt21_bound ,gt21_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_gt12_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt12_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt12_bound ,gt12_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt21_bound, - "ML_BSSN::gt21", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt12_bound, + "ML_BSSN::gt12", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt21!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt12!"); } - if (CCTK_EQUALS(gt31_bound, "scalar")) + if (CCTK_EQUALS(gt13_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_gt31_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt31_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt31_bound ,gt31_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_gt13_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt13_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt13_bound ,gt13_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt31_bound, - "ML_BSSN::gt31", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt13_bound, + "ML_BSSN::gt13", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt31!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt13!"); } @@ -1469,19 +1469,19 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) } - if (CCTK_EQUALS(gt32_bound, "scalar")) + if (CCTK_EQUALS(gt23_bound, "scalar")) { /* apply scalar boundary condition */ - CCTK_INT handle_gt32_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); - if (handle_gt32_bound < 0) CCTK_WARN(-1, "could not create table!"); - if (Util_TableSetReal(handle_gt32_bound ,gt32_bound_scalar, "SCALAR") < 0) + CCTK_INT handle_gt23_bound = Util_TableCreate(UTIL_TABLE_FLAGS_CASE_INSENSITIVE); + if (handle_gt23_bound < 0) CCTK_WARN(-1, "could not create table!"); + if (Util_TableSetReal(handle_gt23_bound ,gt23_bound_scalar, "SCALAR") < 0) CCTK_WARN(-1, "could not set SCALAR value in table!"); - ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt32_bound, - "ML_BSSN::gt32", "scalar"); + ierr = Boundary_SelectVarForBC(cctkGH, CCTK_ALL_FACES, 1, handle_gt23_bound, + "ML_BSSN::gt23", "scalar"); if (ierr < 0) - CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt32!"); + CCTK_WARN(-1, "Error in registering Scalar BC for ML_BSSN::gt23!"); } @@ -1620,25 +1620,25 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) #$bound$#ML_BSSN::At11_bound_limit = 0.0 #$bound$#ML_BSSN::At11_bound_scalar = 0.0 -#$bound$#ML_BSSN::At21_bound = "skip" -#$bound$#ML_BSSN::At21_bound_speed = 1.0 -#$bound$#ML_BSSN::At21_bound_limit = 0.0 -#$bound$#ML_BSSN::At21_bound_scalar = 0.0 +#$bound$#ML_BSSN::At12_bound = "skip" +#$bound$#ML_BSSN::At12_bound_speed = 1.0 +#$bound$#ML_BSSN::At12_bound_limit = 0.0 +#$bound$#ML_BSSN::At12_bound_scalar = 0.0 -#$bound$#ML_BSSN::At31_bound = "skip" -#$bound$#ML_BSSN::At31_bound_speed = 1.0 -#$bound$#ML_BSSN::At31_bound_limit = 0.0 -#$bound$#ML_BSSN::At31_bound_scalar = 0.0 +#$bound$#ML_BSSN::At13_bound = "skip" +#$bound$#ML_BSSN::At13_bound_speed = 1.0 +#$bound$#ML_BSSN::At13_bound_limit = 0.0 +#$bound$#ML_BSSN::At13_bound_scalar = 0.0 #$bound$#ML_BSSN::At22_bound = "skip" #$bound$#ML_BSSN::At22_bound_speed = 1.0 #$bound$#ML_BSSN::At22_bound_limit = 0.0 #$bound$#ML_BSSN::At22_bound_scalar = 0.0 -#$bound$#ML_BSSN::At32_bound = "skip" -#$bound$#ML_BSSN::At32_bound_speed = 1.0 -#$bound$#ML_BSSN::At32_bound_limit = 0.0 -#$bound$#ML_BSSN::At32_bound_scalar = 0.0 +#$bound$#ML_BSSN::At23_bound = "skip" +#$bound$#ML_BSSN::At23_bound_speed = 1.0 +#$bound$#ML_BSSN::At23_bound_limit = 0.0 +#$bound$#ML_BSSN::At23_bound_scalar = 0.0 #$bound$#ML_BSSN::At33_bound = "skip" #$bound$#ML_BSSN::At33_bound_speed = 1.0 @@ -1695,25 +1695,25 @@ void ML_BSSN_ApplyBoundConds(CCTK_ARGUMENTS) #$bound$#ML_BSSN::gt11_bound_limit = 0.0 #$bound$#ML_BSSN::gt11_bound_scalar = 0.0 -#$bound$#ML_BSSN::gt21_bound = "skip" -#$bound$#ML_BSSN::gt21_bound_speed = 1.0 -#$bound$#ML_BSSN::gt21_bound_limit = 0.0 -#$bound$#ML_BSSN::gt21_bound_scalar = 0.0 +#$bound$#ML_BSSN::gt12_bound = "skip" +#$bound$#ML_BSSN::gt12_bound_speed = 1.0 +#$bound$#ML_BSSN::gt12_bound_limit = 0.0 +#$bound$#ML_BSSN::gt12_bound_scalar = 0.0 -#$bound$#ML_BSSN::gt31_bound = "skip" -#$bound$#ML_BSSN::gt31_bound_speed = 1.0 -#$bound$#ML_BSSN::gt31_bound_limit = 0.0 -#$bound$#ML_BSSN::gt31_bound_scalar = 0.0 +#$bound$#ML_BSSN::gt13_bound = "skip" +#$bound$#ML_BSSN::gt13_bound_speed = 1.0 +#$bound$#ML_BSSN::gt13_bound_limit = 0.0 +#$bound$#ML_BSSN::gt13_bound_scalar = 0.0 #$bound$#ML_BSSN::gt22_bound = "skip" #$bound$#ML_BSSN::gt22_bound_speed = 1.0 #$bound$#ML_BSSN::gt22_bound_limit = 0.0 #$bound$#ML_BSSN::gt22_bound_scalar = 0.0 -#$bound$#ML_BSSN::gt32_bound = "skip" -#$bound$#ML_BSSN::gt32_bound_speed = 1.0 -#$bound$#ML_BSSN::gt32_bound_limit = 0.0 -#$bound$#ML_BSSN::gt32_bound_scalar = 0.0 +#$bound$#ML_BSSN::gt23_bound = "skip" +#$bound$#ML_BSSN::gt23_bound_speed = 1.0 +#$bound$#ML_BSSN::gt23_bound_limit = 0.0 +#$bound$#ML_BSSN::gt23_bound_scalar = 0.0 #$bound$#ML_BSSN::gt33_bound = "skip" #$bound$#ML_BSSN::gt33_bound_speed = 1.0 diff --git a/ML_BSSN/src/ML_BSSN_Minkowski.c b/ML_BSSN/src/ML_BSSN_Minkowski.c index 698abe5..37dd6ad 100644 --- a/ML_BSSN/src/ML_BSSN_Minkowski.c +++ b/ML_BSSN/src/ML_BSSN_Minkowski.c @@ -97,11 +97,11 @@ void ML_BSSN_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL /* Declare local copies of grid functions */ CCTK_REAL alphaL = INITVALUE; - CCTK_REAL At11L = INITVALUE, At21L = INITVALUE, At22L = INITVALUE, At31L = INITVALUE, At32L = INITVALUE, At33L = INITVALUE; + CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta2L = INITVALUE, beta3L = INITVALUE; CCTK_REAL dtalphaL = INITVALUE; CCTK_REAL dtbeta1L = INITVALUE, dtbeta2L = INITVALUE, dtbeta3L = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; CCTK_REAL phiL = INITVALUE; CCTK_REAL trKL = INITVALUE; CCTK_REAL Xt1L = INITVALUE, Xt2L = INITVALUE, Xt3L = INITVALUE; @@ -124,13 +124,13 @@ void ML_BSSN_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL gt11L = 1; - gt21L = 0; + gt12L = 0; - gt31L = 0; + gt13L = 0; gt22L = 1; - gt32L = 0; + gt23L = 0; gt33L = 1; @@ -138,13 +138,13 @@ void ML_BSSN_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL At11L = 0; - At21L = 0; + At12L = 0; - At31L = 0; + At13L = 0; At22L = 0; - At32L = 0; + At23L = 0; At33L = 0; @@ -174,10 +174,10 @@ void ML_BSSN_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL /* Copy local copies back to grid functions */ alpha[index] = alphaL; At11[index] = At11L; - At21[index] = At21L; + At12[index] = At12L; + At13[index] = At13L; At22[index] = At22L; - At31[index] = At31L; - At32[index] = At32L; + At23[index] = At23L; At33[index] = At33L; beta1[index] = beta1L; beta2[index] = beta2L; @@ -187,10 +187,10 @@ void ML_BSSN_Minkowski_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL dtbeta2[index] = dtbeta2L; dtbeta3[index] = dtbeta3L; gt11[index] = gt11L; - gt21[index] = gt21L; + gt12[index] = gt12L; + gt13[index] = gt13L; gt22[index] = gt22L; - gt31[index] = gt31L; - gt32[index] = gt32L; + gt23[index] = gt23L; gt33[index] = gt33L; phi[index] = phiL; trK[index] = trKL; diff --git a/ML_BSSN/src/ML_BSSN_RHS.c b/ML_BSSN/src/ML_BSSN_RHS.c index a11173b..e97f2b5 100644 --- a/ML_BSSN/src/ML_BSSN_RHS.c +++ b/ML_BSSN/src/ML_BSSN_RHS.c @@ -96,50 +96,50 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal /* Declare shorthands */ CCTK_REAL Atm11 = INITVALUE, Atm12 = INITVALUE, Atm13 = INITVALUE, Atm21 = INITVALUE, Atm22 = INITVALUE, Atm23 = INITVALUE; CCTK_REAL Atm31 = INITVALUE, Atm32 = INITVALUE, Atm33 = INITVALUE; - CCTK_REAL Atu11 = INITVALUE, Atu12 = INITVALUE, Atu13 = INITVALUE, Atu22 = INITVALUE, Atu23 = INITVALUE, Atu33 = INITVALUE; + CCTK_REAL Atu11 = INITVALUE, Atu21 = INITVALUE, Atu22 = INITVALUE, Atu31 = INITVALUE, Atu32 = INITVALUE, Atu33 = INITVALUE; CCTK_REAL ddetg1 = INITVALUE, ddetg2 = INITVALUE, ddetg3 = INITVALUE; CCTK_REAL ddetgt1 = INITVALUE, ddetgt2 = INITVALUE, ddetgt3 = INITVALUE; - CCTK_REAL ddgtu1111 = INITVALUE, ddgtu1121 = INITVALUE, ddgtu1131 = INITVALUE, ddgtu1211 = INITVALUE, ddgtu1221 = INITVALUE, ddgtu1222 = INITVALUE; - CCTK_REAL ddgtu1231 = INITVALUE, ddgtu1232 = INITVALUE, ddgtu1311 = INITVALUE, ddgtu1321 = INITVALUE, ddgtu1331 = INITVALUE, ddgtu1332 = INITVALUE; - CCTK_REAL ddgtu1333 = INITVALUE, ddgtu2221 = INITVALUE, ddgtu2222 = INITVALUE, ddgtu2232 = INITVALUE, ddgtu2321 = INITVALUE, ddgtu2322 = INITVALUE; - CCTK_REAL ddgtu2331 = INITVALUE, ddgtu2332 = INITVALUE, ddgtu2333 = INITVALUE, ddgtu3331 = INITVALUE, ddgtu3332 = INITVALUE, ddgtu3333 = INITVALUE; + CCTK_REAL ddgtu1111 = INITVALUE, ddgtu1112 = INITVALUE, ddgtu1113 = INITVALUE, ddgtu2111 = INITVALUE, ddgtu2112 = INITVALUE, ddgtu2113 = INITVALUE; + CCTK_REAL ddgtu2122 = INITVALUE, ddgtu2123 = INITVALUE, ddgtu2212 = INITVALUE, ddgtu2222 = INITVALUE, ddgtu2223 = INITVALUE, ddgtu3111 = INITVALUE; + CCTK_REAL ddgtu3112 = INITVALUE, ddgtu3113 = INITVALUE, ddgtu3123 = INITVALUE, ddgtu3133 = INITVALUE, ddgtu3212 = INITVALUE, ddgtu3213 = INITVALUE; + CCTK_REAL ddgtu3222 = INITVALUE, ddgtu3223 = INITVALUE, ddgtu3233 = INITVALUE, ddgtu3313 = INITVALUE, ddgtu3323 = INITVALUE, ddgtu3333 = INITVALUE; CCTK_REAL detg = INITVALUE; CCTK_REAL detgt = INITVALUE; - CCTK_REAL dgtu111 = INITVALUE, dgtu112 = INITVALUE, dgtu113 = INITVALUE, dgtu121 = INITVALUE, dgtu122 = INITVALUE, dgtu123 = INITVALUE; - CCTK_REAL dgtu131 = INITVALUE, dgtu132 = INITVALUE, dgtu133 = INITVALUE, dgtu221 = INITVALUE, dgtu222 = INITVALUE, dgtu223 = INITVALUE; - CCTK_REAL dgtu231 = INITVALUE, dgtu232 = INITVALUE, dgtu233 = INITVALUE, dgtu331 = INITVALUE, dgtu332 = INITVALUE, dgtu333 = INITVALUE; + CCTK_REAL dgtu111 = INITVALUE, dgtu112 = INITVALUE, dgtu113 = INITVALUE, dgtu211 = INITVALUE, dgtu212 = INITVALUE, dgtu213 = INITVALUE; + CCTK_REAL dgtu221 = INITVALUE, dgtu222 = INITVALUE, dgtu223 = INITVALUE, dgtu311 = INITVALUE, dgtu312 = INITVALUE, dgtu313 = INITVALUE; + CCTK_REAL dgtu321 = INITVALUE, dgtu322 = INITVALUE, dgtu323 = INITVALUE, dgtu331 = INITVALUE, dgtu332 = INITVALUE, dgtu333 = INITVALUE; CCTK_REAL e4phi = INITVALUE; CCTK_REAL em4phi = INITVALUE; CCTK_REAL g11 = INITVALUE; - CCTK_REAL G111 = INITVALUE, G121 = INITVALUE, G122 = INITVALUE, G131 = INITVALUE, G132 = INITVALUE, G133 = INITVALUE; - CCTK_REAL g21 = INITVALUE; - CCTK_REAL G211 = INITVALUE; + CCTK_REAL G111 = INITVALUE, G112 = INITVALUE, G113 = INITVALUE; + CCTK_REAL g12 = INITVALUE; + CCTK_REAL G122 = INITVALUE, G123 = INITVALUE; + CCTK_REAL g13 = INITVALUE; + CCTK_REAL G133 = INITVALUE, G211 = INITVALUE, G212 = INITVALUE, G213 = INITVALUE; CCTK_REAL g22 = INITVALUE; - CCTK_REAL G221 = INITVALUE, G222 = INITVALUE, G231 = INITVALUE, G232 = INITVALUE, G233 = INITVALUE; - CCTK_REAL g31 = INITVALUE; - CCTK_REAL G311 = INITVALUE; - CCTK_REAL g32 = INITVALUE; - CCTK_REAL G321 = INITVALUE, G322 = INITVALUE; + CCTK_REAL G222 = INITVALUE, G223 = INITVALUE; + CCTK_REAL g23 = INITVALUE; + CCTK_REAL G233 = INITVALUE, G311 = INITVALUE, G312 = INITVALUE, G313 = INITVALUE, G322 = INITVALUE, G323 = INITVALUE; CCTK_REAL g33 = INITVALUE; - CCTK_REAL G331 = INITVALUE, G332 = INITVALUE, G333 = INITVALUE; - CCTK_REAL Gt111 = INITVALUE, Gt121 = INITVALUE, Gt122 = INITVALUE, Gt131 = INITVALUE, Gt132 = INITVALUE, Gt133 = INITVALUE; - CCTK_REAL Gt211 = INITVALUE, Gt221 = INITVALUE, Gt222 = INITVALUE, Gt231 = INITVALUE, Gt232 = INITVALUE, Gt233 = INITVALUE; - CCTK_REAL Gt311 = INITVALUE, Gt321 = INITVALUE, Gt322 = INITVALUE, Gt331 = INITVALUE, Gt332 = INITVALUE, Gt333 = INITVALUE; - CCTK_REAL gtu11 = INITVALUE, gtu12 = INITVALUE, gtu13 = INITVALUE, gtu22 = INITVALUE, gtu23 = INITVALUE, gtu33 = INITVALUE; - CCTK_REAL gu11 = INITVALUE, gu12 = INITVALUE, gu13 = INITVALUE, gu22 = INITVALUE, gu23 = INITVALUE, gu33 = INITVALUE; - CCTK_REAL R11 = INITVALUE, R21 = INITVALUE, R22 = INITVALUE, R31 = INITVALUE, R32 = INITVALUE, R33 = INITVALUE; - CCTK_REAL Rphi11 = INITVALUE, Rphi21 = INITVALUE, Rphi22 = INITVALUE, Rphi31 = INITVALUE, Rphi32 = INITVALUE, Rphi33 = INITVALUE; - CCTK_REAL Rt11 = INITVALUE, Rt21 = INITVALUE, Rt22 = INITVALUE, Rt31 = INITVALUE, Rt32 = INITVALUE, Rt33 = INITVALUE; + CCTK_REAL G333 = INITVALUE; + CCTK_REAL Gt111 = INITVALUE, Gt112 = INITVALUE, Gt113 = INITVALUE, Gt122 = INITVALUE, Gt123 = INITVALUE, Gt133 = INITVALUE; + CCTK_REAL Gt211 = INITVALUE, Gt212 = INITVALUE, Gt213 = INITVALUE, Gt222 = INITVALUE, Gt223 = INITVALUE, Gt233 = INITVALUE; + CCTK_REAL Gt311 = INITVALUE, Gt312 = INITVALUE, Gt313 = INITVALUE, Gt322 = INITVALUE, Gt323 = INITVALUE, Gt333 = INITVALUE; + CCTK_REAL gtu11 = INITVALUE, gtu21 = INITVALUE, gtu22 = INITVALUE, gtu31 = INITVALUE, gtu32 = INITVALUE, gtu33 = INITVALUE; + CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE; + CCTK_REAL R11 = INITVALUE, R12 = INITVALUE, R13 = INITVALUE, R22 = INITVALUE, R23 = INITVALUE, R33 = INITVALUE; + CCTK_REAL Rphi11 = INITVALUE, Rphi12 = INITVALUE, Rphi13 = INITVALUE, Rphi22 = INITVALUE, Rphi23 = INITVALUE, Rphi33 = INITVALUE; + CCTK_REAL Rt11 = INITVALUE, Rt12 = INITVALUE, Rt13 = INITVALUE, Rt22 = INITVALUE, Rt23 = INITVALUE, Rt33 = INITVALUE; /* Declare local copies of grid functions */ CCTK_REAL alphaL = INITVALUE, alpharhsL = INITVALUE; - CCTK_REAL At11L = INITVALUE, At11rhsL = INITVALUE, At21L = INITVALUE, At21rhsL = INITVALUE, At22L = INITVALUE, At22rhsL = INITVALUE; - CCTK_REAL At31L = INITVALUE, At31rhsL = INITVALUE, At32L = INITVALUE, At32rhsL = INITVALUE, At33L = INITVALUE, At33rhsL = INITVALUE; + CCTK_REAL At11L = INITVALUE, At11rhsL = INITVALUE, At12L = INITVALUE, At12rhsL = INITVALUE, At13L = INITVALUE, At13rhsL = INITVALUE; + CCTK_REAL At22L = INITVALUE, At22rhsL = INITVALUE, At23L = INITVALUE, At23rhsL = INITVALUE, At33L = INITVALUE, At33rhsL = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta1rhsL = INITVALUE, beta2L = INITVALUE, beta2rhsL = INITVALUE, beta3L = INITVALUE, beta3rhsL = INITVALUE; CCTK_REAL dtalphaL = INITVALUE, dtalpharhsL = INITVALUE; CCTK_REAL dtbeta1L = INITVALUE, dtbeta1rhsL = INITVALUE, dtbeta2L = INITVALUE, dtbeta2rhsL = INITVALUE, dtbeta3L = INITVALUE, dtbeta3rhsL = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt11rhsL = INITVALUE, gt21L = INITVALUE, gt21rhsL = INITVALUE, gt22L = INITVALUE, gt22rhsL = INITVALUE; - CCTK_REAL gt31L = INITVALUE, gt31rhsL = INITVALUE, gt32L = INITVALUE, gt32rhsL = INITVALUE, gt33L = INITVALUE, gt33rhsL = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt11rhsL = INITVALUE, gt12L = INITVALUE, gt12rhsL = INITVALUE, gt13L = INITVALUE, gt13rhsL = INITVALUE; + CCTK_REAL gt22L = INITVALUE, gt22rhsL = INITVALUE, gt23L = INITVALUE, gt23rhsL = INITVALUE, gt33L = INITVALUE, gt33rhsL = INITVALUE; CCTK_REAL phiL = INITVALUE, phirhsL = INITVALUE; CCTK_REAL trKL = INITVALUE, trKrhsL = INITVALUE; CCTK_REAL Xt1L = INITVALUE, Xt1rhsL = INITVALUE, Xt2L = INITVALUE, Xt2rhsL = INITVALUE, Xt3L = INITVALUE, Xt3rhsL = INITVALUE; @@ -161,18 +161,18 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal CCTK_REAL PDstandard4th1At11 = INITVALUE; CCTK_REAL PDstandard4th2At11 = INITVALUE; CCTK_REAL PDstandard4th3At11 = INITVALUE; - CCTK_REAL PDstandard4th1At21 = INITVALUE; - CCTK_REAL PDstandard4th2At21 = INITVALUE; - CCTK_REAL PDstandard4th3At21 = INITVALUE; + CCTK_REAL PDstandard4th1At12 = INITVALUE; + CCTK_REAL PDstandard4th2At12 = INITVALUE; + CCTK_REAL PDstandard4th3At12 = INITVALUE; + CCTK_REAL PDstandard4th1At13 = INITVALUE; + CCTK_REAL PDstandard4th2At13 = INITVALUE; + CCTK_REAL PDstandard4th3At13 = INITVALUE; CCTK_REAL PDstandard4th1At22 = INITVALUE; CCTK_REAL PDstandard4th2At22 = INITVALUE; CCTK_REAL PDstandard4th3At22 = INITVALUE; - CCTK_REAL PDstandard4th1At31 = INITVALUE; - CCTK_REAL PDstandard4th2At31 = INITVALUE; - CCTK_REAL PDstandard4th3At31 = INITVALUE; - CCTK_REAL PDstandard4th1At32 = INITVALUE; - CCTK_REAL PDstandard4th2At32 = INITVALUE; - CCTK_REAL PDstandard4th3At32 = INITVALUE; + CCTK_REAL PDstandard4th1At23 = INITVALUE; + CCTK_REAL PDstandard4th2At23 = INITVALUE; + CCTK_REAL PDstandard4th3At23 = INITVALUE; CCTK_REAL PDstandard4th1At33 = INITVALUE; CCTK_REAL PDstandard4th2At33 = INITVALUE; CCTK_REAL PDstandard4th3At33 = INITVALUE; @@ -224,18 +224,30 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal CCTK_REAL PDstandard4th23gt11 = INITVALUE; CCTK_REAL PDstandard4th31gt11 = INITVALUE; CCTK_REAL PDstandard4th32gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt21 = INITVALUE; - CCTK_REAL PDstandard4th2gt21 = INITVALUE; - CCTK_REAL PDstandard4th3gt21 = INITVALUE; - CCTK_REAL PDstandard4th11gt21 = INITVALUE; - CCTK_REAL PDstandard4th22gt21 = INITVALUE; - CCTK_REAL PDstandard4th33gt21 = INITVALUE; - CCTK_REAL PDstandard4th12gt21 = INITVALUE; - CCTK_REAL PDstandard4th13gt21 = INITVALUE; - CCTK_REAL PDstandard4th21gt21 = INITVALUE; - CCTK_REAL PDstandard4th23gt21 = INITVALUE; - CCTK_REAL PDstandard4th31gt21 = INITVALUE; - CCTK_REAL PDstandard4th32gt21 = INITVALUE; + CCTK_REAL PDstandard4th1gt12 = INITVALUE; + CCTK_REAL PDstandard4th2gt12 = INITVALUE; + CCTK_REAL PDstandard4th3gt12 = INITVALUE; + CCTK_REAL PDstandard4th11gt12 = INITVALUE; + CCTK_REAL PDstandard4th22gt12 = INITVALUE; + CCTK_REAL PDstandard4th33gt12 = INITVALUE; + CCTK_REAL PDstandard4th12gt12 = INITVALUE; + CCTK_REAL PDstandard4th13gt12 = INITVALUE; + CCTK_REAL PDstandard4th21gt12 = INITVALUE; + CCTK_REAL PDstandard4th23gt12 = INITVALUE; + CCTK_REAL PDstandard4th31gt12 = INITVALUE; + CCTK_REAL PDstandard4th32gt12 = INITVALUE; + CCTK_REAL PDstandard4th1gt13 = INITVALUE; + CCTK_REAL PDstandard4th2gt13 = INITVALUE; + CCTK_REAL PDstandard4th3gt13 = INITVALUE; + CCTK_REAL PDstandard4th11gt13 = INITVALUE; + CCTK_REAL PDstandard4th22gt13 = INITVALUE; + CCTK_REAL PDstandard4th33gt13 = INITVALUE; + CCTK_REAL PDstandard4th12gt13 = INITVALUE; + CCTK_REAL PDstandard4th13gt13 = INITVALUE; + CCTK_REAL PDstandard4th21gt13 = INITVALUE; + CCTK_REAL PDstandard4th23gt13 = INITVALUE; + CCTK_REAL PDstandard4th31gt13 = INITVALUE; + CCTK_REAL PDstandard4th32gt13 = INITVALUE; CCTK_REAL PDstandard4th1gt22 = INITVALUE; CCTK_REAL PDstandard4th2gt22 = INITVALUE; CCTK_REAL PDstandard4th3gt22 = INITVALUE; @@ -248,30 +260,18 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal CCTK_REAL PDstandard4th23gt22 = INITVALUE; CCTK_REAL PDstandard4th31gt22 = INITVALUE; CCTK_REAL PDstandard4th32gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt31 = INITVALUE; - CCTK_REAL PDstandard4th2gt31 = INITVALUE; - CCTK_REAL PDstandard4th3gt31 = INITVALUE; - CCTK_REAL PDstandard4th11gt31 = INITVALUE; - CCTK_REAL PDstandard4th22gt31 = INITVALUE; - CCTK_REAL PDstandard4th33gt31 = INITVALUE; - CCTK_REAL PDstandard4th12gt31 = INITVALUE; - CCTK_REAL PDstandard4th13gt31 = INITVALUE; - CCTK_REAL PDstandard4th21gt31 = INITVALUE; - CCTK_REAL PDstandard4th23gt31 = INITVALUE; - CCTK_REAL PDstandard4th31gt31 = INITVALUE; - CCTK_REAL PDstandard4th32gt31 = INITVALUE; - CCTK_REAL PDstandard4th1gt32 = INITVALUE; - CCTK_REAL PDstandard4th2gt32 = INITVALUE; - CCTK_REAL PDstandard4th3gt32 = INITVALUE; - CCTK_REAL PDstandard4th11gt32 = INITVALUE; - CCTK_REAL PDstandard4th22gt32 = INITVALUE; - CCTK_REAL PDstandard4th33gt32 = INITVALUE; - CCTK_REAL PDstandard4th12gt32 = INITVALUE; - CCTK_REAL PDstandard4th13gt32 = INITVALUE; - CCTK_REAL PDstandard4th21gt32 = INITVALUE; - CCTK_REAL PDstandard4th23gt32 = INITVALUE; - CCTK_REAL PDstandard4th31gt32 = INITVALUE; - CCTK_REAL PDstandard4th32gt32 = INITVALUE; + CCTK_REAL PDstandard4th1gt23 = INITVALUE; + CCTK_REAL PDstandard4th2gt23 = INITVALUE; + CCTK_REAL PDstandard4th3gt23 = INITVALUE; + CCTK_REAL PDstandard4th11gt23 = INITVALUE; + CCTK_REAL PDstandard4th22gt23 = INITVALUE; + CCTK_REAL PDstandard4th33gt23 = INITVALUE; + CCTK_REAL PDstandard4th12gt23 = INITVALUE; + CCTK_REAL PDstandard4th13gt23 = INITVALUE; + CCTK_REAL PDstandard4th21gt23 = INITVALUE; + CCTK_REAL PDstandard4th23gt23 = INITVALUE; + CCTK_REAL PDstandard4th31gt23 = INITVALUE; + CCTK_REAL PDstandard4th32gt23 = INITVALUE; CCTK_REAL PDstandard4th1gt33 = INITVALUE; CCTK_REAL PDstandard4th2gt33 = INITVALUE; CCTK_REAL PDstandard4th3gt33 = INITVALUE; @@ -312,10 +312,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal /* Assign local copies of grid functions */ alphaL = alpha[index]; At11L = At11[index]; - At21L = At21[index]; + At12L = At12[index]; + At13L = At13[index]; At22L = At22[index]; - At31L = At31[index]; - At32L = At32[index]; + At23L = At23[index]; At33L = At33[index]; beta1L = beta1[index]; beta2L = beta2[index]; @@ -325,10 +325,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal dtbeta2L = dtbeta2[index]; dtbeta3L = dtbeta3[index]; gt11L = gt11[index]; - gt21L = gt21[index]; + gt12L = gt12[index]; + gt13L = gt13[index]; gt22L = gt22[index]; - gt31L = gt31[index]; - gt32L = gt32[index]; + gt23L = gt23[index]; gt33L = gt33[index]; phiL = phi[index]; trKL = trK[index]; @@ -357,18 +357,18 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal PDstandard4th1At11 = PDstandard4th1(At11, i, j, k); PDstandard4th2At11 = PDstandard4th2(At11, i, j, k); PDstandard4th3At11 = PDstandard4th3(At11, i, j, k); - PDstandard4th1At21 = PDstandard4th1(At21, i, j, k); - PDstandard4th2At21 = PDstandard4th2(At21, i, j, k); - PDstandard4th3At21 = PDstandard4th3(At21, i, j, k); + PDstandard4th1At12 = PDstandard4th1(At12, i, j, k); + PDstandard4th2At12 = PDstandard4th2(At12, i, j, k); + PDstandard4th3At12 = PDstandard4th3(At12, i, j, k); + PDstandard4th1At13 = PDstandard4th1(At13, i, j, k); + PDstandard4th2At13 = PDstandard4th2(At13, i, j, k); + PDstandard4th3At13 = PDstandard4th3(At13, i, j, k); PDstandard4th1At22 = PDstandard4th1(At22, i, j, k); PDstandard4th2At22 = PDstandard4th2(At22, i, j, k); PDstandard4th3At22 = PDstandard4th3(At22, i, j, k); - PDstandard4th1At31 = PDstandard4th1(At31, i, j, k); - PDstandard4th2At31 = PDstandard4th2(At31, i, j, k); - PDstandard4th3At31 = PDstandard4th3(At31, i, j, k); - PDstandard4th1At32 = PDstandard4th1(At32, i, j, k); - PDstandard4th2At32 = PDstandard4th2(At32, i, j, k); - PDstandard4th3At32 = PDstandard4th3(At32, i, j, k); + PDstandard4th1At23 = PDstandard4th1(At23, i, j, k); + PDstandard4th2At23 = PDstandard4th2(At23, i, j, k); + PDstandard4th3At23 = PDstandard4th3(At23, i, j, k); PDstandard4th1At33 = PDstandard4th1(At33, i, j, k); PDstandard4th2At33 = PDstandard4th2(At33, i, j, k); PDstandard4th3At33 = PDstandard4th3(At33, i, j, k); @@ -408,15 +408,24 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal PDstandard4th12gt11 = PDstandard4th12(gt11, i, j, k); PDstandard4th13gt11 = PDstandard4th13(gt11, i, j, k); PDstandard4th23gt11 = PDstandard4th23(gt11, i, j, k); - PDstandard4th1gt21 = PDstandard4th1(gt21, i, j, k); - PDstandard4th2gt21 = PDstandard4th2(gt21, i, j, k); - PDstandard4th3gt21 = PDstandard4th3(gt21, i, j, k); - PDstandard4th11gt21 = PDstandard4th11(gt21, i, j, k); - PDstandard4th22gt21 = PDstandard4th22(gt21, i, j, k); - PDstandard4th33gt21 = PDstandard4th33(gt21, i, j, k); - PDstandard4th12gt21 = PDstandard4th12(gt21, i, j, k); - PDstandard4th13gt21 = PDstandard4th13(gt21, i, j, k); - PDstandard4th23gt21 = PDstandard4th23(gt21, i, j, k); + PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); + PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); + PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); + PDstandard4th11gt12 = PDstandard4th11(gt12, i, j, k); + PDstandard4th22gt12 = PDstandard4th22(gt12, i, j, k); + PDstandard4th33gt12 = PDstandard4th33(gt12, i, j, k); + PDstandard4th12gt12 = PDstandard4th12(gt12, i, j, k); + PDstandard4th13gt12 = PDstandard4th13(gt12, i, j, k); + PDstandard4th23gt12 = PDstandard4th23(gt12, i, j, k); + PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); + PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); + PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); + PDstandard4th11gt13 = PDstandard4th11(gt13, i, j, k); + PDstandard4th22gt13 = PDstandard4th22(gt13, i, j, k); + PDstandard4th33gt13 = PDstandard4th33(gt13, i, j, k); + PDstandard4th12gt13 = PDstandard4th12(gt13, i, j, k); + PDstandard4th13gt13 = PDstandard4th13(gt13, i, j, k); + PDstandard4th23gt13 = PDstandard4th23(gt13, i, j, k); PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); @@ -426,24 +435,15 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal PDstandard4th12gt22 = PDstandard4th12(gt22, i, j, k); PDstandard4th13gt22 = PDstandard4th13(gt22, i, j, k); PDstandard4th23gt22 = PDstandard4th23(gt22, i, j, k); - PDstandard4th1gt31 = PDstandard4th1(gt31, i, j, k); - PDstandard4th2gt31 = PDstandard4th2(gt31, i, j, k); - PDstandard4th3gt31 = PDstandard4th3(gt31, i, j, k); - PDstandard4th11gt31 = PDstandard4th11(gt31, i, j, k); - PDstandard4th22gt31 = PDstandard4th22(gt31, i, j, k); - PDstandard4th33gt31 = PDstandard4th33(gt31, i, j, k); - PDstandard4th12gt31 = PDstandard4th12(gt31, i, j, k); - PDstandard4th13gt31 = PDstandard4th13(gt31, i, j, k); - PDstandard4th23gt31 = PDstandard4th23(gt31, i, j, k); - PDstandard4th1gt32 = PDstandard4th1(gt32, i, j, k); - PDstandard4th2gt32 = PDstandard4th2(gt32, i, j, k); - PDstandard4th3gt32 = PDstandard4th3(gt32, i, j, k); - PDstandard4th11gt32 = PDstandard4th11(gt32, i, j, k); - PDstandard4th22gt32 = PDstandard4th22(gt32, i, j, k); - PDstandard4th33gt32 = PDstandard4th33(gt32, i, j, k); - PDstandard4th12gt32 = PDstandard4th12(gt32, i, j, k); - PDstandard4th13gt32 = PDstandard4th13(gt32, i, j, k); - PDstandard4th23gt32 = PDstandard4th23(gt32, i, j, k); + PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); + PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); + PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); + PDstandard4th11gt23 = PDstandard4th11(gt23, i, j, k); + PDstandard4th22gt23 = PDstandard4th22(gt23, i, j, k); + PDstandard4th33gt23 = PDstandard4th33(gt23, i, j, k); + PDstandard4th12gt23 = PDstandard4th12(gt23, i, j, k); + PDstandard4th13gt23 = PDstandard4th13(gt23, i, j, k); + PDstandard4th23gt23 = PDstandard4th23(gt23, i, j, k); PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); @@ -486,700 +486,690 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal ddetgt3 = 0; - gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt32L)); + gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); - gtu12 = (gt31L*gt32L - gt21L*gt33L)*INV(detgt); + gtu21 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); - gtu13 = (-(gt22L*gt31L) + gt21L*gt32L)*INV(detgt); + gtu31 = (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt); - gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt31L)); + gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt13L)); - gtu23 = (gt21L*gt31L - gt11L*gt32L)*INV(detgt); + gtu32 = (gt12L*gt13L - gt11L*gt23L)*INV(detgt); - gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt21L)); + gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - dgtu111 = -2*(gtu11*gtu12*PDstandard4th1gt21 + gtu11*gtu13*PDstandard4th1gt31 + gtu12*gtu13*PDstandard4th1gt32) - - PDstandard4th1gt11*SQR(gtu11) - PDstandard4th1gt22*SQR(gtu12) - PDstandard4th1gt33*SQR(gtu13); + dgtu111 = -2*(gtu11*gtu21*PDstandard4th1gt12 + gtu11*gtu31*PDstandard4th1gt13 + gtu21*gtu31*PDstandard4th1gt23) - + PDstandard4th1gt11*SQR(gtu11) - PDstandard4th1gt22*SQR(gtu21) - PDstandard4th1gt33*SQR(gtu31); - dgtu121 = -(gtu11*gtu12*PDstandard4th1gt11) - gtu11*gtu22*PDstandard4th1gt21 - gtu12*gtu22*PDstandard4th1gt22 - - gtu12*gtu13*PDstandard4th1gt31 - gtu11*gtu23*PDstandard4th1gt31 - gtu13*gtu22*PDstandard4th1gt32 - - gtu12*gtu23*PDstandard4th1gt32 - gtu13*gtu23*PDstandard4th1gt33 - PDstandard4th1gt21*SQR(gtu12); + dgtu211 = -(gtu11*gtu21*PDstandard4th1gt11) - gtu11*gtu22*PDstandard4th1gt12 - gtu21*gtu31*PDstandard4th1gt13 - + gtu11*gtu32*PDstandard4th1gt13 - gtu21*gtu22*PDstandard4th1gt22 - gtu22*gtu31*PDstandard4th1gt23 - + gtu21*gtu32*PDstandard4th1gt23 - gtu31*gtu32*PDstandard4th1gt33 - PDstandard4th1gt12*SQR(gtu21); - dgtu131 = -(gtu11*gtu13*PDstandard4th1gt11) - gtu12*gtu13*PDstandard4th1gt21 - gtu11*gtu23*PDstandard4th1gt21 - - gtu12*gtu23*PDstandard4th1gt22 - gtu11*gtu33*PDstandard4th1gt31 - gtu13*gtu23*PDstandard4th1gt32 - - gtu12*gtu33*PDstandard4th1gt32 - gtu13*gtu33*PDstandard4th1gt33 - PDstandard4th1gt31*SQR(gtu13); - - dgtu221 = -2*(gtu12*gtu22*PDstandard4th1gt21 + gtu12*gtu23*PDstandard4th1gt31 + gtu22*gtu23*PDstandard4th1gt32) - - PDstandard4th1gt11*SQR(gtu12) - PDstandard4th1gt22*SQR(gtu22) - PDstandard4th1gt33*SQR(gtu23); - - dgtu231 = -(gtu12*gtu13*PDstandard4th1gt11) - gtu13*gtu22*PDstandard4th1gt21 - gtu12*gtu23*PDstandard4th1gt21 - - gtu22*gtu23*PDstandard4th1gt22 - gtu13*gtu23*PDstandard4th1gt31 - gtu12*gtu33*PDstandard4th1gt31 - - gtu22*gtu33*PDstandard4th1gt32 - gtu23*gtu33*PDstandard4th1gt33 - PDstandard4th1gt32*SQR(gtu23); - - dgtu331 = -2*(gtu13*gtu23*PDstandard4th1gt21 + gtu13*gtu33*PDstandard4th1gt31 + gtu23*gtu33*PDstandard4th1gt32) - - PDstandard4th1gt11*SQR(gtu13) - PDstandard4th1gt22*SQR(gtu23) - PDstandard4th1gt33*SQR(gtu33); - - dgtu112 = -2*(gtu11*gtu12*PDstandard4th2gt21 + gtu11*gtu13*PDstandard4th2gt31 + gtu12*gtu13*PDstandard4th2gt32) - - PDstandard4th2gt11*SQR(gtu11) - PDstandard4th2gt22*SQR(gtu12) - PDstandard4th2gt33*SQR(gtu13); - - dgtu122 = -(gtu11*gtu12*PDstandard4th2gt11) - gtu11*gtu22*PDstandard4th2gt21 - gtu12*gtu22*PDstandard4th2gt22 - - gtu12*gtu13*PDstandard4th2gt31 - gtu11*gtu23*PDstandard4th2gt31 - gtu13*gtu22*PDstandard4th2gt32 - - gtu12*gtu23*PDstandard4th2gt32 - gtu13*gtu23*PDstandard4th2gt33 - PDstandard4th2gt21*SQR(gtu12); - - dgtu132 = -(gtu11*gtu13*PDstandard4th2gt11) - gtu12*gtu13*PDstandard4th2gt21 - gtu11*gtu23*PDstandard4th2gt21 - - gtu12*gtu23*PDstandard4th2gt22 - gtu11*gtu33*PDstandard4th2gt31 - gtu13*gtu23*PDstandard4th2gt32 - - gtu12*gtu33*PDstandard4th2gt32 - gtu13*gtu33*PDstandard4th2gt33 - PDstandard4th2gt31*SQR(gtu13); - - dgtu222 = -2*(gtu12*gtu22*PDstandard4th2gt21 + gtu12*gtu23*PDstandard4th2gt31 + gtu22*gtu23*PDstandard4th2gt32) - - PDstandard4th2gt11*SQR(gtu12) - PDstandard4th2gt22*SQR(gtu22) - PDstandard4th2gt33*SQR(gtu23); - - dgtu232 = -(gtu12*gtu13*PDstandard4th2gt11) - gtu13*gtu22*PDstandard4th2gt21 - gtu12*gtu23*PDstandard4th2gt21 - - gtu22*gtu23*PDstandard4th2gt22 - gtu13*gtu23*PDstandard4th2gt31 - gtu12*gtu33*PDstandard4th2gt31 - - gtu22*gtu33*PDstandard4th2gt32 - gtu23*gtu33*PDstandard4th2gt33 - PDstandard4th2gt32*SQR(gtu23); - - dgtu332 = -2*(gtu13*gtu23*PDstandard4th2gt21 + gtu13*gtu33*PDstandard4th2gt31 + gtu23*gtu33*PDstandard4th2gt32) - - PDstandard4th2gt11*SQR(gtu13) - PDstandard4th2gt22*SQR(gtu23) - PDstandard4th2gt33*SQR(gtu33); - - dgtu113 = -2*(gtu11*gtu12*PDstandard4th3gt21 + gtu11*gtu13*PDstandard4th3gt31 + gtu12*gtu13*PDstandard4th3gt32) - - PDstandard4th3gt11*SQR(gtu11) - PDstandard4th3gt22*SQR(gtu12) - PDstandard4th3gt33*SQR(gtu13); - - dgtu123 = -(gtu11*gtu12*PDstandard4th3gt11) - gtu11*gtu22*PDstandard4th3gt21 - gtu12*gtu22*PDstandard4th3gt22 - - gtu12*gtu13*PDstandard4th3gt31 - gtu11*gtu23*PDstandard4th3gt31 - gtu13*gtu22*PDstandard4th3gt32 - - gtu12*gtu23*PDstandard4th3gt32 - gtu13*gtu23*PDstandard4th3gt33 - PDstandard4th3gt21*SQR(gtu12); - - dgtu133 = -(gtu11*gtu13*PDstandard4th3gt11) - gtu12*gtu13*PDstandard4th3gt21 - gtu11*gtu23*PDstandard4th3gt21 - - gtu12*gtu23*PDstandard4th3gt22 - gtu11*gtu33*PDstandard4th3gt31 - gtu13*gtu23*PDstandard4th3gt32 - - gtu12*gtu33*PDstandard4th3gt32 - gtu13*gtu33*PDstandard4th3gt33 - PDstandard4th3gt31*SQR(gtu13); - - dgtu223 = -2*(gtu12*gtu22*PDstandard4th3gt21 + gtu12*gtu23*PDstandard4th3gt31 + gtu22*gtu23*PDstandard4th3gt32) - - PDstandard4th3gt11*SQR(gtu12) - PDstandard4th3gt22*SQR(gtu22) - PDstandard4th3gt33*SQR(gtu23); - - dgtu233 = -(gtu12*gtu13*PDstandard4th3gt11) - gtu13*gtu22*PDstandard4th3gt21 - gtu12*gtu23*PDstandard4th3gt21 - - gtu22*gtu23*PDstandard4th3gt22 - gtu13*gtu23*PDstandard4th3gt31 - gtu12*gtu33*PDstandard4th3gt31 - - gtu22*gtu33*PDstandard4th3gt32 - gtu23*gtu33*PDstandard4th3gt33 - PDstandard4th3gt32*SQR(gtu23); - - dgtu333 = -2*(gtu13*gtu23*PDstandard4th3gt21 + gtu13*gtu33*PDstandard4th3gt31 + gtu23*gtu33*PDstandard4th3gt32) - - PDstandard4th3gt11*SQR(gtu13) - PDstandard4th3gt22*SQR(gtu23) - PDstandard4th3gt33*SQR(gtu33); - - ddgtu1111 = -2*(gtu11*gtu12*PDstandard4th11gt21 + gtu11*gtu13*PDstandard4th11gt31 + gtu12*gtu13*PDstandard4th11gt32 + - dgtu111*gtu11*PDstandard4th1gt11 + dgtu121*gtu11*PDstandard4th1gt21 + dgtu111*gtu12*PDstandard4th1gt21 + - dgtu121*gtu12*PDstandard4th1gt22 + dgtu131*gtu11*PDstandard4th1gt31 + dgtu111*gtu13*PDstandard4th1gt31 + - dgtu131*gtu12*PDstandard4th1gt32 + dgtu121*gtu13*PDstandard4th1gt32 + dgtu131*gtu13*PDstandard4th1gt33) - - PDstandard4th11gt11*SQR(gtu11) - PDstandard4th11gt22*SQR(gtu12) - PDstandard4th11gt33*SQR(gtu13); - - ddgtu1211 = -(gtu11*gtu12*PDstandard4th11gt11) - gtu11*gtu22*PDstandard4th11gt21 - gtu12*gtu22*PDstandard4th11gt22 - - gtu12*gtu13*PDstandard4th11gt31 - gtu11*gtu23*PDstandard4th11gt31 - gtu13*gtu22*PDstandard4th11gt32 - - gtu12*gtu23*PDstandard4th11gt32 - gtu13*gtu23*PDstandard4th11gt33 - dgtu121*gtu11*PDstandard4th1gt11 - - dgtu111*gtu12*PDstandard4th1gt11 - dgtu221*gtu11*PDstandard4th1gt21 - 2*dgtu121*gtu12*PDstandard4th1gt21 - - dgtu111*gtu22*PDstandard4th1gt21 - dgtu221*gtu12*PDstandard4th1gt22 - dgtu121*gtu22*PDstandard4th1gt22 - - dgtu231*gtu11*PDstandard4th1gt31 - dgtu131*gtu12*PDstandard4th1gt31 - dgtu121*gtu13*PDstandard4th1gt31 - - dgtu111*gtu23*PDstandard4th1gt31 - dgtu231*gtu12*PDstandard4th1gt32 - dgtu221*gtu13*PDstandard4th1gt32 - - dgtu131*gtu22*PDstandard4th1gt32 - dgtu121*gtu23*PDstandard4th1gt32 - dgtu231*gtu13*PDstandard4th1gt33 - - dgtu131*gtu23*PDstandard4th1gt33 - PDstandard4th11gt21*SQR(gtu12); - - ddgtu1311 = -(gtu11*gtu13*PDstandard4th11gt11) - gtu12*gtu13*PDstandard4th11gt21 - gtu11*gtu23*PDstandard4th11gt21 - - gtu12*gtu23*PDstandard4th11gt22 - gtu11*gtu33*PDstandard4th11gt31 - gtu13*gtu23*PDstandard4th11gt32 - - gtu12*gtu33*PDstandard4th11gt32 - gtu13*gtu33*PDstandard4th11gt33 - dgtu131*gtu11*PDstandard4th1gt11 - - dgtu111*gtu13*PDstandard4th1gt11 - dgtu231*gtu11*PDstandard4th1gt21 - dgtu131*gtu12*PDstandard4th1gt21 - - dgtu121*gtu13*PDstandard4th1gt21 - dgtu111*gtu23*PDstandard4th1gt21 - dgtu231*gtu12*PDstandard4th1gt22 - - dgtu121*gtu23*PDstandard4th1gt22 - dgtu331*gtu11*PDstandard4th1gt31 - 2*dgtu131*gtu13*PDstandard4th1gt31 - - dgtu111*gtu33*PDstandard4th1gt31 - dgtu331*gtu12*PDstandard4th1gt32 - dgtu231*gtu13*PDstandard4th1gt32 - - dgtu131*gtu23*PDstandard4th1gt32 - dgtu121*gtu33*PDstandard4th1gt32 - dgtu331*gtu13*PDstandard4th1gt33 - - dgtu131*gtu33*PDstandard4th1gt33 - PDstandard4th11gt31*SQR(gtu13); - - ddgtu1121 = -2*(gtu11*gtu12*PDstandard4th12gt21 + gtu11*gtu13*PDstandard4th12gt31 + gtu12*gtu13*PDstandard4th12gt32 + - dgtu112*gtu11*PDstandard4th1gt11 + dgtu122*gtu11*PDstandard4th1gt21 + dgtu112*gtu12*PDstandard4th1gt21 + - dgtu122*gtu12*PDstandard4th1gt22 + dgtu132*gtu11*PDstandard4th1gt31 + dgtu112*gtu13*PDstandard4th1gt31 + - dgtu132*gtu12*PDstandard4th1gt32 + dgtu122*gtu13*PDstandard4th1gt32 + dgtu132*gtu13*PDstandard4th1gt33) - - PDstandard4th12gt11*SQR(gtu11) - PDstandard4th12gt22*SQR(gtu12) - PDstandard4th12gt33*SQR(gtu13); - - ddgtu1221 = -(gtu11*gtu12*PDstandard4th12gt11) - gtu11*gtu22*PDstandard4th12gt21 - gtu12*gtu22*PDstandard4th12gt22 - - gtu12*gtu13*PDstandard4th12gt31 - gtu11*gtu23*PDstandard4th12gt31 - gtu13*gtu22*PDstandard4th12gt32 - - gtu12*gtu23*PDstandard4th12gt32 - gtu13*gtu23*PDstandard4th12gt33 - dgtu122*gtu11*PDstandard4th1gt11 - - dgtu112*gtu12*PDstandard4th1gt11 - dgtu222*gtu11*PDstandard4th1gt21 - 2*dgtu122*gtu12*PDstandard4th1gt21 - - dgtu112*gtu22*PDstandard4th1gt21 - dgtu222*gtu12*PDstandard4th1gt22 - dgtu122*gtu22*PDstandard4th1gt22 - - dgtu232*gtu11*PDstandard4th1gt31 - dgtu132*gtu12*PDstandard4th1gt31 - dgtu122*gtu13*PDstandard4th1gt31 - - dgtu112*gtu23*PDstandard4th1gt31 - dgtu232*gtu12*PDstandard4th1gt32 - dgtu222*gtu13*PDstandard4th1gt32 - - dgtu132*gtu22*PDstandard4th1gt32 - dgtu122*gtu23*PDstandard4th1gt32 - dgtu232*gtu13*PDstandard4th1gt33 - - dgtu132*gtu23*PDstandard4th1gt33 - PDstandard4th12gt21*SQR(gtu12); - - ddgtu1321 = -(gtu11*gtu13*PDstandard4th12gt11) - gtu12*gtu13*PDstandard4th12gt21 - gtu11*gtu23*PDstandard4th12gt21 - - gtu12*gtu23*PDstandard4th12gt22 - gtu11*gtu33*PDstandard4th12gt31 - gtu13*gtu23*PDstandard4th12gt32 - - gtu12*gtu33*PDstandard4th12gt32 - gtu13*gtu33*PDstandard4th12gt33 - dgtu132*gtu11*PDstandard4th1gt11 - - dgtu112*gtu13*PDstandard4th1gt11 - dgtu232*gtu11*PDstandard4th1gt21 - dgtu132*gtu12*PDstandard4th1gt21 - - dgtu122*gtu13*PDstandard4th1gt21 - dgtu112*gtu23*PDstandard4th1gt21 - dgtu232*gtu12*PDstandard4th1gt22 - - dgtu122*gtu23*PDstandard4th1gt22 - dgtu332*gtu11*PDstandard4th1gt31 - 2*dgtu132*gtu13*PDstandard4th1gt31 - - dgtu112*gtu33*PDstandard4th1gt31 - dgtu332*gtu12*PDstandard4th1gt32 - dgtu232*gtu13*PDstandard4th1gt32 - - dgtu132*gtu23*PDstandard4th1gt32 - dgtu122*gtu33*PDstandard4th1gt32 - dgtu332*gtu13*PDstandard4th1gt33 - - dgtu132*gtu33*PDstandard4th1gt33 - PDstandard4th12gt31*SQR(gtu13); - - ddgtu2221 = -2*(gtu12*gtu22*PDstandard4th12gt21 + gtu12*gtu23*PDstandard4th12gt31 + gtu22*gtu23*PDstandard4th12gt32 + - dgtu122*gtu12*PDstandard4th1gt11 + dgtu222*gtu12*PDstandard4th1gt21 + dgtu122*gtu22*PDstandard4th1gt21 + - dgtu222*gtu22*PDstandard4th1gt22 + dgtu232*gtu12*PDstandard4th1gt31 + dgtu122*gtu23*PDstandard4th1gt31 + - dgtu232*gtu22*PDstandard4th1gt32 + dgtu222*gtu23*PDstandard4th1gt32 + dgtu232*gtu23*PDstandard4th1gt33) - - PDstandard4th12gt11*SQR(gtu12) - PDstandard4th12gt22*SQR(gtu22) - PDstandard4th12gt33*SQR(gtu23); - - ddgtu2321 = -(gtu12*gtu13*PDstandard4th12gt11) - gtu13*gtu22*PDstandard4th12gt21 - gtu12*gtu23*PDstandard4th12gt21 - - gtu22*gtu23*PDstandard4th12gt22 - gtu13*gtu23*PDstandard4th12gt31 - gtu12*gtu33*PDstandard4th12gt31 - - gtu22*gtu33*PDstandard4th12gt32 - gtu23*gtu33*PDstandard4th12gt33 - dgtu132*gtu12*PDstandard4th1gt11 - - dgtu122*gtu13*PDstandard4th1gt11 - dgtu232*gtu12*PDstandard4th1gt21 - dgtu222*gtu13*PDstandard4th1gt21 - - dgtu132*gtu22*PDstandard4th1gt21 - dgtu122*gtu23*PDstandard4th1gt21 - dgtu232*gtu22*PDstandard4th1gt22 - - dgtu222*gtu23*PDstandard4th1gt22 - dgtu332*gtu12*PDstandard4th1gt31 - dgtu232*gtu13*PDstandard4th1gt31 - - dgtu132*gtu23*PDstandard4th1gt31 - dgtu122*gtu33*PDstandard4th1gt31 - dgtu332*gtu22*PDstandard4th1gt32 - - 2*dgtu232*gtu23*PDstandard4th1gt32 - dgtu222*gtu33*PDstandard4th1gt32 - dgtu332*gtu23*PDstandard4th1gt33 - - dgtu232*gtu33*PDstandard4th1gt33 - PDstandard4th12gt32*SQR(gtu23); - - ddgtu1131 = -2*(gtu11*gtu12*PDstandard4th13gt21 + gtu11*gtu13*PDstandard4th13gt31 + gtu12*gtu13*PDstandard4th13gt32 + - dgtu113*gtu11*PDstandard4th1gt11 + dgtu123*gtu11*PDstandard4th1gt21 + dgtu113*gtu12*PDstandard4th1gt21 + - dgtu123*gtu12*PDstandard4th1gt22 + dgtu133*gtu11*PDstandard4th1gt31 + dgtu113*gtu13*PDstandard4th1gt31 + - dgtu133*gtu12*PDstandard4th1gt32 + dgtu123*gtu13*PDstandard4th1gt32 + dgtu133*gtu13*PDstandard4th1gt33) - - PDstandard4th13gt11*SQR(gtu11) - PDstandard4th13gt22*SQR(gtu12) - PDstandard4th13gt33*SQR(gtu13); - - ddgtu1231 = -(gtu11*gtu12*PDstandard4th13gt11) - gtu11*gtu22*PDstandard4th13gt21 - gtu12*gtu22*PDstandard4th13gt22 - - gtu12*gtu13*PDstandard4th13gt31 - gtu11*gtu23*PDstandard4th13gt31 - gtu13*gtu22*PDstandard4th13gt32 - - gtu12*gtu23*PDstandard4th13gt32 - gtu13*gtu23*PDstandard4th13gt33 - dgtu123*gtu11*PDstandard4th1gt11 - - dgtu113*gtu12*PDstandard4th1gt11 - dgtu223*gtu11*PDstandard4th1gt21 - 2*dgtu123*gtu12*PDstandard4th1gt21 - - dgtu113*gtu22*PDstandard4th1gt21 - dgtu223*gtu12*PDstandard4th1gt22 - dgtu123*gtu22*PDstandard4th1gt22 - - dgtu233*gtu11*PDstandard4th1gt31 - dgtu133*gtu12*PDstandard4th1gt31 - dgtu123*gtu13*PDstandard4th1gt31 - - dgtu113*gtu23*PDstandard4th1gt31 - dgtu233*gtu12*PDstandard4th1gt32 - dgtu223*gtu13*PDstandard4th1gt32 - - dgtu133*gtu22*PDstandard4th1gt32 - dgtu123*gtu23*PDstandard4th1gt32 - dgtu233*gtu13*PDstandard4th1gt33 - - dgtu133*gtu23*PDstandard4th1gt33 - PDstandard4th13gt21*SQR(gtu12); - - ddgtu1331 = -(gtu11*gtu13*PDstandard4th13gt11) - gtu12*gtu13*PDstandard4th13gt21 - gtu11*gtu23*PDstandard4th13gt21 - - gtu12*gtu23*PDstandard4th13gt22 - gtu11*gtu33*PDstandard4th13gt31 - gtu13*gtu23*PDstandard4th13gt32 - - gtu12*gtu33*PDstandard4th13gt32 - gtu13*gtu33*PDstandard4th13gt33 - dgtu133*gtu11*PDstandard4th1gt11 - - dgtu113*gtu13*PDstandard4th1gt11 - dgtu233*gtu11*PDstandard4th1gt21 - dgtu133*gtu12*PDstandard4th1gt21 - - dgtu123*gtu13*PDstandard4th1gt21 - dgtu113*gtu23*PDstandard4th1gt21 - dgtu233*gtu12*PDstandard4th1gt22 - - dgtu123*gtu23*PDstandard4th1gt22 - dgtu333*gtu11*PDstandard4th1gt31 - 2*dgtu133*gtu13*PDstandard4th1gt31 - - dgtu113*gtu33*PDstandard4th1gt31 - dgtu333*gtu12*PDstandard4th1gt32 - dgtu233*gtu13*PDstandard4th1gt32 - - dgtu133*gtu23*PDstandard4th1gt32 - dgtu123*gtu33*PDstandard4th1gt32 - dgtu333*gtu13*PDstandard4th1gt33 - - dgtu133*gtu33*PDstandard4th1gt33 - PDstandard4th13gt31*SQR(gtu13); - - ddgtu2331 = -(gtu12*gtu13*PDstandard4th13gt11) - gtu13*gtu22*PDstandard4th13gt21 - gtu12*gtu23*PDstandard4th13gt21 - - gtu22*gtu23*PDstandard4th13gt22 - gtu13*gtu23*PDstandard4th13gt31 - gtu12*gtu33*PDstandard4th13gt31 - - gtu22*gtu33*PDstandard4th13gt32 - gtu23*gtu33*PDstandard4th13gt33 - dgtu133*gtu12*PDstandard4th1gt11 - - dgtu123*gtu13*PDstandard4th1gt11 - dgtu233*gtu12*PDstandard4th1gt21 - dgtu223*gtu13*PDstandard4th1gt21 - - dgtu133*gtu22*PDstandard4th1gt21 - dgtu123*gtu23*PDstandard4th1gt21 - dgtu233*gtu22*PDstandard4th1gt22 - - dgtu223*gtu23*PDstandard4th1gt22 - dgtu333*gtu12*PDstandard4th1gt31 - dgtu233*gtu13*PDstandard4th1gt31 - - dgtu133*gtu23*PDstandard4th1gt31 - dgtu123*gtu33*PDstandard4th1gt31 - dgtu333*gtu22*PDstandard4th1gt32 - - 2*dgtu233*gtu23*PDstandard4th1gt32 - dgtu223*gtu33*PDstandard4th1gt32 - dgtu333*gtu23*PDstandard4th1gt33 - - dgtu233*gtu33*PDstandard4th1gt33 - PDstandard4th13gt32*SQR(gtu23); - - ddgtu3331 = -2*(gtu13*gtu23*PDstandard4th13gt21 + gtu13*gtu33*PDstandard4th13gt31 + gtu23*gtu33*PDstandard4th13gt32 + - dgtu133*gtu13*PDstandard4th1gt11 + dgtu233*gtu13*PDstandard4th1gt21 + dgtu133*gtu23*PDstandard4th1gt21 + - dgtu233*gtu23*PDstandard4th1gt22 + dgtu333*gtu13*PDstandard4th1gt31 + dgtu133*gtu33*PDstandard4th1gt31 + - dgtu333*gtu23*PDstandard4th1gt32 + dgtu233*gtu33*PDstandard4th1gt32 + dgtu333*gtu33*PDstandard4th1gt33) - - PDstandard4th13gt11*SQR(gtu13) - PDstandard4th13gt22*SQR(gtu23) - PDstandard4th13gt33*SQR(gtu33); - - ddgtu1222 = -(gtu11*gtu12*PDstandard4th22gt11) - gtu11*gtu22*PDstandard4th22gt21 - gtu12*gtu22*PDstandard4th22gt22 - - gtu12*gtu13*PDstandard4th22gt31 - gtu11*gtu23*PDstandard4th22gt31 - gtu13*gtu22*PDstandard4th22gt32 - - gtu12*gtu23*PDstandard4th22gt32 - gtu13*gtu23*PDstandard4th22gt33 - dgtu122*gtu11*PDstandard4th2gt11 - - dgtu112*gtu12*PDstandard4th2gt11 - dgtu222*gtu11*PDstandard4th2gt21 - 2*dgtu122*gtu12*PDstandard4th2gt21 - - dgtu112*gtu22*PDstandard4th2gt21 - dgtu222*gtu12*PDstandard4th2gt22 - dgtu122*gtu22*PDstandard4th2gt22 - - dgtu232*gtu11*PDstandard4th2gt31 - dgtu132*gtu12*PDstandard4th2gt31 - dgtu122*gtu13*PDstandard4th2gt31 - - dgtu112*gtu23*PDstandard4th2gt31 - dgtu232*gtu12*PDstandard4th2gt32 - dgtu222*gtu13*PDstandard4th2gt32 - - dgtu132*gtu22*PDstandard4th2gt32 - dgtu122*gtu23*PDstandard4th2gt32 - dgtu232*gtu13*PDstandard4th2gt33 - - dgtu132*gtu23*PDstandard4th2gt33 - PDstandard4th22gt21*SQR(gtu12); - - ddgtu2222 = -2*(gtu12*gtu22*PDstandard4th22gt21 + gtu12*gtu23*PDstandard4th22gt31 + gtu22*gtu23*PDstandard4th22gt32 + - dgtu122*gtu12*PDstandard4th2gt11 + dgtu222*gtu12*PDstandard4th2gt21 + dgtu122*gtu22*PDstandard4th2gt21 + - dgtu222*gtu22*PDstandard4th2gt22 + dgtu232*gtu12*PDstandard4th2gt31 + dgtu122*gtu23*PDstandard4th2gt31 + - dgtu232*gtu22*PDstandard4th2gt32 + dgtu222*gtu23*PDstandard4th2gt32 + dgtu232*gtu23*PDstandard4th2gt33) - - PDstandard4th22gt11*SQR(gtu12) - PDstandard4th22gt22*SQR(gtu22) - PDstandard4th22gt33*SQR(gtu23); - - ddgtu2322 = -(gtu12*gtu13*PDstandard4th22gt11) - gtu13*gtu22*PDstandard4th22gt21 - gtu12*gtu23*PDstandard4th22gt21 - - gtu22*gtu23*PDstandard4th22gt22 - gtu13*gtu23*PDstandard4th22gt31 - gtu12*gtu33*PDstandard4th22gt31 - - gtu22*gtu33*PDstandard4th22gt32 - gtu23*gtu33*PDstandard4th22gt33 - dgtu132*gtu12*PDstandard4th2gt11 - - dgtu122*gtu13*PDstandard4th2gt11 - dgtu232*gtu12*PDstandard4th2gt21 - dgtu222*gtu13*PDstandard4th2gt21 - - dgtu132*gtu22*PDstandard4th2gt21 - dgtu122*gtu23*PDstandard4th2gt21 - dgtu232*gtu22*PDstandard4th2gt22 - - dgtu222*gtu23*PDstandard4th2gt22 - dgtu332*gtu12*PDstandard4th2gt31 - dgtu232*gtu13*PDstandard4th2gt31 - - dgtu132*gtu23*PDstandard4th2gt31 - dgtu122*gtu33*PDstandard4th2gt31 - dgtu332*gtu22*PDstandard4th2gt32 - - 2*dgtu232*gtu23*PDstandard4th2gt32 - dgtu222*gtu33*PDstandard4th2gt32 - dgtu332*gtu23*PDstandard4th2gt33 - - dgtu232*gtu33*PDstandard4th2gt33 - PDstandard4th22gt32*SQR(gtu23); - - ddgtu1232 = -(gtu11*gtu12*PDstandard4th23gt11) - gtu11*gtu22*PDstandard4th23gt21 - gtu12*gtu22*PDstandard4th23gt22 - - gtu12*gtu13*PDstandard4th23gt31 - gtu11*gtu23*PDstandard4th23gt31 - gtu13*gtu22*PDstandard4th23gt32 - - gtu12*gtu23*PDstandard4th23gt32 - gtu13*gtu23*PDstandard4th23gt33 - dgtu123*gtu11*PDstandard4th2gt11 - - dgtu113*gtu12*PDstandard4th2gt11 - dgtu223*gtu11*PDstandard4th2gt21 - 2*dgtu123*gtu12*PDstandard4th2gt21 - - dgtu113*gtu22*PDstandard4th2gt21 - dgtu223*gtu12*PDstandard4th2gt22 - dgtu123*gtu22*PDstandard4th2gt22 - - dgtu233*gtu11*PDstandard4th2gt31 - dgtu133*gtu12*PDstandard4th2gt31 - dgtu123*gtu13*PDstandard4th2gt31 - - dgtu113*gtu23*PDstandard4th2gt31 - dgtu233*gtu12*PDstandard4th2gt32 - dgtu223*gtu13*PDstandard4th2gt32 - - dgtu133*gtu22*PDstandard4th2gt32 - dgtu123*gtu23*PDstandard4th2gt32 - dgtu233*gtu13*PDstandard4th2gt33 - - dgtu133*gtu23*PDstandard4th2gt33 - PDstandard4th23gt21*SQR(gtu12); - - ddgtu1332 = -(gtu11*gtu13*PDstandard4th23gt11) - gtu12*gtu13*PDstandard4th23gt21 - gtu11*gtu23*PDstandard4th23gt21 - - gtu12*gtu23*PDstandard4th23gt22 - gtu11*gtu33*PDstandard4th23gt31 - gtu13*gtu23*PDstandard4th23gt32 - - gtu12*gtu33*PDstandard4th23gt32 - gtu13*gtu33*PDstandard4th23gt33 - dgtu133*gtu11*PDstandard4th2gt11 - - dgtu113*gtu13*PDstandard4th2gt11 - dgtu233*gtu11*PDstandard4th2gt21 - dgtu133*gtu12*PDstandard4th2gt21 - - dgtu123*gtu13*PDstandard4th2gt21 - dgtu113*gtu23*PDstandard4th2gt21 - dgtu233*gtu12*PDstandard4th2gt22 - - dgtu123*gtu23*PDstandard4th2gt22 - dgtu333*gtu11*PDstandard4th2gt31 - 2*dgtu133*gtu13*PDstandard4th2gt31 - - dgtu113*gtu33*PDstandard4th2gt31 - dgtu333*gtu12*PDstandard4th2gt32 - dgtu233*gtu13*PDstandard4th2gt32 - - dgtu133*gtu23*PDstandard4th2gt32 - dgtu123*gtu33*PDstandard4th2gt32 - dgtu333*gtu13*PDstandard4th2gt33 - - dgtu133*gtu33*PDstandard4th2gt33 - PDstandard4th23gt31*SQR(gtu13); - - ddgtu2232 = -2*(gtu12*gtu22*PDstandard4th23gt21 + gtu12*gtu23*PDstandard4th23gt31 + gtu22*gtu23*PDstandard4th23gt32 + - dgtu123*gtu12*PDstandard4th2gt11 + dgtu223*gtu12*PDstandard4th2gt21 + dgtu123*gtu22*PDstandard4th2gt21 + - dgtu223*gtu22*PDstandard4th2gt22 + dgtu233*gtu12*PDstandard4th2gt31 + dgtu123*gtu23*PDstandard4th2gt31 + - dgtu233*gtu22*PDstandard4th2gt32 + dgtu223*gtu23*PDstandard4th2gt32 + dgtu233*gtu23*PDstandard4th2gt33) - - PDstandard4th23gt11*SQR(gtu12) - PDstandard4th23gt22*SQR(gtu22) - PDstandard4th23gt33*SQR(gtu23); - - ddgtu2332 = -(gtu12*gtu13*PDstandard4th23gt11) - gtu13*gtu22*PDstandard4th23gt21 - gtu12*gtu23*PDstandard4th23gt21 - - gtu22*gtu23*PDstandard4th23gt22 - gtu13*gtu23*PDstandard4th23gt31 - gtu12*gtu33*PDstandard4th23gt31 - - gtu22*gtu33*PDstandard4th23gt32 - gtu23*gtu33*PDstandard4th23gt33 - dgtu133*gtu12*PDstandard4th2gt11 - - dgtu123*gtu13*PDstandard4th2gt11 - dgtu233*gtu12*PDstandard4th2gt21 - dgtu223*gtu13*PDstandard4th2gt21 - - dgtu133*gtu22*PDstandard4th2gt21 - dgtu123*gtu23*PDstandard4th2gt21 - dgtu233*gtu22*PDstandard4th2gt22 - - dgtu223*gtu23*PDstandard4th2gt22 - dgtu333*gtu12*PDstandard4th2gt31 - dgtu233*gtu13*PDstandard4th2gt31 - - dgtu133*gtu23*PDstandard4th2gt31 - dgtu123*gtu33*PDstandard4th2gt31 - dgtu333*gtu22*PDstandard4th2gt32 - - 2*dgtu233*gtu23*PDstandard4th2gt32 - dgtu223*gtu33*PDstandard4th2gt32 - dgtu333*gtu23*PDstandard4th2gt33 - - dgtu233*gtu33*PDstandard4th2gt33 - PDstandard4th23gt32*SQR(gtu23); - - ddgtu3332 = -2*(gtu13*gtu23*PDstandard4th23gt21 + gtu13*gtu33*PDstandard4th23gt31 + gtu23*gtu33*PDstandard4th23gt32 + - dgtu133*gtu13*PDstandard4th2gt11 + dgtu233*gtu13*PDstandard4th2gt21 + dgtu133*gtu23*PDstandard4th2gt21 + - dgtu233*gtu23*PDstandard4th2gt22 + dgtu333*gtu13*PDstandard4th2gt31 + dgtu133*gtu33*PDstandard4th2gt31 + - dgtu333*gtu23*PDstandard4th2gt32 + dgtu233*gtu33*PDstandard4th2gt32 + dgtu333*gtu33*PDstandard4th2gt33) - - PDstandard4th23gt11*SQR(gtu13) - PDstandard4th23gt22*SQR(gtu23) - PDstandard4th23gt33*SQR(gtu33); - - ddgtu1333 = -(gtu11*gtu13*PDstandard4th33gt11) - gtu12*gtu13*PDstandard4th33gt21 - gtu11*gtu23*PDstandard4th33gt21 - - gtu12*gtu23*PDstandard4th33gt22 - gtu11*gtu33*PDstandard4th33gt31 - gtu13*gtu23*PDstandard4th33gt32 - - gtu12*gtu33*PDstandard4th33gt32 - gtu13*gtu33*PDstandard4th33gt33 - dgtu133*gtu11*PDstandard4th3gt11 - - dgtu113*gtu13*PDstandard4th3gt11 - dgtu233*gtu11*PDstandard4th3gt21 - dgtu133*gtu12*PDstandard4th3gt21 - - dgtu123*gtu13*PDstandard4th3gt21 - dgtu113*gtu23*PDstandard4th3gt21 - dgtu233*gtu12*PDstandard4th3gt22 - - dgtu123*gtu23*PDstandard4th3gt22 - dgtu333*gtu11*PDstandard4th3gt31 - 2*dgtu133*gtu13*PDstandard4th3gt31 - - dgtu113*gtu33*PDstandard4th3gt31 - dgtu333*gtu12*PDstandard4th3gt32 - dgtu233*gtu13*PDstandard4th3gt32 - - dgtu133*gtu23*PDstandard4th3gt32 - dgtu123*gtu33*PDstandard4th3gt32 - dgtu333*gtu13*PDstandard4th3gt33 - - dgtu133*gtu33*PDstandard4th3gt33 - PDstandard4th33gt31*SQR(gtu13); - - ddgtu2333 = -(gtu12*gtu13*PDstandard4th33gt11) - gtu13*gtu22*PDstandard4th33gt21 - gtu12*gtu23*PDstandard4th33gt21 - - gtu22*gtu23*PDstandard4th33gt22 - gtu13*gtu23*PDstandard4th33gt31 - gtu12*gtu33*PDstandard4th33gt31 - - gtu22*gtu33*PDstandard4th33gt32 - gtu23*gtu33*PDstandard4th33gt33 - dgtu133*gtu12*PDstandard4th3gt11 - - dgtu123*gtu13*PDstandard4th3gt11 - dgtu233*gtu12*PDstandard4th3gt21 - dgtu223*gtu13*PDstandard4th3gt21 - - dgtu133*gtu22*PDstandard4th3gt21 - dgtu123*gtu23*PDstandard4th3gt21 - dgtu233*gtu22*PDstandard4th3gt22 - - dgtu223*gtu23*PDstandard4th3gt22 - dgtu333*gtu12*PDstandard4th3gt31 - dgtu233*gtu13*PDstandard4th3gt31 - - dgtu133*gtu23*PDstandard4th3gt31 - dgtu123*gtu33*PDstandard4th3gt31 - dgtu333*gtu22*PDstandard4th3gt32 - - 2*dgtu233*gtu23*PDstandard4th3gt32 - dgtu223*gtu33*PDstandard4th3gt32 - dgtu333*gtu23*PDstandard4th3gt33 - - dgtu233*gtu33*PDstandard4th3gt33 - PDstandard4th33gt32*SQR(gtu23); - - ddgtu3333 = -2*(gtu13*gtu23*PDstandard4th33gt21 + gtu13*gtu33*PDstandard4th33gt31 + gtu23*gtu33*PDstandard4th33gt32 + - dgtu133*gtu13*PDstandard4th3gt11 + dgtu233*gtu13*PDstandard4th3gt21 + dgtu133*gtu23*PDstandard4th3gt21 + - dgtu233*gtu23*PDstandard4th3gt22 + dgtu333*gtu13*PDstandard4th3gt31 + dgtu133*gtu33*PDstandard4th3gt31 + - dgtu333*gtu23*PDstandard4th3gt32 + dgtu233*gtu33*PDstandard4th3gt32 + dgtu333*gtu33*PDstandard4th3gt33) - - PDstandard4th33gt11*SQR(gtu13) - PDstandard4th33gt22*SQR(gtu23) - PDstandard4th33gt33*SQR(gtu33); - - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu12*PDstandard4th1gt21 + gtu13*PDstandard4th1gt31) - - gtu12*PDstandard4th2gt11 - gtu13*PDstandard4th3gt11); - - Gt211 = khalf*(gtu12*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt21 + gtu23*PDstandard4th1gt31) - - gtu22*PDstandard4th2gt11 - gtu23*PDstandard4th3gt11); - - Gt311 = khalf*(gtu13*PDstandard4th1gt11 + 2*(gtu23*PDstandard4th1gt21 + gtu33*PDstandard4th1gt31) - - gtu23*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); - - Gt121 = khalf*(gtu12*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu13*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); - - Gt221 = khalf*(gtu22*PDstandard4th1gt22 + gtu12*PDstandard4th2gt11 + - gtu23*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); - - Gt321 = khalf*(gtu23*PDstandard4th1gt22 + gtu13*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); - - Gt131 = khalf*(gtu13*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu12*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); - - Gt231 = khalf*(gtu23*PDstandard4th1gt33 + gtu12*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); - - Gt331 = khalf*(gtu33*PDstandard4th1gt33 + gtu13*PDstandard4th3gt11 + - gtu23*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); - - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu12*PDstandard4th2gt22 + - gtu13*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); - - Gt222 = khalf*(gtu12*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu22*PDstandard4th2gt22 + - gtu23*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); - - Gt322 = khalf*(gtu13*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu23*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); - - Gt132 = khalf*(gtu13*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu12*PDstandard4th3gt22); - - Gt232 = khalf*(gtu23*PDstandard4th2gt33 + gtu12*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + + dgtu311 = -(gtu11*gtu31*PDstandard4th1gt11) - gtu21*gtu31*PDstandard4th1gt12 - gtu11*gtu32*PDstandard4th1gt12 - + gtu11*gtu33*PDstandard4th1gt13 - gtu21*gtu32*PDstandard4th1gt22 - gtu31*gtu32*PDstandard4th1gt23 - + gtu21*gtu33*PDstandard4th1gt23 - gtu31*gtu33*PDstandard4th1gt33 - PDstandard4th1gt13*SQR(gtu31); + + dgtu221 = -2*(gtu21*gtu22*PDstandard4th1gt12 + gtu21*gtu32*PDstandard4th1gt13 + gtu22*gtu32*PDstandard4th1gt23) - + PDstandard4th1gt11*SQR(gtu21) - PDstandard4th1gt22*SQR(gtu22) - PDstandard4th1gt33*SQR(gtu32); + + dgtu321 = -(gtu21*gtu31*PDstandard4th1gt11) - gtu22*gtu31*PDstandard4th1gt12 - gtu21*gtu32*PDstandard4th1gt12 - + gtu31*gtu32*PDstandard4th1gt13 - gtu21*gtu33*PDstandard4th1gt13 - gtu22*gtu32*PDstandard4th1gt22 - + gtu22*gtu33*PDstandard4th1gt23 - gtu32*gtu33*PDstandard4th1gt33 - PDstandard4th1gt23*SQR(gtu32); + + dgtu331 = -2*(gtu31*gtu32*PDstandard4th1gt12 + gtu31*gtu33*PDstandard4th1gt13 + gtu32*gtu33*PDstandard4th1gt23) - + PDstandard4th1gt11*SQR(gtu31) - PDstandard4th1gt22*SQR(gtu32) - PDstandard4th1gt33*SQR(gtu33); + + dgtu112 = -2*(gtu11*gtu21*PDstandard4th2gt12 + gtu11*gtu31*PDstandard4th2gt13 + gtu21*gtu31*PDstandard4th2gt23) - + PDstandard4th2gt11*SQR(gtu11) - PDstandard4th2gt22*SQR(gtu21) - PDstandard4th2gt33*SQR(gtu31); + + dgtu212 = -(gtu11*gtu21*PDstandard4th2gt11) - gtu11*gtu22*PDstandard4th2gt12 - gtu21*gtu31*PDstandard4th2gt13 - + gtu11*gtu32*PDstandard4th2gt13 - gtu21*gtu22*PDstandard4th2gt22 - gtu22*gtu31*PDstandard4th2gt23 - + gtu21*gtu32*PDstandard4th2gt23 - gtu31*gtu32*PDstandard4th2gt33 - PDstandard4th2gt12*SQR(gtu21); + + dgtu312 = -(gtu11*gtu31*PDstandard4th2gt11) - gtu21*gtu31*PDstandard4th2gt12 - gtu11*gtu32*PDstandard4th2gt12 - + gtu11*gtu33*PDstandard4th2gt13 - gtu21*gtu32*PDstandard4th2gt22 - gtu31*gtu32*PDstandard4th2gt23 - + gtu21*gtu33*PDstandard4th2gt23 - gtu31*gtu33*PDstandard4th2gt33 - PDstandard4th2gt13*SQR(gtu31); + + dgtu222 = -2*(gtu21*gtu22*PDstandard4th2gt12 + gtu21*gtu32*PDstandard4th2gt13 + gtu22*gtu32*PDstandard4th2gt23) - + PDstandard4th2gt11*SQR(gtu21) - PDstandard4th2gt22*SQR(gtu22) - PDstandard4th2gt33*SQR(gtu32); + + dgtu322 = -(gtu21*gtu31*PDstandard4th2gt11) - gtu22*gtu31*PDstandard4th2gt12 - gtu21*gtu32*PDstandard4th2gt12 - + gtu31*gtu32*PDstandard4th2gt13 - gtu21*gtu33*PDstandard4th2gt13 - gtu22*gtu32*PDstandard4th2gt22 - + gtu22*gtu33*PDstandard4th2gt23 - gtu32*gtu33*PDstandard4th2gt33 - PDstandard4th2gt23*SQR(gtu32); + + dgtu332 = -2*(gtu31*gtu32*PDstandard4th2gt12 + gtu31*gtu33*PDstandard4th2gt13 + gtu32*gtu33*PDstandard4th2gt23) - + PDstandard4th2gt11*SQR(gtu31) - PDstandard4th2gt22*SQR(gtu32) - PDstandard4th2gt33*SQR(gtu33); + + dgtu113 = -2*(gtu11*gtu21*PDstandard4th3gt12 + gtu11*gtu31*PDstandard4th3gt13 + gtu21*gtu31*PDstandard4th3gt23) - + PDstandard4th3gt11*SQR(gtu11) - PDstandard4th3gt22*SQR(gtu21) - PDstandard4th3gt33*SQR(gtu31); + + dgtu213 = -(gtu11*gtu21*PDstandard4th3gt11) - gtu11*gtu22*PDstandard4th3gt12 - gtu21*gtu31*PDstandard4th3gt13 - + gtu11*gtu32*PDstandard4th3gt13 - gtu21*gtu22*PDstandard4th3gt22 - gtu22*gtu31*PDstandard4th3gt23 - + gtu21*gtu32*PDstandard4th3gt23 - gtu31*gtu32*PDstandard4th3gt33 - PDstandard4th3gt12*SQR(gtu21); + + dgtu313 = -(gtu11*gtu31*PDstandard4th3gt11) - gtu21*gtu31*PDstandard4th3gt12 - gtu11*gtu32*PDstandard4th3gt12 - + gtu11*gtu33*PDstandard4th3gt13 - gtu21*gtu32*PDstandard4th3gt22 - gtu31*gtu32*PDstandard4th3gt23 - + gtu21*gtu33*PDstandard4th3gt23 - gtu31*gtu33*PDstandard4th3gt33 - PDstandard4th3gt13*SQR(gtu31); + + dgtu223 = -2*(gtu21*gtu22*PDstandard4th3gt12 + gtu21*gtu32*PDstandard4th3gt13 + gtu22*gtu32*PDstandard4th3gt23) - + PDstandard4th3gt11*SQR(gtu21) - PDstandard4th3gt22*SQR(gtu22) - PDstandard4th3gt33*SQR(gtu32); + + dgtu323 = -(gtu21*gtu31*PDstandard4th3gt11) - gtu22*gtu31*PDstandard4th3gt12 - gtu21*gtu32*PDstandard4th3gt12 - + gtu31*gtu32*PDstandard4th3gt13 - gtu21*gtu33*PDstandard4th3gt13 - gtu22*gtu32*PDstandard4th3gt22 - + gtu22*gtu33*PDstandard4th3gt23 - gtu32*gtu33*PDstandard4th3gt33 - PDstandard4th3gt23*SQR(gtu32); + + dgtu333 = -2*(gtu31*gtu32*PDstandard4th3gt12 + gtu31*gtu33*PDstandard4th3gt13 + gtu32*gtu33*PDstandard4th3gt23) - + PDstandard4th3gt11*SQR(gtu31) - PDstandard4th3gt22*SQR(gtu32) - PDstandard4th3gt33*SQR(gtu33); + + ddgtu1111 = -2*(gtu11*gtu21*PDstandard4th11gt12 + gtu11*gtu31*PDstandard4th11gt13 + gtu21*gtu31*PDstandard4th11gt23 + + dgtu111*gtu11*PDstandard4th1gt11 + dgtu211*gtu11*PDstandard4th1gt12 + dgtu111*gtu21*PDstandard4th1gt12 + + dgtu311*gtu11*PDstandard4th1gt13 + dgtu111*gtu31*PDstandard4th1gt13 + dgtu211*gtu21*PDstandard4th1gt22 + + dgtu311*gtu21*PDstandard4th1gt23 + dgtu211*gtu31*PDstandard4th1gt23 + dgtu311*gtu31*PDstandard4th1gt33) - + PDstandard4th11gt11*SQR(gtu11) - PDstandard4th11gt22*SQR(gtu21) - PDstandard4th11gt33*SQR(gtu31); + + ddgtu2111 = -(gtu11*gtu21*PDstandard4th11gt11) - gtu11*gtu22*PDstandard4th11gt12 - gtu21*gtu31*PDstandard4th11gt13 - + gtu11*gtu32*PDstandard4th11gt13 - gtu21*gtu22*PDstandard4th11gt22 - gtu22*gtu31*PDstandard4th11gt23 - + gtu21*gtu32*PDstandard4th11gt23 - gtu31*gtu32*PDstandard4th11gt33 - dgtu211*gtu11*PDstandard4th1gt11 - + dgtu111*gtu21*PDstandard4th1gt11 - dgtu221*gtu11*PDstandard4th1gt12 - 2*dgtu211*gtu21*PDstandard4th1gt12 - + dgtu111*gtu22*PDstandard4th1gt12 - dgtu321*gtu11*PDstandard4th1gt13 - dgtu311*gtu21*PDstandard4th1gt13 - + dgtu211*gtu31*PDstandard4th1gt13 - dgtu111*gtu32*PDstandard4th1gt13 - dgtu221*gtu21*PDstandard4th1gt22 - + dgtu211*gtu22*PDstandard4th1gt22 - dgtu321*gtu21*PDstandard4th1gt23 - dgtu311*gtu22*PDstandard4th1gt23 - + dgtu221*gtu31*PDstandard4th1gt23 - dgtu211*gtu32*PDstandard4th1gt23 - dgtu321*gtu31*PDstandard4th1gt33 - + dgtu311*gtu32*PDstandard4th1gt33 - PDstandard4th11gt12*SQR(gtu21); + + ddgtu3111 = -(gtu11*gtu31*PDstandard4th11gt11) - gtu21*gtu31*PDstandard4th11gt12 - gtu11*gtu32*PDstandard4th11gt12 - + gtu11*gtu33*PDstandard4th11gt13 - gtu21*gtu32*PDstandard4th11gt22 - gtu31*gtu32*PDstandard4th11gt23 - + gtu21*gtu33*PDstandard4th11gt23 - gtu31*gtu33*PDstandard4th11gt33 - dgtu311*gtu11*PDstandard4th1gt11 - + dgtu111*gtu31*PDstandard4th1gt11 - dgtu321*gtu11*PDstandard4th1gt12 - dgtu311*gtu21*PDstandard4th1gt12 - + dgtu211*gtu31*PDstandard4th1gt12 - dgtu111*gtu32*PDstandard4th1gt12 - dgtu331*gtu11*PDstandard4th1gt13 - + 2*dgtu311*gtu31*PDstandard4th1gt13 - dgtu111*gtu33*PDstandard4th1gt13 - dgtu321*gtu21*PDstandard4th1gt22 - + dgtu211*gtu32*PDstandard4th1gt22 - dgtu331*gtu21*PDstandard4th1gt23 - dgtu321*gtu31*PDstandard4th1gt23 - + dgtu311*gtu32*PDstandard4th1gt23 - dgtu211*gtu33*PDstandard4th1gt23 - dgtu331*gtu31*PDstandard4th1gt33 - + dgtu311*gtu33*PDstandard4th1gt33 - PDstandard4th11gt13*SQR(gtu31); + + ddgtu1112 = -2*(gtu11*gtu21*PDstandard4th12gt12 + gtu11*gtu31*PDstandard4th12gt13 + gtu21*gtu31*PDstandard4th12gt23 + + dgtu112*gtu11*PDstandard4th1gt11 + dgtu212*gtu11*PDstandard4th1gt12 + dgtu112*gtu21*PDstandard4th1gt12 + + dgtu312*gtu11*PDstandard4th1gt13 + dgtu112*gtu31*PDstandard4th1gt13 + dgtu212*gtu21*PDstandard4th1gt22 + + dgtu312*gtu21*PDstandard4th1gt23 + dgtu212*gtu31*PDstandard4th1gt23 + dgtu312*gtu31*PDstandard4th1gt33) - + PDstandard4th12gt11*SQR(gtu11) - PDstandard4th12gt22*SQR(gtu21) - PDstandard4th12gt33*SQR(gtu31); + + ddgtu2112 = -(gtu11*gtu21*PDstandard4th12gt11) - gtu11*gtu22*PDstandard4th12gt12 - gtu21*gtu31*PDstandard4th12gt13 - + gtu11*gtu32*PDstandard4th12gt13 - gtu21*gtu22*PDstandard4th12gt22 - gtu22*gtu31*PDstandard4th12gt23 - + gtu21*gtu32*PDstandard4th12gt23 - gtu31*gtu32*PDstandard4th12gt33 - dgtu212*gtu11*PDstandard4th1gt11 - + dgtu112*gtu21*PDstandard4th1gt11 - dgtu222*gtu11*PDstandard4th1gt12 - 2*dgtu212*gtu21*PDstandard4th1gt12 - + dgtu112*gtu22*PDstandard4th1gt12 - dgtu322*gtu11*PDstandard4th1gt13 - dgtu312*gtu21*PDstandard4th1gt13 - + dgtu212*gtu31*PDstandard4th1gt13 - dgtu112*gtu32*PDstandard4th1gt13 - dgtu222*gtu21*PDstandard4th1gt22 - + dgtu212*gtu22*PDstandard4th1gt22 - dgtu322*gtu21*PDstandard4th1gt23 - dgtu312*gtu22*PDstandard4th1gt23 - + dgtu222*gtu31*PDstandard4th1gt23 - dgtu212*gtu32*PDstandard4th1gt23 - dgtu322*gtu31*PDstandard4th1gt33 - + dgtu312*gtu32*PDstandard4th1gt33 - PDstandard4th12gt12*SQR(gtu21); + + ddgtu3112 = -(gtu11*gtu31*PDstandard4th12gt11) - gtu21*gtu31*PDstandard4th12gt12 - gtu11*gtu32*PDstandard4th12gt12 - + gtu11*gtu33*PDstandard4th12gt13 - gtu21*gtu32*PDstandard4th12gt22 - gtu31*gtu32*PDstandard4th12gt23 - + gtu21*gtu33*PDstandard4th12gt23 - gtu31*gtu33*PDstandard4th12gt33 - dgtu312*gtu11*PDstandard4th1gt11 - + dgtu112*gtu31*PDstandard4th1gt11 - dgtu322*gtu11*PDstandard4th1gt12 - dgtu312*gtu21*PDstandard4th1gt12 - + dgtu212*gtu31*PDstandard4th1gt12 - dgtu112*gtu32*PDstandard4th1gt12 - dgtu332*gtu11*PDstandard4th1gt13 - + 2*dgtu312*gtu31*PDstandard4th1gt13 - dgtu112*gtu33*PDstandard4th1gt13 - dgtu322*gtu21*PDstandard4th1gt22 - + dgtu212*gtu32*PDstandard4th1gt22 - dgtu332*gtu21*PDstandard4th1gt23 - dgtu322*gtu31*PDstandard4th1gt23 - + dgtu312*gtu32*PDstandard4th1gt23 - dgtu212*gtu33*PDstandard4th1gt23 - dgtu332*gtu31*PDstandard4th1gt33 - + dgtu312*gtu33*PDstandard4th1gt33 - PDstandard4th12gt13*SQR(gtu31); + + ddgtu2212 = -2*(gtu21*gtu22*PDstandard4th12gt12 + gtu21*gtu32*PDstandard4th12gt13 + gtu22*gtu32*PDstandard4th12gt23 + + dgtu212*gtu21*PDstandard4th1gt11 + dgtu222*gtu21*PDstandard4th1gt12 + dgtu212*gtu22*PDstandard4th1gt12 + + dgtu322*gtu21*PDstandard4th1gt13 + dgtu212*gtu32*PDstandard4th1gt13 + dgtu222*gtu22*PDstandard4th1gt22 + + dgtu322*gtu22*PDstandard4th1gt23 + dgtu222*gtu32*PDstandard4th1gt23 + dgtu322*gtu32*PDstandard4th1gt33) - + PDstandard4th12gt11*SQR(gtu21) - PDstandard4th12gt22*SQR(gtu22) - PDstandard4th12gt33*SQR(gtu32); + + ddgtu3212 = -(gtu21*gtu31*PDstandard4th12gt11) - gtu22*gtu31*PDstandard4th12gt12 - gtu21*gtu32*PDstandard4th12gt12 - + gtu31*gtu32*PDstandard4th12gt13 - gtu21*gtu33*PDstandard4th12gt13 - gtu22*gtu32*PDstandard4th12gt22 - + gtu22*gtu33*PDstandard4th12gt23 - gtu32*gtu33*PDstandard4th12gt33 - dgtu312*gtu21*PDstandard4th1gt11 - + dgtu212*gtu31*PDstandard4th1gt11 - dgtu322*gtu21*PDstandard4th1gt12 - dgtu312*gtu22*PDstandard4th1gt12 - + dgtu222*gtu31*PDstandard4th1gt12 - dgtu212*gtu32*PDstandard4th1gt12 - dgtu332*gtu21*PDstandard4th1gt13 - + dgtu322*gtu31*PDstandard4th1gt13 - dgtu312*gtu32*PDstandard4th1gt13 - dgtu212*gtu33*PDstandard4th1gt13 - + dgtu322*gtu22*PDstandard4th1gt22 - dgtu222*gtu32*PDstandard4th1gt22 - dgtu332*gtu22*PDstandard4th1gt23 - + 2*dgtu322*gtu32*PDstandard4th1gt23 - dgtu222*gtu33*PDstandard4th1gt23 - dgtu332*gtu32*PDstandard4th1gt33 - + dgtu322*gtu33*PDstandard4th1gt33 - PDstandard4th12gt23*SQR(gtu32); + + ddgtu1113 = -2*(gtu11*gtu21*PDstandard4th13gt12 + gtu11*gtu31*PDstandard4th13gt13 + gtu21*gtu31*PDstandard4th13gt23 + + dgtu113*gtu11*PDstandard4th1gt11 + dgtu213*gtu11*PDstandard4th1gt12 + dgtu113*gtu21*PDstandard4th1gt12 + + dgtu313*gtu11*PDstandard4th1gt13 + dgtu113*gtu31*PDstandard4th1gt13 + dgtu213*gtu21*PDstandard4th1gt22 + + dgtu313*gtu21*PDstandard4th1gt23 + dgtu213*gtu31*PDstandard4th1gt23 + dgtu313*gtu31*PDstandard4th1gt33) - + PDstandard4th13gt11*SQR(gtu11) - PDstandard4th13gt22*SQR(gtu21) - PDstandard4th13gt33*SQR(gtu31); + + ddgtu2113 = -(gtu11*gtu21*PDstandard4th13gt11) - gtu11*gtu22*PDstandard4th13gt12 - gtu21*gtu31*PDstandard4th13gt13 - + gtu11*gtu32*PDstandard4th13gt13 - gtu21*gtu22*PDstandard4th13gt22 - gtu22*gtu31*PDstandard4th13gt23 - + gtu21*gtu32*PDstandard4th13gt23 - gtu31*gtu32*PDstandard4th13gt33 - dgtu213*gtu11*PDstandard4th1gt11 - + dgtu113*gtu21*PDstandard4th1gt11 - dgtu223*gtu11*PDstandard4th1gt12 - 2*dgtu213*gtu21*PDstandard4th1gt12 - + dgtu113*gtu22*PDstandard4th1gt12 - dgtu323*gtu11*PDstandard4th1gt13 - dgtu313*gtu21*PDstandard4th1gt13 - + dgtu213*gtu31*PDstandard4th1gt13 - dgtu113*gtu32*PDstandard4th1gt13 - dgtu223*gtu21*PDstandard4th1gt22 - + dgtu213*gtu22*PDstandard4th1gt22 - dgtu323*gtu21*PDstandard4th1gt23 - dgtu313*gtu22*PDstandard4th1gt23 - + dgtu223*gtu31*PDstandard4th1gt23 - dgtu213*gtu32*PDstandard4th1gt23 - dgtu323*gtu31*PDstandard4th1gt33 - + dgtu313*gtu32*PDstandard4th1gt33 - PDstandard4th13gt12*SQR(gtu21); + + ddgtu3113 = -(gtu11*gtu31*PDstandard4th13gt11) - gtu21*gtu31*PDstandard4th13gt12 - gtu11*gtu32*PDstandard4th13gt12 - + gtu11*gtu33*PDstandard4th13gt13 - gtu21*gtu32*PDstandard4th13gt22 - gtu31*gtu32*PDstandard4th13gt23 - + gtu21*gtu33*PDstandard4th13gt23 - gtu31*gtu33*PDstandard4th13gt33 - dgtu313*gtu11*PDstandard4th1gt11 - + dgtu113*gtu31*PDstandard4th1gt11 - dgtu323*gtu11*PDstandard4th1gt12 - dgtu313*gtu21*PDstandard4th1gt12 - + dgtu213*gtu31*PDstandard4th1gt12 - dgtu113*gtu32*PDstandard4th1gt12 - dgtu333*gtu11*PDstandard4th1gt13 - + 2*dgtu313*gtu31*PDstandard4th1gt13 - dgtu113*gtu33*PDstandard4th1gt13 - dgtu323*gtu21*PDstandard4th1gt22 - + dgtu213*gtu32*PDstandard4th1gt22 - dgtu333*gtu21*PDstandard4th1gt23 - dgtu323*gtu31*PDstandard4th1gt23 - + dgtu313*gtu32*PDstandard4th1gt23 - dgtu213*gtu33*PDstandard4th1gt23 - dgtu333*gtu31*PDstandard4th1gt33 - + dgtu313*gtu33*PDstandard4th1gt33 - PDstandard4th13gt13*SQR(gtu31); + + ddgtu3213 = -(gtu21*gtu31*PDstandard4th13gt11) - gtu22*gtu31*PDstandard4th13gt12 - gtu21*gtu32*PDstandard4th13gt12 - + gtu31*gtu32*PDstandard4th13gt13 - gtu21*gtu33*PDstandard4th13gt13 - gtu22*gtu32*PDstandard4th13gt22 - + gtu22*gtu33*PDstandard4th13gt23 - gtu32*gtu33*PDstandard4th13gt33 - dgtu313*gtu21*PDstandard4th1gt11 - + dgtu213*gtu31*PDstandard4th1gt11 - dgtu323*gtu21*PDstandard4th1gt12 - dgtu313*gtu22*PDstandard4th1gt12 - + dgtu223*gtu31*PDstandard4th1gt12 - dgtu213*gtu32*PDstandard4th1gt12 - dgtu333*gtu21*PDstandard4th1gt13 - + dgtu323*gtu31*PDstandard4th1gt13 - dgtu313*gtu32*PDstandard4th1gt13 - dgtu213*gtu33*PDstandard4th1gt13 - + dgtu323*gtu22*PDstandard4th1gt22 - dgtu223*gtu32*PDstandard4th1gt22 - dgtu333*gtu22*PDstandard4th1gt23 - + 2*dgtu323*gtu32*PDstandard4th1gt23 - dgtu223*gtu33*PDstandard4th1gt23 - dgtu333*gtu32*PDstandard4th1gt33 - + dgtu323*gtu33*PDstandard4th1gt33 - PDstandard4th13gt23*SQR(gtu32); + + ddgtu3313 = -2*(gtu31*gtu32*PDstandard4th13gt12 + gtu31*gtu33*PDstandard4th13gt13 + gtu32*gtu33*PDstandard4th13gt23 + + dgtu313*gtu31*PDstandard4th1gt11 + dgtu323*gtu31*PDstandard4th1gt12 + dgtu313*gtu32*PDstandard4th1gt12 + + dgtu333*gtu31*PDstandard4th1gt13 + dgtu313*gtu33*PDstandard4th1gt13 + dgtu323*gtu32*PDstandard4th1gt22 + + dgtu333*gtu32*PDstandard4th1gt23 + dgtu323*gtu33*PDstandard4th1gt23 + dgtu333*gtu33*PDstandard4th1gt33) - + PDstandard4th13gt11*SQR(gtu31) - PDstandard4th13gt22*SQR(gtu32) - PDstandard4th13gt33*SQR(gtu33); + + ddgtu2122 = -(gtu11*gtu21*PDstandard4th22gt11) - gtu11*gtu22*PDstandard4th22gt12 - gtu21*gtu31*PDstandard4th22gt13 - + gtu11*gtu32*PDstandard4th22gt13 - gtu21*gtu22*PDstandard4th22gt22 - gtu22*gtu31*PDstandard4th22gt23 - + gtu21*gtu32*PDstandard4th22gt23 - gtu31*gtu32*PDstandard4th22gt33 - dgtu212*gtu11*PDstandard4th2gt11 - + dgtu112*gtu21*PDstandard4th2gt11 - dgtu222*gtu11*PDstandard4th2gt12 - 2*dgtu212*gtu21*PDstandard4th2gt12 - + dgtu112*gtu22*PDstandard4th2gt12 - dgtu322*gtu11*PDstandard4th2gt13 - dgtu312*gtu21*PDstandard4th2gt13 - + dgtu212*gtu31*PDstandard4th2gt13 - dgtu112*gtu32*PDstandard4th2gt13 - dgtu222*gtu21*PDstandard4th2gt22 - + dgtu212*gtu22*PDstandard4th2gt22 - dgtu322*gtu21*PDstandard4th2gt23 - dgtu312*gtu22*PDstandard4th2gt23 - + dgtu222*gtu31*PDstandard4th2gt23 - dgtu212*gtu32*PDstandard4th2gt23 - dgtu322*gtu31*PDstandard4th2gt33 - + dgtu312*gtu32*PDstandard4th2gt33 - PDstandard4th22gt12*SQR(gtu21); + + ddgtu2222 = -2*(gtu21*gtu22*PDstandard4th22gt12 + gtu21*gtu32*PDstandard4th22gt13 + gtu22*gtu32*PDstandard4th22gt23 + + dgtu212*gtu21*PDstandard4th2gt11 + dgtu222*gtu21*PDstandard4th2gt12 + dgtu212*gtu22*PDstandard4th2gt12 + + dgtu322*gtu21*PDstandard4th2gt13 + dgtu212*gtu32*PDstandard4th2gt13 + dgtu222*gtu22*PDstandard4th2gt22 + + dgtu322*gtu22*PDstandard4th2gt23 + dgtu222*gtu32*PDstandard4th2gt23 + dgtu322*gtu32*PDstandard4th2gt33) - + PDstandard4th22gt11*SQR(gtu21) - PDstandard4th22gt22*SQR(gtu22) - PDstandard4th22gt33*SQR(gtu32); + + ddgtu3222 = -(gtu21*gtu31*PDstandard4th22gt11) - gtu22*gtu31*PDstandard4th22gt12 - gtu21*gtu32*PDstandard4th22gt12 - + gtu31*gtu32*PDstandard4th22gt13 - gtu21*gtu33*PDstandard4th22gt13 - gtu22*gtu32*PDstandard4th22gt22 - + gtu22*gtu33*PDstandard4th22gt23 - gtu32*gtu33*PDstandard4th22gt33 - dgtu312*gtu21*PDstandard4th2gt11 - + dgtu212*gtu31*PDstandard4th2gt11 - dgtu322*gtu21*PDstandard4th2gt12 - dgtu312*gtu22*PDstandard4th2gt12 - + dgtu222*gtu31*PDstandard4th2gt12 - dgtu212*gtu32*PDstandard4th2gt12 - dgtu332*gtu21*PDstandard4th2gt13 - + dgtu322*gtu31*PDstandard4th2gt13 - dgtu312*gtu32*PDstandard4th2gt13 - dgtu212*gtu33*PDstandard4th2gt13 - + dgtu322*gtu22*PDstandard4th2gt22 - dgtu222*gtu32*PDstandard4th2gt22 - dgtu332*gtu22*PDstandard4th2gt23 - + 2*dgtu322*gtu32*PDstandard4th2gt23 - dgtu222*gtu33*PDstandard4th2gt23 - dgtu332*gtu32*PDstandard4th2gt33 - + dgtu322*gtu33*PDstandard4th2gt33 - PDstandard4th22gt23*SQR(gtu32); + + ddgtu2123 = -(gtu11*gtu21*PDstandard4th23gt11) - gtu11*gtu22*PDstandard4th23gt12 - gtu21*gtu31*PDstandard4th23gt13 - + gtu11*gtu32*PDstandard4th23gt13 - gtu21*gtu22*PDstandard4th23gt22 - gtu22*gtu31*PDstandard4th23gt23 - + gtu21*gtu32*PDstandard4th23gt23 - gtu31*gtu32*PDstandard4th23gt33 - dgtu213*gtu11*PDstandard4th2gt11 - + dgtu113*gtu21*PDstandard4th2gt11 - dgtu223*gtu11*PDstandard4th2gt12 - 2*dgtu213*gtu21*PDstandard4th2gt12 - + dgtu113*gtu22*PDstandard4th2gt12 - dgtu323*gtu11*PDstandard4th2gt13 - dgtu313*gtu21*PDstandard4th2gt13 - + dgtu213*gtu31*PDstandard4th2gt13 - dgtu113*gtu32*PDstandard4th2gt13 - dgtu223*gtu21*PDstandard4th2gt22 - + dgtu213*gtu22*PDstandard4th2gt22 - dgtu323*gtu21*PDstandard4th2gt23 - dgtu313*gtu22*PDstandard4th2gt23 - + dgtu223*gtu31*PDstandard4th2gt23 - dgtu213*gtu32*PDstandard4th2gt23 - dgtu323*gtu31*PDstandard4th2gt33 - + dgtu313*gtu32*PDstandard4th2gt33 - PDstandard4th23gt12*SQR(gtu21); + + ddgtu3123 = -(gtu11*gtu31*PDstandard4th23gt11) - gtu21*gtu31*PDstandard4th23gt12 - gtu11*gtu32*PDstandard4th23gt12 - + gtu11*gtu33*PDstandard4th23gt13 - gtu21*gtu32*PDstandard4th23gt22 - gtu31*gtu32*PDstandard4th23gt23 - + gtu21*gtu33*PDstandard4th23gt23 - gtu31*gtu33*PDstandard4th23gt33 - dgtu313*gtu11*PDstandard4th2gt11 - + dgtu113*gtu31*PDstandard4th2gt11 - dgtu323*gtu11*PDstandard4th2gt12 - dgtu313*gtu21*PDstandard4th2gt12 - + dgtu213*gtu31*PDstandard4th2gt12 - dgtu113*gtu32*PDstandard4th2gt12 - dgtu333*gtu11*PDstandard4th2gt13 - + 2*dgtu313*gtu31*PDstandard4th2gt13 - dgtu113*gtu33*PDstandard4th2gt13 - dgtu323*gtu21*PDstandard4th2gt22 - + dgtu213*gtu32*PDstandard4th2gt22 - dgtu333*gtu21*PDstandard4th2gt23 - dgtu323*gtu31*PDstandard4th2gt23 - + dgtu313*gtu32*PDstandard4th2gt23 - dgtu213*gtu33*PDstandard4th2gt23 - dgtu333*gtu31*PDstandard4th2gt33 - + dgtu313*gtu33*PDstandard4th2gt33 - PDstandard4th23gt13*SQR(gtu31); + + ddgtu2223 = -2*(gtu21*gtu22*PDstandard4th23gt12 + gtu21*gtu32*PDstandard4th23gt13 + gtu22*gtu32*PDstandard4th23gt23 + + dgtu213*gtu21*PDstandard4th2gt11 + dgtu223*gtu21*PDstandard4th2gt12 + dgtu213*gtu22*PDstandard4th2gt12 + + dgtu323*gtu21*PDstandard4th2gt13 + dgtu213*gtu32*PDstandard4th2gt13 + dgtu223*gtu22*PDstandard4th2gt22 + + dgtu323*gtu22*PDstandard4th2gt23 + dgtu223*gtu32*PDstandard4th2gt23 + dgtu323*gtu32*PDstandard4th2gt33) - + PDstandard4th23gt11*SQR(gtu21) - PDstandard4th23gt22*SQR(gtu22) - PDstandard4th23gt33*SQR(gtu32); + + ddgtu3223 = -(gtu21*gtu31*PDstandard4th23gt11) - gtu22*gtu31*PDstandard4th23gt12 - gtu21*gtu32*PDstandard4th23gt12 - + gtu31*gtu32*PDstandard4th23gt13 - gtu21*gtu33*PDstandard4th23gt13 - gtu22*gtu32*PDstandard4th23gt22 - + gtu22*gtu33*PDstandard4th23gt23 - gtu32*gtu33*PDstandard4th23gt33 - dgtu313*gtu21*PDstandard4th2gt11 - + dgtu213*gtu31*PDstandard4th2gt11 - dgtu323*gtu21*PDstandard4th2gt12 - dgtu313*gtu22*PDstandard4th2gt12 - + dgtu223*gtu31*PDstandard4th2gt12 - dgtu213*gtu32*PDstandard4th2gt12 - dgtu333*gtu21*PDstandard4th2gt13 - + dgtu323*gtu31*PDstandard4th2gt13 - dgtu313*gtu32*PDstandard4th2gt13 - dgtu213*gtu33*PDstandard4th2gt13 - + dgtu323*gtu22*PDstandard4th2gt22 - dgtu223*gtu32*PDstandard4th2gt22 - dgtu333*gtu22*PDstandard4th2gt23 - + 2*dgtu323*gtu32*PDstandard4th2gt23 - dgtu223*gtu33*PDstandard4th2gt23 - dgtu333*gtu32*PDstandard4th2gt33 - + dgtu323*gtu33*PDstandard4th2gt33 - PDstandard4th23gt23*SQR(gtu32); + + ddgtu3323 = -2*(gtu31*gtu32*PDstandard4th23gt12 + gtu31*gtu33*PDstandard4th23gt13 + gtu32*gtu33*PDstandard4th23gt23 + + dgtu313*gtu31*PDstandard4th2gt11 + dgtu323*gtu31*PDstandard4th2gt12 + dgtu313*gtu32*PDstandard4th2gt12 + + dgtu333*gtu31*PDstandard4th2gt13 + dgtu313*gtu33*PDstandard4th2gt13 + dgtu323*gtu32*PDstandard4th2gt22 + + dgtu333*gtu32*PDstandard4th2gt23 + dgtu323*gtu33*PDstandard4th2gt23 + dgtu333*gtu33*PDstandard4th2gt33) - + PDstandard4th23gt11*SQR(gtu31) - PDstandard4th23gt22*SQR(gtu32) - PDstandard4th23gt33*SQR(gtu33); + + ddgtu3133 = -(gtu11*gtu31*PDstandard4th33gt11) - gtu21*gtu31*PDstandard4th33gt12 - gtu11*gtu32*PDstandard4th33gt12 - + gtu11*gtu33*PDstandard4th33gt13 - gtu21*gtu32*PDstandard4th33gt22 - gtu31*gtu32*PDstandard4th33gt23 - + gtu21*gtu33*PDstandard4th33gt23 - gtu31*gtu33*PDstandard4th33gt33 - dgtu313*gtu11*PDstandard4th3gt11 - + dgtu113*gtu31*PDstandard4th3gt11 - dgtu323*gtu11*PDstandard4th3gt12 - dgtu313*gtu21*PDstandard4th3gt12 - + dgtu213*gtu31*PDstandard4th3gt12 - dgtu113*gtu32*PDstandard4th3gt12 - dgtu333*gtu11*PDstandard4th3gt13 - + 2*dgtu313*gtu31*PDstandard4th3gt13 - dgtu113*gtu33*PDstandard4th3gt13 - dgtu323*gtu21*PDstandard4th3gt22 - + dgtu213*gtu32*PDstandard4th3gt22 - dgtu333*gtu21*PDstandard4th3gt23 - dgtu323*gtu31*PDstandard4th3gt23 - + dgtu313*gtu32*PDstandard4th3gt23 - dgtu213*gtu33*PDstandard4th3gt23 - dgtu333*gtu31*PDstandard4th3gt33 - + dgtu313*gtu33*PDstandard4th3gt33 - PDstandard4th33gt13*SQR(gtu31); + + ddgtu3233 = -(gtu21*gtu31*PDstandard4th33gt11) - gtu22*gtu31*PDstandard4th33gt12 - gtu21*gtu32*PDstandard4th33gt12 - + gtu31*gtu32*PDstandard4th33gt13 - gtu21*gtu33*PDstandard4th33gt13 - gtu22*gtu32*PDstandard4th33gt22 - + gtu22*gtu33*PDstandard4th33gt23 - gtu32*gtu33*PDstandard4th33gt33 - dgtu313*gtu21*PDstandard4th3gt11 - + dgtu213*gtu31*PDstandard4th3gt11 - dgtu323*gtu21*PDstandard4th3gt12 - dgtu313*gtu22*PDstandard4th3gt12 - + dgtu223*gtu31*PDstandard4th3gt12 - dgtu213*gtu32*PDstandard4th3gt12 - dgtu333*gtu21*PDstandard4th3gt13 - + dgtu323*gtu31*PDstandard4th3gt13 - dgtu313*gtu32*PDstandard4th3gt13 - dgtu213*gtu33*PDstandard4th3gt13 - + dgtu323*gtu22*PDstandard4th3gt22 - dgtu223*gtu32*PDstandard4th3gt22 - dgtu333*gtu22*PDstandard4th3gt23 - + 2*dgtu323*gtu32*PDstandard4th3gt23 - dgtu223*gtu33*PDstandard4th3gt23 - dgtu333*gtu32*PDstandard4th3gt33 - + dgtu323*gtu33*PDstandard4th3gt33 - PDstandard4th33gt23*SQR(gtu32); + + ddgtu3333 = -2*(gtu31*gtu32*PDstandard4th33gt12 + gtu31*gtu33*PDstandard4th33gt13 + gtu32*gtu33*PDstandard4th33gt23 + + dgtu313*gtu31*PDstandard4th3gt11 + dgtu323*gtu31*PDstandard4th3gt12 + dgtu313*gtu32*PDstandard4th3gt12 + + dgtu333*gtu31*PDstandard4th3gt13 + dgtu313*gtu33*PDstandard4th3gt13 + dgtu323*gtu32*PDstandard4th3gt22 + + dgtu333*gtu32*PDstandard4th3gt23 + dgtu323*gtu33*PDstandard4th3gt23 + dgtu333*gtu33*PDstandard4th3gt33) - + PDstandard4th33gt11*SQR(gtu31) - PDstandard4th33gt22*SQR(gtu32) - PDstandard4th33gt33*SQR(gtu33); + + Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - + gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); + + Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - + gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); + + Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - + gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); + + Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + + gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + + Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + + gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + + Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + + gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); + + Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + + gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + + Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + + gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + + Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + + gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); + + Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + + gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + + Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + + gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + + Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + + gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); + + Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu21*PDstandard4th3gt22); + + Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + gtu22*PDstandard4th3gt22); - Gt332 = khalf*(gtu33*PDstandard4th2gt33 + gtu13*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu23*PDstandard4th3gt22); - - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu12*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt31 + - 2*gtu12*PDstandard4th3gt32 + gtu13*PDstandard4th3gt33); - - Gt233 = khalf*(-(gtu12*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu12*PDstandard4th3gt31 + - 2*gtu22*PDstandard4th3gt32 + gtu23*PDstandard4th3gt33); - - Gt333 = khalf*(-(gtu13*PDstandard4th1gt33) - gtu23*PDstandard4th2gt33 + 2*gtu13*PDstandard4th3gt31 + - 2*gtu23*PDstandard4th3gt32 + gtu33*PDstandard4th3gt33); - - Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu12* - (2*Gt211*Gt221*gt22L + 4*gt21L*Gt232*Gt311 + 6*Gt121*Gt311*gt31L + 4*gt11L*Gt131*Gt321 + 4*Gt221*gt31L*Gt321 + - 4*Gt211*gt31L*Gt322 + 2*Gt221*Gt311*gt32L + 2*Gt211*Gt321*gt32L + 4*gt31L*Gt321*Gt331 + 4*Gt311*gt31L*Gt332 + - 2*Gt311*Gt321*gt33L - PDstandard4th12gt11) + - gtu13*(2*Gt231*Gt311*gt32L + 4*gt11L*Gt131*Gt331 + 2*Gt211*gt32L*Gt331 + 4*Gt211*gt31L*Gt332 + - 4*Gt311*gt31L*Gt333 + 2*Gt311*Gt331*gt33L - PDstandard4th13gt11) + 2*gt11L*PDstandard4th1Xt1 + - gt21L*(6*Gt111*Gt221*gtu12 + 4*Gt211*Gt222*gtu12 + 6*Gt131*Gt211*gtu13 + 6*Gt121*Gt221*gtu22 + - 6*Gt131*Gt221*gtu23 + 6*Gt131*Gt231*gtu33 + 2*PDstandard4th1Xt2) + 2*gt31L*PDstandard4th1Xt3 - - gtu22*khalf*PDstandard4th22gt11 - gtu23*PDstandard4th23gt11 - gtu33*khalf*PDstandard4th33gt11 + - Gt111*(10*gt11L*Gt131*gtu13 + 6*gt21L*Gt231*gtu13 + 2*gt11L*Xt1L) + - Gt211*(4*gt11L*Gt121*gtu11 + 6*Gt111*gt21L*gtu11 + 4*gt31L*Gt321*gtu11 + 2*Gt311*gt32L*gtu11 + - 4*gt11L*Gt122*gtu12 + 4*gt11L*Gt132*gtu13 + 2*gt22L*Gt231*gtu13 + 4*gt21L*Gt232*gtu13 + 2*gt21L*Xt1L) + - Gt311*(4*gt21L*Gt231*gtu11 + 6*Gt111*gt31L*gtu11 + 4*gt11L*Gt132*gtu12 + 4*gt11L*Gt133*gtu13 + - 4*gt21L*Gt233*gtu13 + 6*Gt131*gt31L*gtu13 + 2*gt31L*Xt1L) + - Gt121*(10*Gt111*gt11L*gtu12 + 6*Gt211*gt21L*gtu12 + 4*gt11L*Gt231*gtu13 + 6*gt31L*Gt321*gtu22 + - 10*gt11L*Gt131*gtu23 + 2*gt11L*Xt2L) + Gt221* - (4*gt31L*Gt322*gtu22 + 2*Gt321*gt32L*gtu22 + 2*gt22L*Gt231*gtu23 + 2*gt32L*Gt331*gtu23 + 4*gt31L*Gt332*gtu23 + - 2*gt21L*Xt2L) + Gt321*(4*gt21L*Gt231*gtu12 + 6*Gt111*gt31L*gtu12 + 4*Gt231*gt31L*gtu13 + 4*gt11L*Gt132*gtu22 + - 4*gt31L*Gt332*gtu22 + 4*gt11L*Gt133*gtu23 + 4*gt21L*Gt233*gtu23 + 6*Gt131*gt31L*gtu23 + 2*gt31L*Xt2L) + - 2*gt11L*Gt131*Xt3L + Gt231*(4*gt11L*Gt122*gtu23 + 6*Gt121*gt21L*gtu23 + 4*gt31L*Gt322*gtu23 + 2*Gt321*gt32L*gtu23 + - 4*gt11L*Gt132*gtu33 + 2*gt32L*Gt331*gtu33 + 4*gt31L*Gt332*gtu33 + 2*gt21L*Xt3L) + - Gt331*(4*gt21L*Gt231*gtu13 + 6*Gt111*gt31L*gtu13 + 4*gt11L*Gt132*gtu23 + 4*gt21L*Gt232*gtu23 + - 6*Gt121*gt31L*gtu23 + 2*Gt321*gt33L*gtu23 + 4*gt11L*Gt133*gtu33 + 4*gt21L*Gt233*gtu33 + 6*Gt131*gt31L*gtu33 + - 4*gt31L*Gt333*gtu33 + 2*gt31L*Xt3L) + 5*gt11L*gtu11*SQR(Gt111) + 5*gt11L*gtu22*SQR(Gt121) + - 5*gt11L*gtu33*SQR(Gt131) + gt22L*gtu11*SQR(Gt211) + gt22L*gtu22*SQR(Gt221) + - 4*(Gt211*gt21L*Gt221*gtu11 + gt11L*Gt131*Gt311*gtu11 + Gt311*gt31L*Gt331*gtu11 + gt11L*Gt121*Gt221*gtu12 + - gt21L*Gt221*Gt231*gtu13 + gt11L*Gt122*Gt221*gtu22 + gt21L*Gt221*Gt222*gtu22 + gt21L*Gt232*Gt321*gtu22 + - gt11L*Gt132*Gt221*gtu23 + gt21L*Gt222*Gt231*gtu23 + gt21L*Gt221*Gt232*gtu23 + gt31L*Gt331*Gt332*gtu23 + - gt31L*Gt321*Gt333*gtu23 + gt21L*Gt231*Gt232*gtu33 + gt21L*gtu12*SQR(Gt221)) + gt22L*gtu33*SQR(Gt231) + - gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt321) + 4*gt31L*gtu13*SQR(Gt331) + gt33L*gtu33*SQR(Gt331); - - Rt21 = gt22L*PDstandard4th1Xt2 + gt32L*PDstandard4th1Xt3 + gt11L*PDstandard4th2Xt1 + - gt21L*(PDstandard4th1Xt1 + PDstandard4th2Xt2) + gt31L*PDstandard4th2Xt3 + - khalf*(-(gtu11*PDstandard4th11gt21) - 2*gtu12*PDstandard4th12gt21 - 2*gtu13*PDstandard4th13gt21 - - gtu22*PDstandard4th22gt21 - 2*gtu23*PDstandard4th23gt21 - gtu33*PDstandard4th33gt21) + - (gt11L*Gt121 + gt21L*(Gt111 + Gt221) + Gt211*gt22L + gt31L*Gt321 + Gt311*gt32L)*Xt1L + - (gt11L*Gt122 + gt21L*(Gt121 + Gt222) + Gt221*gt22L + gt31L*Gt322 + Gt321*gt32L)*Xt2L + - (gt11L*Gt132 + gt22L*Gt231 + gt21L*(Gt131 + Gt232) + gt32L*Gt331 + gt31L*Gt332)*Xt3L + - gtu11*(gt11L*(Gt121*(3*Gt111 + 2*Gt221) + 2*Gt131*Gt321) + - Gt111*(gt21L*Gt221 + gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - Gt211*(5*Gt121*gt21L + 3*(Gt221*gt22L + Gt321*gt32L)) + gt31L*(3*Gt121*Gt311 + 2*Gt321*(Gt221 + Gt331)) + - Gt311*(Gt221*gt32L + Gt321*gt33L) + 2*(Gt311*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + - gt21L*(Gt231*Gt321 + SQR(Gt111) + SQR(Gt221)))) + - gtu22*(gt11L*(Gt122*(3*Gt121 + 2*Gt222) + 2*Gt132*Gt322) + - Gt121*(gt21L*Gt222 + gt31L*Gt322 + 2*(Gt221*gt22L + Gt321*gt32L)) + - Gt221*(5*Gt122*gt21L + 3*(Gt222*gt22L + Gt322*gt32L)) + gt31L*(3*Gt122*Gt321 + 2*Gt322*(Gt222 + Gt332)) + - Gt321*(Gt222*gt32L + Gt322*gt33L) + 2*(Gt321*(Gt132*gt21L + gt22L*Gt232 + gt32L*Gt332) + - gt21L*(Gt232*Gt322 + SQR(Gt121) + SQR(Gt222)))) + - gtu33*(gt11L*(Gt132*(3*Gt131 + 2*Gt232) + 2*Gt133*Gt332) + - Gt131*(gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331) + gt31L*Gt332) + - Gt231*(5*Gt132*gt21L + 3*(gt22L*Gt232 + gt32L*Gt332)) + - Gt331*(3*Gt132*gt31L + gt32L*(Gt232 + 2*Gt333) + Gt332*gt33L) + - 2*((Gt133*gt21L + gt22L*Gt233)*Gt331 + Gt332*(gt21L*Gt233 + gt31L*(Gt232 + Gt333)) + - gt21L*(SQR(Gt131) + SQR(Gt232)))) + gtu12* - (Gt122*(Gt111*gt11L + 3*Gt211*gt21L + Gt311*gt31L) + - gt21L*(Gt111*Gt222 + Gt221*(4*Gt121 + 2*Gt222) + 2*(Gt132*Gt311 + Gt232*Gt321)) + - gt31L*((Gt111 + 2*Gt221)*Gt322 + Gt321*(4*Gt121 + 2*Gt332)) + - gt32L*(2*Gt221*Gt321 + 3*Gt211*Gt322 + Gt311*(Gt222 + 2*Gt332)) + - gt11L*(2*(Gt122*Gt221 + Gt132*Gt321) + 3*SQR(Gt121)) + gt22L*(3*Gt211*Gt222 + 2*Gt232*Gt311 + SQR(Gt221)) + - 2*(gt11L*(Gt111*Gt122 + Gt121*Gt222 + Gt131*Gt322) + - gt21L*(Gt122*Gt211 + Gt121*(Gt111 + Gt221) + Gt221*Gt222 + Gt131*Gt321 + Gt231*Gt322) + - Gt111*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + gt31L*(Gt122*Gt311 + Gt222*Gt321 + Gt322*Gt331) + - gt32L*(Gt121*Gt311 + Gt321*(Gt221 + Gt331)) + gt22L*(Gt121*Gt211 + Gt231*Gt321 + SQR(Gt221))) + - gt33L*(Gt311*Gt322 + SQR(Gt321))) + gtu13* - (gt22L*(3*Gt211*Gt232 + 2*Gt233*Gt311) + Gt132*(Gt111*gt11L + 3*Gt211*gt21L + Gt311*gt31L) + - gt11L*(3*Gt121*Gt131 + 2*(Gt132*Gt221 + Gt133*Gt321)) + - gt21L*(Gt131*Gt221 + 3*Gt121*Gt231 + Gt111*Gt232 + 2*(Gt133*Gt311 + Gt233*Gt321)) + - Gt221*(gt22L*Gt231 + 2*gt21L*Gt232 + gt32L*Gt331) + gt31L*(3*Gt121*Gt331 + Gt111*Gt332) + - gt32L*(3*Gt211*Gt332 + Gt311*(Gt232 + 2*Gt333)) + Gt311*Gt332*gt33L + - Gt321*(Gt231*gt32L + gt31L*(Gt131 + 2*Gt333) + Gt331*gt33L) + - 2*(Gt111*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + gt22L*(Gt131*Gt211 + Gt231*(Gt221 + Gt331)) + - gt11L*(Gt111*Gt132 + Gt121*Gt232 + Gt131*Gt332) + gt31L*(Gt132*Gt311 + Gt232*Gt321 + (Gt221 + Gt331)*Gt332) + - gt21L*(Gt132*Gt211 + Gt221*Gt232 + Gt131*(Gt111 + Gt331) + Gt231*(Gt121 + Gt332)) + - gt32L*(Gt131*Gt311 + Gt231*Gt321 + SQR(Gt331)))) + - gtu23*(gt22L*(3*Gt221*Gt232 + 2*Gt233*Gt321) + Gt132*(gt11L*Gt121 + 3*gt21L*Gt221 + gt31L*Gt321) + - gt11L*(3*Gt122*Gt131 + 2*(Gt132*Gt222 + Gt133*Gt322)) + - gt21L*(Gt131*Gt222 + 3*Gt122*Gt231 + Gt121*Gt232 + 2*(Gt133*Gt321 + Gt233*Gt322)) + - Gt222*(gt22L*Gt231 + 2*gt21L*Gt232 + gt32L*Gt331) + gt31L*(3*Gt122*Gt331 + Gt121*Gt332) + - gt32L*(3*Gt221*Gt332 + Gt321*(Gt232 + 2*Gt333)) + Gt321*Gt332*gt33L + - Gt322*(Gt231*gt32L + gt31L*(Gt131 + 2*Gt333) + Gt331*gt33L) + - 2*(Gt131*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + Gt231*(Gt122*gt21L + Gt222*gt22L + Gt322*gt32L) + - Gt121*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + Gt331*(Gt132*gt21L + gt22L*Gt232 + gt32L*Gt332) + - gt11L*(Gt122*Gt232 + Gt132*(Gt121 + Gt332)) + gt21L*(Gt132*Gt221 + Gt232*(Gt222 + Gt332)) + - gt31L*(Gt132*Gt321 + Gt232*Gt322 + Gt222*Gt332 + SQR(Gt332)))); - - Rt31 = gt32L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 + - khalf*(-(gtu11*PDstandard4th11gt31) - 2*gtu12*PDstandard4th12gt31 - 2*gtu13*PDstandard4th13gt31 - - gtu22*PDstandard4th22gt31 - 2*gtu23*PDstandard4th23gt31 - gtu33*PDstandard4th33gt31) + gt11L*PDstandard4th3Xt1 + - gt21L*PDstandard4th3Xt2 + gt31L*(PDstandard4th1Xt1 + PDstandard4th3Xt3) + - (gt11L*Gt131 + gt21L*Gt231 + Gt211*gt32L + gt31L*(Gt111 + Gt331) + Gt311*gt33L)*Xt1L + - (gt11L*Gt132 + gt21L*Gt232 + Gt221*gt32L + gt31L*(Gt121 + Gt332) + Gt321*gt33L)*Xt2L + - (gt11L*Gt133 + gt21L*Gt233 + Gt231*gt32L + gt31L*(Gt131 + Gt333) + Gt331*gt33L)*Xt3L + - gtu12*(gt22L*(Gt221*Gt231 + Gt211*Gt232) + Gt132*(Gt111*gt11L + Gt211*gt21L + 3*Gt311*gt31L) + - gt21L*((Gt121 + 2*Gt222)*Gt231 + Gt232*(Gt111 + 2*Gt331)) + - gt11L*(3*Gt121*Gt131 + 2*(Gt122*Gt231 + Gt132*Gt331)) + gt31L*(Gt121*Gt331 + Gt111*Gt332) + - gt32L*(Gt231*Gt321 + Gt221*Gt331 + Gt211*(2*Gt222 + Gt332)) + (2*Gt211*Gt322 + Gt321*Gt331)*gt33L + - 3*(Gt131*(gt21L*Gt221 + gt31L*Gt321) + Gt311*(Gt232*gt32L + Gt332*gt33L)) + - 2*(gt11L*(Gt111*Gt132 + Gt121*Gt232 + Gt131*Gt332) + gt21L*(Gt132*Gt211 + Gt221*Gt232 + Gt231*Gt332) + - gt31L*(Gt122*Gt211 + Gt121*(2*Gt111 + Gt221) + Gt132*Gt311 + (Gt131 + Gt232)*Gt321 + Gt231*Gt322 + - 2*Gt331*Gt332) + (Gt121*Gt311 + Gt321*(Gt221 + Gt331))*gt33L + Gt111*(Gt221*gt32L + Gt321*gt33L) + - gt32L*(Gt121*Gt211 + Gt231*Gt321 + SQR(Gt221)))) + - gtu23*(Gt233*(Gt221*gt22L + 2*gt31L*Gt322 + Gt321*gt32L) + Gt132*(gt11L*Gt131 + gt21L*Gt231 + 3*gt31L*Gt331) + - Gt232*(Gt131*gt21L + gt22L*Gt231 + 3*gt32L*Gt331) + (Gt131*gt31L + Gt231*gt32L)*Gt332 + - gt21L*((Gt121 + 2*Gt222)*Gt233 + 2*Gt232*Gt333) + gt11L*(3*Gt121*Gt133 + 2*(Gt122*Gt233 + Gt132*Gt333)) + - Gt333*(Gt121*gt31L + Gt221*gt32L + Gt321*gt33L) + 3*(Gt133*(gt21L*Gt221 + gt31L*Gt321) + Gt331*Gt332*gt33L) + - 2*((Gt222*Gt231 + Gt221*(Gt131 + Gt232) + Gt233*Gt321)*gt32L + gt11L*(Gt132*(Gt131 + Gt232) + Gt133*Gt332) + - gt31L*(Gt121*Gt131 + Gt122*Gt231 + Gt133*Gt321 + Gt132*(Gt221 + Gt331) + Gt332*(Gt232 + 2*Gt333)) + - (Gt231*Gt322 + Gt221*Gt332 + Gt321*(Gt131 + Gt333))*gt33L + Gt121*(Gt131*gt31L + Gt231*gt32L + Gt331*gt33L) + - gt21L*(Gt132*Gt231 + Gt233*Gt332 + SQR(Gt232)))) + - gtu11*(Gt231*(Gt211*gt22L + 2*(gt21L*Gt221 + gt31L*Gt321) + 3*Gt311*gt32L) + - gt21L*(3*Gt131*Gt211 + Gt231*(Gt111 + 2*Gt331)) + gt11L*(2*Gt121*Gt231 + Gt131*(3*Gt111 + 2*Gt331)) + - 3*Gt311*Gt331*gt33L + Gt211*(gt32L*Gt331 + 2*Gt321*gt33L) + - gt31L*(5*Gt131*Gt311 + Gt111*Gt331 + 2*(Gt121*Gt211 + SQR(Gt111))) + - 2*(Gt211*(Gt111 + Gt221)*gt32L + Gt111*Gt311*gt33L + gt31L*SQR(Gt331))) + - gtu13*(Gt133*(Gt111*gt11L + Gt211*gt21L + 3*Gt311*gt31L) + gt32L*(3*Gt233*Gt311 + 2*Gt231*(Gt111 + Gt331)) + - gt21L*(Gt111*Gt233 + 2*(Gt231*Gt232 + Gt233*Gt331)) + Gt111*(gt31L*Gt333 + 2*Gt331*gt33L) + - Gt211*(gt22L*Gt233 + gt32L*Gt333 + 2*(Gt132*gt31L + Gt232*gt32L + Gt332*gt33L)) + - gt11L*(2*(Gt132*Gt231 + Gt133*Gt331) + 3*SQR(Gt131)) + gt22L*SQR(Gt231) + gt33L*(3*Gt311*Gt333 + SQR(Gt331)) + - 2*(gt32L*(Gt131*Gt211 + Gt231*(Gt221 + Gt331)) + Gt131*(Gt111*gt31L + 2*(gt21L*Gt231 + gt31L*Gt331)) + - gt11L*(Gt111*Gt133 + Gt121*Gt233 + Gt131*Gt333) + gt21L*(Gt133*Gt211 + Gt221*Gt233 + Gt231*Gt333) + - gt31L*(Gt133*Gt311 + Gt233*Gt321 + Gt131*(Gt111 + Gt331) + Gt231*(Gt121 + Gt332) + 2*Gt331*Gt333) + - gt33L*(Gt131*Gt311 + Gt231*Gt321 + SQR(Gt331)))) + - gtu22*(Gt232*(Gt221*gt22L + 2*(gt21L*Gt222 + gt31L*Gt322) + 3*Gt321*gt32L) + - gt21L*(3*Gt132*Gt221 + Gt232*(Gt121 + 2*Gt332)) + gt11L*(2*Gt122*Gt232 + Gt132*(3*Gt121 + 2*Gt332)) + - 3*Gt321*Gt332*gt33L + Gt221*(gt32L*Gt332 + 2*Gt322*gt33L) + - gt31L*(5*Gt132*Gt321 + Gt121*Gt332 + 2*(Gt122*Gt221 + SQR(Gt121))) + - 2*(Gt221*(Gt121 + Gt222)*gt32L + Gt121*Gt321*gt33L + gt31L*SQR(Gt332))) + - gtu33*(Gt233*(gt22L*Gt231 + 2*gt21L*Gt232 + 3*gt32L*Gt331) + gt21L*(3*Gt133*Gt231 + Gt233*(Gt131 + 2*Gt333)) + - gt11L*(2*Gt132*Gt233 + Gt133*(3*Gt131 + 2*Gt333)) + 3*Gt331*Gt333*gt33L + Gt231*(gt32L*Gt333 + 2*Gt332*gt33L) + - gt31L*(5*Gt133*Gt331 + Gt131*Gt333 + 2*SQR(Gt131)) + - 2*(Gt231*(Gt132*gt31L + (Gt131 + Gt232)*gt32L) + Gt131*Gt331*gt33L + gt31L*(Gt233*Gt332 + SQR(Gt333)))); - - Rt22 = 6*(Gt122*gt21L*Gt221*gtu12 + Gt121*gt21L*Gt222*gtu12 + Gt222*Gt321*gt32L*gtu12 + Gt221*Gt322*gt32L*gtu12 + - Gt132*gt21L*Gt221*gtu13 + Gt122*gt21L*Gt222*gtu22 + Gt132*gt21L*Gt222*gtu23 + Gt232*gt32L*Gt332*gtu33) - - gtu11*khalf*PDstandard4th11gt22 + gtu12*(2*Gt122*gt31L*Gt321 + 4*Gt131*gt21L*Gt322 + 4*Gt121*Gt321*gt32L + - 4*Gt322*gt32L*Gt331 + 4*Gt321*gt32L*Gt332 + 2*Gt321*Gt322*gt33L - PDstandard4th12gt22) - - gtu13*PDstandard4th13gt22 - gtu22*khalf*PDstandard4th22gt22 + - gtu23*(2*Gt132*gt31L*Gt322 + 4*Gt122*gt32L*Gt331 + 4*gt22L*Gt232*Gt332 + 4*Gt322*gt32L*Gt333 + - 2*Gt322*Gt332*gt33L - PDstandard4th23gt22) + 2*gt21L*PDstandard4th2Xt1 + - gt22L*(10*Gt221*Gt222*gtu12 + 4*Gt232*Gt321*gtu12 + 4*Gt132*Gt211*gtu13 + 4*Gt122*Gt221*gtu22 + - 4*Gt132*Gt221*gtu23 + 10*Gt222*Gt232*gtu23 + 4*Gt233*Gt322*gtu23 + 4*Gt132*Gt231*gtu33 + 2*PDstandard4th2Xt2) + - gt32L*(4*Gt121*Gt311*gtu11 + 6*Gt221*Gt321*gtu11 + 4*Gt122*Gt311*gtu12 + 4*Gt132*Gt311*gtu13 + - 6*Gt232*Gt321*gtu13 + 4*Gt121*Gt331*gtu13 + 4*Gt122*Gt321*gtu22 + 6*Gt232*Gt322*gtu23 + 4*Gt132*Gt331*gtu33 + - 2*PDstandard4th2Xt3) - gtu33*khalf*PDstandard4th33gt22 + 2*Gt221*gt22L*Xt1L + - Gt121*(4*Gt111*gt21L*gtu11 + 6*gt21L*Gt221*gtu11 + 2*gt11L*Gt122*gtu12 + 2*gt11L*Gt132*gtu13 + - 4*Gt122*gt21L*gtu22 + 4*Gt132*gt21L*gtu23 + 2*gt21L*Xt1L) + - Gt321*(4*gt22L*Gt231*gtu11 + 2*Gt121*gt31L*gtu11 + 4*gt32L*Gt331*gtu11 + 4*Gt132*gt21L*gtu12 + - 4*Gt133*gt21L*gtu13 + 4*gt22L*Gt233*gtu13 + 2*Gt132*gt31L*gtu13 + 2*Gt332*gt33L*gtu13 + 4*Gt132*gt32L*gtu23 + - 2*gt32L*Xt1L) + 2*Gt222*gt22L*Xt2L + Gt122*(2*gt11L*Gt132*gtu23 + 4*gt22L*Gt231*gtu23 + 2*gt21L*Xt2L) + - Gt322*(4*gt22L*Gt231*gtu12 + 2*Gt121*gt31L*gtu12 + 4*Gt132*gt21L*gtu22 + 2*Gt122*gt31L*gtu22 + - 6*Gt222*gt32L*gtu22 + 4*Gt133*gt21L*gtu23 + 2*gt32L*Xt2L) + 2*Gt132*gt21L*Xt3L + - Gt232*(6*Gt121*gt21L*gtu13 + 10*Gt221*gt22L*gtu13 + 4*gt22L*Gt322*gtu22 + 6*Gt122*gt21L*gtu23 + - 6*Gt132*gt21L*gtu33 + 2*gt22L*Xt3L) + Gt332* - (2*Gt121*gt31L*gtu13 + 6*Gt221*gt32L*gtu13 + 4*Gt322*gt32L*gtu22 + 4*Gt132*gt21L*gtu23 + 2*Gt122*gt31L*gtu23 + - 6*Gt222*gt32L*gtu23 + 4*Gt133*gt21L*gtu33 + 4*gt22L*Gt233*gtu33 + 2*Gt132*gt31L*gtu33 + 2*gt32L*Xt3L) + - gt11L*gtu11*SQR(Gt121) + 4*(Gt121*Gt211*gt22L*gtu11 + Gt131*gt21L*Gt321*gtu11 + Gt111*Gt122*gt21L*gtu12 + - Gt122*Gt211*gt22L*gtu12 + Gt121*Gt221*gt22L*gtu12 + Gt121*Gt131*gt21L*gtu13 + Gt111*Gt132*gt21L*gtu13 + - Gt121*gt22L*Gt231*gtu13 + Gt131*gt21L*Gt332*gtu13 + gt22L*Gt231*Gt332*gtu13 + gt32L*Gt331*Gt332*gtu13 + - Gt321*gt32L*Gt333*gtu13 + Gt122*Gt131*gt21L*gtu23 + Gt131*Gt132*gt21L*gtu33 + gt32L*Gt332*Gt333*gtu33 + - gt21L*gtu12*SQR(Gt121)) + gt11L*gtu22*SQR(Gt122) + gt11L*gtu33*SQR(Gt132) + 5*gt22L*gtu11*SQR(Gt221) + - 5*gt22L*gtu22*SQR(Gt222) + 5*gt22L*gtu33*SQR(Gt232) + gt33L*gtu11*SQR(Gt321) + gt33L*gtu22*SQR(Gt322) + - 4*gt32L*gtu23*SQR(Gt332) + gt33L*gtu33*SQR(Gt332); - - Rt32 = gt31L*PDstandard4th2Xt1 + gt33L*PDstandard4th2Xt3 + - khalf*(-(gtu11*PDstandard4th11gt32) - 2*gtu12*PDstandard4th12gt32 - 2*gtu13*PDstandard4th13gt32 - - gtu22*PDstandard4th22gt32 - 2*gtu23*PDstandard4th23gt32 - gtu33*PDstandard4th33gt32) + gt21L*PDstandard4th3Xt1 + - gt22L*PDstandard4th3Xt2 + gt32L*(PDstandard4th2Xt2 + PDstandard4th3Xt3) + - (Gt131*gt21L + gt22L*Gt231 + Gt121*gt31L + gt32L*(Gt221 + Gt331) + Gt321*gt33L)*Xt1L + - (Gt132*gt21L + gt22L*Gt232 + Gt122*gt31L + gt32L*(Gt222 + Gt332) + Gt322*gt33L)*Xt2L + - (Gt133*gt21L + gt22L*Gt233 + Gt132*gt31L + gt32L*(Gt232 + Gt333) + Gt332*gt33L)*Xt3L + - gtu12*(gt11L*(Gt122*Gt131 + Gt121*Gt132) + gt32L* - (2*(Gt132*Gt311 + Gt131*Gt321) + 5*(Gt232*Gt321 + Gt231*Gt322) + Gt222*(4*Gt221 + Gt331) + - (Gt221 + 4*Gt331)*Gt332) + gt21L*(3*Gt122*Gt231 + Gt132*(Gt221 + 2*Gt331) + Gt131*(Gt222 + 2*Gt332)) + - 3*(Gt121*gt21L*Gt232 + gt22L*(Gt222*Gt231 + Gt221*Gt232) + gt31L*(Gt132*Gt321 + Gt131*Gt322) + - (Gt322*Gt331 + Gt321*Gt332)*gt33L) + 2* - ((Gt122*Gt221 + Gt121*Gt222)*gt31L + Gt111*(Gt132*gt21L + Gt122*gt31L) + - gt22L*(Gt132*Gt211 + Gt131*Gt221 + Gt232*Gt331 + Gt231*Gt332) + (Gt222*Gt321 + Gt221*Gt322)*gt33L + - Gt122*(Gt211*gt32L + Gt311*gt33L) + Gt121*(Gt131*gt21L + Gt221*gt32L + Gt321*gt33L)) + - gt31L*(Gt122*Gt331 + Gt121*Gt332 + 2*SQR(Gt121))) + - gtu13*(gt11L*(Gt131*Gt132 + Gt121*Gt133) + Gt133*(gt21L*Gt221 + 3*gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - gt32L*(5*Gt233*Gt321 + Gt232*(4*Gt221 + Gt331) + Gt231*(2*Gt121 + 5*Gt332) + Gt221*Gt333) + - Gt331*(2*gt22L*Gt233 + Gt132*gt31L + 4*gt32L*Gt333) + - Gt131*(2*(gt22L*Gt231 + Gt121*gt31L + gt32L*Gt331) + gt31L*Gt332 + gt21L*(Gt232 + 2*Gt333)) + - Gt121*(gt31L*Gt333 + 2*Gt331*gt33L) + 3*(Gt231*(Gt132*gt21L + gt22L*Gt232) + (Gt121*gt21L + Gt221*gt22L)*Gt233 + - (Gt331*Gt332 + Gt321*Gt333)*gt33L) + 2* - (Gt111*(Gt133*gt21L + Gt132*gt31L) + gt31L*(Gt132*Gt221 + Gt121*Gt232 + Gt131*Gt332) + gt22L*Gt231*Gt333 + - (Gt232*Gt321 + Gt221*Gt332)*gt33L + Gt132*(Gt211*gt32L + Gt311*gt33L) + gt21L*(Gt133*Gt331 + SQR(Gt131)))) + - gtu11*(Gt131*(gt11L*Gt121 + gt21L*Gt221 + 3*gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - (Gt121*gt31L + Gt221*gt32L)*Gt331 + Gt231*(5*Gt321*gt32L + 2*gt22L*Gt331) + - 3*((Gt121*gt21L + Gt221*gt22L)*Gt231 + Gt321*Gt331*gt33L) + - 2*(Gt111*(Gt131*gt21L + Gt121*gt31L) + Gt131*gt21L*Gt331 + Gt221*Gt321*gt33L + - Gt121*(Gt221*gt31L + Gt211*gt32L + Gt311*gt33L) + gt32L*(SQR(Gt221) + SQR(Gt331)))) + - gtu23*(Gt233*(Gt122*gt21L + Gt222*gt22L + 3*Gt322*gt32L) + - Gt133*(gt11L*Gt122 + 3*gt31L*Gt322 + gt21L*(Gt222 + 2*Gt332)) + - Gt132*(4*gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331 + gt31L*(Gt222 + Gt332))) + - gt32L*(4*Gt232*Gt332 + Gt222*Gt333) + Gt122*(gt31L*Gt333 + 2*Gt331*gt33L) + gt11L*SQR(Gt132) + - 3*(Gt322*Gt333*gt33L + gt22L*SQR(Gt232)) + gt33L*SQR(Gt332) + - 2*(Gt131*(Gt132*gt21L + Gt122*gt31L) + Gt133*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + - gt31L*(Gt122*Gt232 + Gt132*(Gt121 + Gt332)) + Gt233*(Gt122*gt21L + Gt322*gt32L + gt22L*(Gt222 + Gt332)) + - (Gt132*gt21L + gt22L*Gt232)*Gt333 + gt32L* - (Gt132*Gt221 + Gt122*Gt231 + Gt232*(2*Gt222 + Gt332) + 2*Gt332*Gt333) + - gt33L*(Gt132*Gt321 + Gt232*Gt322 + Gt222*Gt332 + SQR(Gt332)))) + - gtu22*(Gt132*(gt11L*Gt122 + gt21L*Gt222 + 3*gt31L*Gt322 + 2*(Gt221*gt22L + Gt321*gt32L)) + - (Gt122*gt31L + Gt222*gt32L)*Gt332 + Gt232*(5*Gt322*gt32L + 2*gt22L*Gt332) + - 3*((Gt122*gt21L + Gt222*gt22L)*Gt232 + Gt322*Gt332*gt33L) + - 2*(Gt121*(Gt132*gt21L + Gt122*gt31L) + Gt132*gt21L*Gt332 + Gt222*Gt322*gt33L + - Gt122*(Gt222*gt31L + Gt221*gt32L + Gt321*gt33L) + gt32L*(SQR(Gt222) + SQR(Gt332)))) + - gtu33*(Gt133*(gt11L*Gt132 + gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331)) + (Gt132*gt31L + Gt232*gt32L)*Gt333 + - Gt233*(5*gt32L*Gt332 + 2*gt22L*Gt333) + 3* - ((Gt132*gt21L + gt22L*Gt232)*Gt233 + Gt332*(Gt133*gt31L + Gt333*gt33L)) + - 2*(Gt131*(Gt133*gt21L + Gt132*gt31L) + Gt133*gt21L*Gt333 + Gt232*Gt332*gt33L + - Gt132*(Gt232*gt31L + Gt231*gt32L + Gt331*gt33L) + gt32L*(SQR(Gt232) + SQR(Gt333)))); - - Rt33 = 6*(Gt133*gt31L*Gt331*gtu13 + Gt233*gt32L*Gt331*gtu13 + Gt131*gt31L*Gt333*gtu13 + Gt231*gt32L*Gt333*gtu13 + - Gt132*gt31L*Gt332*gtu22 + Gt133*gt31L*Gt332*gtu23 + Gt132*gt31L*Gt333*gtu23 + Gt232*gt32L*Gt333*gtu23 + - Gt133*gt31L*Gt333*gtu33) + gtu12*(2*gt22L*Gt231*Gt232 + 4*Gt111*Gt132*gt31L + 4*Gt132*Gt211*gt32L + - 4*Gt221*Gt232*gt32L + 6*Gt132*gt31L*Gt331 + 6*Gt232*gt32L*Gt331 + 6*Gt131*gt31L*Gt332 + 6*Gt231*gt32L*Gt332 + - 4*Gt132*Gt311*gt33L - PDstandard4th12gt33) - gtu13*PDstandard4th13gt33 - gtu22*khalf*PDstandard4th22gt33 - - gtu23*PDstandard4th23gt33 - gtu33*khalf*PDstandard4th33gt33 + - 2*(Gt132*gt21L*Gt231*gtu12 + Gt131*gt21L*Gt232*gtu12 + Gt133*gt21L*Gt231*gtu13 + Gt131*gt21L*Gt233*gtu13 + - gt22L*Gt231*Gt233*gtu13 + Gt132*gt21L*Gt232*gtu22 + gt11L*Gt132*Gt133*gtu23 + Gt132*gt21L*Gt233*gtu23 + - gt22L*Gt232*Gt233*gtu23 + Gt133*gt21L*Gt233*gtu33 + gt31L*PDstandard4th3Xt1) + 2*gt32L*PDstandard4th3Xt2 + - gt33L*(4*Gt231*Gt322*gtu12 + 10*Gt331*Gt332*gtu12 + 4*Gt133*Gt311*gtu13 + 4*Gt231*Gt332*gtu13 + - 10*Gt331*Gt333*gtu13 + 4*Gt132*Gt321*gtu22 + 4*Gt133*Gt321*gtu23 + 4*Gt133*Gt331*gtu33 + 2*PDstandard4th3Xt3) + - 2*Gt231*gt32L*Xt1L + 2*Gt331*gt33L*Xt1L + Gt131* - (2*gt21L*Gt231*gtu11 + 4*Gt111*gt31L*gtu11 + 2*gt11L*Gt132*gtu12 + 2*gt11L*Gt133*gtu13 + 4*Gt132*gt31L*gtu23 + - 4*Gt133*gt31L*gtu33 + 2*gt31L*Xt1L) + 2*Gt132*gt31L*Xt2L + - Gt232*(4*Gt222*gt32L*gtu22 + 6*gt32L*Gt332*gtu22 + 2*Gt133*gt21L*gtu23 + 4*Gt233*gt32L*gtu33 + 2*gt32L*Xt2L) + - Gt332*(4*Gt232*gt33L*gtu23 + 10*Gt333*gt33L*gtu23 + 4*Gt233*gt33L*gtu33 + 2*gt33L*Xt2L) + 2*Gt133*gt31L*Xt3L + - 2*Gt333*gt33L*Xt3L + Gt233*(4*Gt222*gt32L*gtu23 + 6*gt32L*Gt332*gtu23 + 4*Gt132*gt31L*gtu33 + 6*gt32L*Gt333*gtu33 + - 2*gt32L*Xt3L) + gtu11*(4*Gt221*Gt231*gt32L + 6*Gt131*gt31L*Gt331 + 6*Gt231*gt32L*Gt331 + 4*Gt131*Gt311*gt33L + - 4*Gt231*Gt321*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt131)) + - 4*(Gt121*Gt231*gt31L*gtu11 + Gt131*Gt211*gt32L*gtu11 + Gt121*Gt131*gt31L*gtu12 + Gt122*Gt231*gt31L*gtu12 + - Gt121*Gt232*gt31L*gtu12 + Gt131*Gt221*gt32L*gtu12 + Gt222*Gt231*gt32L*gtu12 + Gt131*Gt321*gt33L*gtu12 + - Gt232*Gt321*gt33L*gtu12 + Gt111*Gt133*gt31L*gtu13 + Gt132*Gt231*gt31L*gtu13 + Gt121*Gt233*gt31L*gtu13 + - Gt133*Gt211*gt32L*gtu13 + Gt131*Gt231*gt32L*gtu13 + Gt231*Gt232*gt32L*gtu13 + Gt221*Gt233*gt32L*gtu13 + - Gt233*Gt321*gt33L*gtu13 + Gt131*Gt331*gt33L*gtu13 + Gt121*Gt132*gt31L*gtu22 + Gt122*Gt232*gt31L*gtu22 + - Gt132*Gt221*gt32L*gtu22 + Gt232*Gt322*gt33L*gtu22 + Gt121*Gt133*gt31L*gtu23 + Gt132*Gt232*gt31L*gtu23 + - Gt122*Gt233*gt31L*gtu23 + Gt133*Gt221*gt32L*gtu23 + Gt132*Gt231*gt32L*gtu23 + Gt233*Gt322*gt33L*gtu23 + - Gt132*Gt331*gt33L*gtu23 + Gt133*Gt231*gt32L*gtu33 + gt31L*gtu13*SQR(Gt131)) + gt11L*gtu22*SQR(Gt132) + - gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt231) + gt22L*gtu22*SQR(Gt232) + 4*gt32L*gtu23*SQR(Gt232) + - gt22L*gtu33*SQR(Gt233) + 5*gt33L*gtu11*SQR(Gt331) + 5*gt33L*gtu22*SQR(Gt332) + 5*gt33L*gtu33*SQR(Gt333); - - Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu12*PDstandard4th12phi - - 2*gt11L*gtu13*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu23*PDstandard4th23phi - + Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu32*PDstandard4th3gt22); + + Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + + 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); + + Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + + 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); + + Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + + 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); + + Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu21* + (2*Gt211*Gt212*gt22L + 6*Gt112*gt13L*Gt311 + 4*Gt113*gt11L*Gt312 + 4*gt13L*Gt312*Gt313 + 4*gt13L*Gt211*Gt322 + + 4*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandard4th12gt11) - gtu31*PDstandard4th13gt11 + + 2*gt11L*PDstandard4th1Xt1 + gt12L*(6*Gt111*Gt212*gtu21 + 4*Gt211*Gt222*gtu21 + 4*Gt212*Gt222*gtu22 + + 6*Gt113*Gt211*gtu31 + 6*Gt113*Gt212*gtu32 + 6*Gt113*Gt213*gtu33 + 2*PDstandard4th1Xt2) + + gt13L*(6*Gt111*Gt312*gtu21 + 4*Gt212*Gt312*gtu21 + 6*Gt112*Gt312*gtu22 + 6*Gt113*Gt311*gtu31 + + 6*Gt113*Gt312*gtu32 + 6*Gt113*Gt313*gtu33 + 2*PDstandard4th1Xt3) - gtu22*khalf*PDstandard4th22gt11 + + gtu32*(2*Gt212*Gt213*gt22L + 4*gt12L*Gt233*Gt312 + 2*Gt213*gt23L*Gt312 + 6*Gt112*gt13L*Gt313 + + 4*gt13L*Gt213*Gt322 + 4*gt13L*Gt212*Gt323 + 4*gt13L*Gt313*Gt323 + 4*gt13L*Gt312*Gt333 + 2*Gt312*Gt313*gt33L - + PDstandard4th23gt11) - gtu33*khalf*PDstandard4th33gt11 + + Gt111*(10*Gt113*gt11L*gtu31 + 6*gt12L*Gt213*gtu31 + 2*gt11L*Xt1L) + + Gt211*(4*Gt112*gt11L*gtu11 + 6*Gt111*gt12L*gtu11 + 2*gt23L*Gt311*gtu11 + 4*gt13L*Gt312*gtu11 + + 6*Gt112*gt12L*gtu21 + 4*gt11L*Gt123*gtu31 + 4*gt12L*Gt223*gtu31 + 2*Gt213*gt22L*gtu31 + 2*gt12L*Xt1L) + + Gt311*(6*Gt111*gt13L*gtu11 + 4*gt12L*Gt213*gtu11 + 4*gt13L*Gt313*gtu11 + 4*gt11L*Gt123*gtu21 + + 4*gt12L*Gt223*gtu21 + 2*Gt212*gt23L*gtu21 + 4*gt11L*Gt133*gtu31 + 4*gt12L*Gt233*gtu31 + 2*Gt213*gt23L*gtu31 + + 2*Gt313*gt33L*gtu31 + 2*gt13L*Xt1L) + 2*gt12L*Gt212*Xt2L + + Gt112*(10*Gt111*gt11L*gtu21 + 4*gt11L*Gt212*gtu21 + 6*gt12L*Gt212*gtu22 + 4*gt11L*Gt213*gtu31 + + 10*Gt113*gt11L*gtu32 + 2*gt11L*Xt2L) + Gt312* + (4*gt12L*Gt213*gtu21 + 2*Gt211*gt23L*gtu21 + 4*gt11L*Gt123*gtu22 + 4*gt12L*Gt223*gtu22 + 2*Gt212*gt23L*gtu22 + + 4*gt13L*Gt213*gtu31 + 4*gt11L*Gt133*gtu32 + 2*gt13L*Xt2L) + 2*Gt113*gt11L*Xt3L + + Gt213*(4*gt11L*Gt122*gtu32 + 6*Gt112*gt12L*gtu32 + 4*gt11L*Gt123*gtu33 + 2*gt12L*Xt3L) + + Gt313*(4*Gt113*gt11L*gtu31 + 6*Gt111*gt13L*gtu31 + 4*gt12L*Gt213*gtu31 + 2*Gt211*gt23L*gtu31 + + 4*gt11L*Gt123*gtu32 + 4*gt12L*Gt223*gtu32 + 2*Gt212*gt23L*gtu32 + 4*gt11L*Gt133*gtu33 + 4*gt12L*Gt233*gtu33 + + 2*Gt213*gt23L*gtu33 + 2*gt13L*Xt3L) + 5*gt11L*gtu11*SQR(Gt111) + 5*gt11L*gtu22*SQR(Gt112) + + 5*gt11L*gtu33*SQR(Gt113) + gt22L*gtu11*SQR(Gt211) + gt22L*gtu22*SQR(Gt212) + + 4*(gt12L*Gt211*Gt212*gtu11 + Gt113*gt11L*Gt311*gtu11 + gt11L*Gt122*Gt211*gtu21 + gt11L*Gt122*Gt212*gtu22 + + gt13L*Gt212*Gt322*gtu22 + gt13L*Gt312*Gt323*gtu22 + gt12L*Gt212*Gt213*gtu31 + gt13L*Gt211*Gt323*gtu31 + + gt13L*Gt311*Gt333*gtu31 + gt11L*Gt123*Gt212*gtu32 + gt12L*Gt213*Gt222*gtu32 + gt12L*Gt212*Gt223*gtu32 + + gt12L*Gt213*Gt223*gtu33 + gt13L*Gt213*Gt323*gtu33 + gt13L*Gt313*Gt333*gtu33 + gt12L*gtu21*SQR(Gt212)) + + gt22L*gtu33*SQR(Gt213) + gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt312) + 4*gt13L*gtu31*SQR(Gt313) + + gt33L*gtu33*SQR(Gt313); + + Rt12 = gt22L*PDstandard4th1Xt2 + gt23L*PDstandard4th1Xt3 + gt11L*PDstandard4th2Xt1 + + gt12L*(PDstandard4th1Xt1 + PDstandard4th2Xt2) + gt13L*PDstandard4th2Xt3 + + khalf*(-(gtu11*PDstandard4th11gt12) - 2*gtu21*PDstandard4th12gt12 - 2*gtu31*PDstandard4th13gt12 - + gtu22*PDstandard4th22gt12 - 2*gtu32*PDstandard4th23gt12 - gtu33*PDstandard4th33gt12) + + (Gt112*gt11L + gt12L*(Gt111 + Gt212) + Gt211*gt22L + gt23L*Gt311 + gt13L*Gt312)*Xt1L + + (gt11L*Gt122 + gt12L*(Gt112 + Gt222) + Gt212*gt22L + gt23L*Gt312 + gt13L*Gt322)*Xt2L + + (gt11L*Gt123 + gt12L*(Gt113 + Gt223) + Gt213*gt22L + gt23L*Gt313 + gt13L*Gt323)*Xt3L + + gtu11*(gt11L*(Gt112*(3*Gt111 + 2*Gt212) + 2*Gt113*Gt312) + + Gt111*(gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311) + gt13L*Gt312) + + Gt211*(5*Gt112*gt12L + 3*(Gt212*gt22L + gt23L*Gt312)) + + Gt311*(3*Gt112*gt13L + Gt212*gt23L + 2*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + Gt312*gt33L) + + 2*(Gt312*(gt12L*Gt213 + gt13L*(Gt212 + Gt313)) + gt12L*(SQR(Gt111) + SQR(Gt212)))) + + gtu22*(Gt112*(3*gt11L*Gt122 + gt12L*Gt222 + 2*(Gt212*gt22L + gt23L*Gt312) + gt13L*Gt322) + + Gt222*(3*Gt212*gt22L + gt23L*Gt312 + 2*(gt11L*Gt122 + gt13L*Gt322)) + + Gt312*(3*Gt122*gt13L + 2*(Gt223*gt22L + gt23L*Gt323)) + + Gt322*(3*Gt212*gt23L + 2*(gt11L*Gt123 + gt13L*Gt323) + Gt312*gt33L) + + gt12L*(5*Gt122*Gt212 + 2*(Gt123*Gt312 + Gt223*Gt322 + SQR(Gt112) + SQR(Gt222)))) + + gtu33*(Gt113*(3*gt11L*Gt123 + gt12L*Gt223 + 2*(Gt213*gt22L + gt23L*Gt313) + gt13L*Gt323) + + Gt223*(3*Gt213*gt22L + gt23L*Gt313 + 2*(gt11L*Gt123 + gt13L*Gt323)) + + Gt313*(3*Gt123*gt13L + 2*(gt22L*Gt233 + gt23L*Gt333)) + + Gt323*(3*Gt213*gt23L + 2*(gt11L*Gt133 + gt13L*Gt333) + Gt313*gt33L) + + gt12L*(5*Gt123*Gt213 + 2*(Gt133*Gt313 + Gt233*Gt323 + SQR(Gt113) + SQR(Gt223)))) + + gtu21*(Gt111*(3*gt11L*Gt122 + gt12L*(2*Gt112 + Gt222) + gt13L*Gt322) + + 2*(Gt112*(gt11L*Gt222 + Gt211*gt22L) + Gt223*gt22L*Gt311 + Gt111*(Gt112*gt12L + Gt212*gt22L + gt23L*Gt312) + + (Gt113*gt11L + gt13L*Gt313)*Gt322 + gt13L*(Gt222*Gt312 + Gt212*Gt322)) + + gt12L*(5*Gt122*Gt211 + Gt212*(4*Gt112 + 2*Gt222) + + 2*(Gt212*(Gt112 + Gt222) + Gt123*Gt311 + (Gt113 + Gt223)*Gt312 + Gt213*Gt322)) + + Gt312*(2*(Gt213*gt22L + gt23L*Gt313) + gt13L*(4*Gt112 + 2*Gt323)) + + gt23L*(4*Gt212*Gt312 + Gt311*(Gt222 + 2*(Gt112 + Gt323))) + + gt11L*(2*(Gt122*Gt212 + Gt123*Gt312) + 3*SQR(Gt112)) + + 3*(Gt122*gt13L*Gt311 + Gt211*(Gt222*gt22L + gt23L*Gt322) + gt22L*SQR(Gt212)) + gt33L*(Gt311*Gt322 + SQR(Gt312)))\ + + gtu31*(Gt111*(3*gt11L*Gt123 + gt12L*(2*Gt113 + Gt223) + gt13L*Gt323) + + gt11L*(2*(Gt123*Gt212 + Gt133*Gt312) + Gt113*(3*Gt112 + 2*Gt323)) + + 3*((Gt212*Gt213 + Gt211*Gt223)*gt22L + Gt123*gt13L*Gt311 + gt23L*(Gt213*Gt312 + Gt211*Gt323)) + + gt12L*(5*Gt123*Gt211 + 3*Gt112*Gt213 + Gt212*(Gt113 + 2*Gt223) + + 2*(Gt212*Gt223 + Gt133*Gt311 + Gt233*Gt312 + Gt113*Gt313 + Gt213*(Gt112 + Gt323))) + + gt13L*(3*Gt112*Gt313 + 2*Gt212*Gt323 + Gt312*(Gt113 + 2*Gt333)) + + gt23L*(Gt212*Gt313 + Gt311*(Gt223 + 2*(Gt113 + Gt333))) + (Gt312*Gt313 + Gt311*Gt323)*gt33L + + 2*(Gt223*(Gt112*gt11L + gt13L*Gt312) + gt22L*(Gt113*Gt211 + Gt233*Gt311 + Gt213*Gt313) + + Gt111*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + gt13L*Gt313*Gt323 + gt23L*SQR(Gt313))) + + gtu32*(3*((Gt213*Gt222 + Gt212*Gt223)*gt22L + gt13L*(Gt123*Gt312 + Gt122*Gt313) + Gt213*gt23L*Gt322) + + Gt112*(3*gt11L*Gt123 + gt12L*(2*Gt113 + Gt223) + gt13L*Gt323) + + gt12L*(5*(Gt123*Gt212 + Gt122*Gt213) + Gt222*(Gt113 + 4*Gt223) + + 2*(Gt133*Gt312 + Gt123*Gt313 + Gt233*Gt322 + Gt223*Gt323)) + + gt11L*(3*Gt113*Gt122 + 2*(Gt133*Gt322 + Gt123*(Gt222 + Gt323))) + + gt13L*(2*Gt222*Gt323 + Gt322*(Gt113 + 2*Gt333)) + + gt23L*(Gt222*Gt313 + 3*Gt212*Gt323 + Gt312*(Gt223 + 2*(Gt113 + Gt333))) + (Gt313*Gt322 + Gt312*Gt323)*gt33L + + 2*(gt22L*(Gt113*Gt212 + Gt233*Gt312) + Gt112*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + + Gt223*(gt11L*Gt122 + gt22L*Gt313 + gt13L*Gt322) + gt23L*Gt313*Gt323 + gt13L*SQR(Gt323))); + + Rt13 = gt23L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 + + khalf*(-(gtu11*PDstandard4th11gt13) - 2*gtu21*PDstandard4th12gt13 - 2*gtu31*PDstandard4th13gt13 - + gtu22*PDstandard4th22gt13 - 2*gtu32*PDstandard4th23gt13 - gtu33*PDstandard4th33gt13) + gt11L*PDstandard4th3Xt1 + + gt12L*PDstandard4th3Xt2 + gt13L*(PDstandard4th1Xt1 + PDstandard4th3Xt3) + + (Gt113*gt11L + gt12L*Gt213 + Gt211*gt23L + gt13L*(Gt111 + Gt313) + Gt311*gt33L)*Xt1L + + (gt11L*Gt123 + gt12L*Gt223 + Gt212*gt23L + gt13L*(Gt112 + Gt323) + Gt312*gt33L)*Xt2L + + (gt11L*Gt133 + gt12L*Gt233 + Gt213*gt23L + gt13L*(Gt113 + Gt333) + Gt313*gt33L)*Xt3L + + gtu21*((Gt212*Gt213 + Gt211*Gt223)*gt22L + Gt123*(Gt111*gt11L + gt12L*Gt211 + 3*gt13L*Gt311) + + gt12L*(3*Gt113*Gt212 + Gt112*Gt213 + Gt223*(Gt111 + 2*Gt313)) + + gt11L*(3*Gt112*Gt113 + 2*(Gt122*Gt213 + Gt123*Gt313)) + gt13L*(Gt112*Gt313 + Gt111*Gt323) + + gt23L*(Gt213*Gt312 + Gt212*Gt313 + Gt211*Gt323) + Gt312*Gt313*gt33L + + 3*(Gt113*gt13L*Gt312 + Gt311*(Gt223*gt23L + Gt323*gt33L)) + + 2*(Gt213*(gt12L*Gt222 + gt13L*Gt322) + gt11L*(Gt111*Gt123 + Gt112*Gt223 + Gt113*Gt323) + + gt12L*(Gt123*Gt211 + Gt212*Gt223 + Gt213*Gt323) + + gt13L*(Gt112*(Gt111 + Gt212) + Gt123*Gt311 + (Gt113 + Gt223)*Gt312 + 2*Gt313*Gt323) + + (Gt112*Gt311 + Gt312*(Gt212 + Gt313))*gt33L + Gt111*(Gt112*gt13L + Gt212*gt23L + Gt312*gt33L) + + Gt211*(Gt122*gt13L + Gt222*gt23L + Gt322*gt33L) + gt23L*(Gt112*Gt211 + Gt213*Gt312 + SQR(Gt212)))) + + gtu32*(gt11L*(Gt123*(3*Gt113 + 2*Gt223) + 2*Gt133*Gt323) + Gt223*(gt23L*(2*Gt212 + 3*Gt313) + 2*gt13L*Gt323) + + Gt233*(Gt212*gt22L + 3*gt23L*Gt312 + 2*(gt11L*Gt122 + gt12L*Gt323)) + + Gt123*(3*gt12L*Gt213 + gt13L*(2*Gt212 + 5*Gt313) + 2*gt11L*Gt333) + + gt13L*(5*Gt133*Gt312 + 2*Gt233*Gt322 + 4*Gt323*Gt333) + 3*(Gt313*Gt323 + Gt312*Gt333)*gt33L + + Gt212*(gt23L*Gt333 + 2*Gt323*gt33L) + Gt113*(gt12L*Gt223 + gt13L*Gt323 + 2*(Gt212*gt23L + Gt312*gt33L)) + + Gt112*(3*gt11L*Gt133 + gt12L*Gt233 + gt13L*(2*Gt113 + Gt333) + 2*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L)) + + Gt213*(Gt223*gt22L + gt23L*Gt323 + 2*(Gt122*gt13L + Gt222*gt23L + Gt322*gt33L)) + + gt12L*(3*Gt133*Gt212 + 2*(Gt222*Gt233 + Gt223*Gt333 + SQR(Gt223)))) + + gtu31*(Gt133*(Gt111*gt11L + gt12L*Gt211 + 3*gt13L*Gt311) + Gt233*(Gt211*gt22L + 3*gt23L*Gt311) + + gt12L*(4*Gt113*Gt213 + Gt233*(Gt111 + 2*Gt313)) + gt13L*(4*Gt113*Gt313 + 2*Gt213*Gt323 + Gt111*Gt333) + + Gt211*(gt23L*Gt333 + 2*Gt323*gt33L) + gt11L*(2*(Gt123*Gt213 + Gt133*Gt313) + 3*SQR(Gt113)) + gt22L*SQR(Gt213) + + gt33L*(3*Gt311*Gt333 + SQR(Gt313)) + 2*(Gt211*(Gt123*gt13L + Gt223*gt23L) + Gt213*(gt12L*Gt223 + gt23L*Gt313) + + gt23L*(Gt113*Gt211 + Gt213*(Gt212 + Gt313)) + gt11L*(Gt111*Gt133 + Gt112*Gt233 + Gt113*Gt333) + + gt12L*(Gt133*Gt211 + Gt212*Gt233 + Gt213*Gt333) + + gt13L*(Gt112*Gt213 + Gt133*Gt311 + Gt233*Gt312 + Gt113*(Gt111 + Gt313) + 2*Gt313*Gt333) + + Gt111*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L) + gt33L*(Gt113*Gt311 + Gt213*Gt312 + SQR(Gt313)))) + + gtu11*(Gt211*(3*Gt113*gt12L + 2*Gt112*gt13L + Gt213*gt22L + gt23L*Gt313) + + gt11L*(2*Gt112*Gt213 + Gt113*(3*Gt111 + 2*Gt313)) + + Gt111*(gt12L*Gt213 + gt13L*Gt313 + 2*(Gt211*gt23L + Gt311*gt33L)) + + Gt311*(5*Gt113*gt13L + 3*(Gt213*gt23L + Gt313*gt33L)) + + 2*(Gt212*(gt12L*Gt213 + Gt211*gt23L) + Gt213*(gt13L*Gt312 + gt12L*Gt313) + Gt211*Gt312*gt33L + + gt13L*(SQR(Gt111) + SQR(Gt313)))) + gtu22* + (Gt212*(3*Gt123*gt12L + 2*Gt122*gt13L + Gt223*gt22L + gt23L*Gt323) + + gt11L*(2*Gt122*Gt223 + Gt123*(3*Gt112 + 2*Gt323)) + + Gt112*(gt12L*Gt223 + gt13L*Gt323 + 2*(Gt212*gt23L + Gt312*gt33L)) + + Gt312*(5*Gt123*gt13L + 3*(Gt223*gt23L + Gt323*gt33L)) + + 2*(Gt222*(gt12L*Gt223 + Gt212*gt23L) + Gt223*(gt13L*Gt322 + gt12L*Gt323) + Gt212*Gt322*gt33L + + gt13L*(SQR(Gt112) + SQR(Gt323)))) + gtu33* + (gt12L*(3*Gt133*Gt213 + 2*Gt233*(Gt223 + Gt333)) + Gt213*(gt22L*Gt233 + gt23L*(2*Gt223 + Gt333)) + + Gt113*(3*gt11L*Gt133 + gt12L*Gt233 + gt13L*Gt333 + 2*(Gt213*gt23L + Gt313*gt33L)) + + Gt313*(5*Gt133*gt13L + 3*(Gt233*gt23L + Gt333*gt33L)) + + 2*(Gt123*(gt13L*Gt213 + gt11L*Gt233) + gt11L*Gt133*Gt333 + Gt323*(gt13L*Gt233 + Gt213*gt33L) + + gt13L*(SQR(Gt113) + SQR(Gt333)))); + + Rt22 = 6*(Gt122*gt12L*Gt212*gtu21 + Gt112*gt12L*Gt222*gtu21 + Gt122*gt12L*Gt222*gtu22 + Gt123*gt12L*Gt212*gtu31 + + Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandard4th11gt22 + + gtu21*(10*Gt212*Gt222*gt22L + 4*Gt122*gt23L*Gt311 + 2*Gt122*gt13L*Gt312 + 6*Gt222*gt23L*Gt312 + + 4*Gt113*gt12L*Gt322 + 4*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandard4th12gt22) + + gtu31*(10*Gt212*Gt223*gt22L + 2*Gt123*gt13L*Gt312 + 4*Gt112*gt23L*Gt313 + 4*Gt113*gt12L*Gt323 + + 4*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandard4th13gt22) - gtu22*khalf*PDstandard4th22gt22 + + gtu32*(6*Gt223*gt23L*Gt322 + 2*Gt122*gt13L*Gt323 + 4*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - + PDstandard4th23gt22) + gt12L*(4*Gt111*Gt123*gtu31 + 6*Gt112*Gt223*gtu31 + 4*Gt113*Gt122*gtu32 + + 4*Gt113*Gt123*gtu33 + 2*PDstandard4th2Xt1) + + gt22L*(4*Gt122*Gt213*gtu32 + 10*Gt222*Gt223*gtu32 + 4*Gt123*Gt213*gtu33 + 2*PDstandard4th2Xt2) + + gt23L*(6*Gt212*Gt322*gtu21 + 4*Gt313*Gt322*gtu21 + 6*Gt222*Gt322*gtu22 + 4*Gt123*Gt311*gtu31 + + 6*Gt212*Gt323*gtu31 + 4*Gt313*Gt323*gtu31 + 4*Gt122*Gt313*gtu32 + 6*Gt223*Gt323*gtu33 + 2*PDstandard4th2Xt3) - + gtu33*khalf*PDstandard4th33gt22 + 2*Gt212*gt22L*Xt1L + + Gt112*(4*Gt111*gt12L*gtu11 + 6*gt12L*Gt212*gtu11 + 2*gt11L*Gt122*gtu21 + 4*Gt122*gt12L*gtu22 + + 2*gt11L*Gt123*gtu31 + 4*Gt123*gt12L*gtu32 + 2*gt12L*Xt1L) + + Gt312*(4*Gt113*gt12L*gtu11 + 2*Gt112*gt13L*gtu11 + 4*Gt213*gt22L*gtu11 + 6*Gt212*gt23L*gtu11 + + 4*gt23L*Gt313*gtu11 + 4*Gt123*gt12L*gtu21 + 4*Gt122*gt23L*gtu22 + 4*gt12L*Gt133*gtu31 + 4*gt22L*Gt233*gtu31 + + 6*Gt223*gt23L*gtu31 + 4*Gt123*gt23L*gtu32 + 2*gt23L*Xt1L) + 2*Gt222*gt22L*Xt2L + + Gt122*(2*gt11L*Gt123*gtu32 + 6*gt12L*Gt223*gtu32 + 2*gt12L*Xt2L) + + Gt322*(2*Gt112*gt13L*gtu21 + 4*Gt213*gt22L*gtu21 + 4*Gt123*gt12L*gtu22 + 2*Gt122*gt13L*gtu22 + + 4*Gt223*gt22L*gtu22 + 4*gt23L*Gt323*gtu22 + 4*gt12L*Gt133*gtu32 + 2*Gt123*gt13L*gtu32 + 4*gt22L*Gt233*gtu32 + + 2*gt23L*Xt2L) + 2*Gt123*gt12L*Xt3L + 2*Gt223*gt22L*Xt3L + + Gt323*(2*Gt112*gt13L*gtu31 + 4*Gt213*gt22L*gtu31 + 4*Gt123*gt12L*gtu32 + 4*Gt223*gt22L*gtu32 + + 6*Gt222*gt23L*gtu32 + 4*gt12L*Gt133*gtu33 + 2*Gt123*gt13L*gtu33 + 4*gt22L*Gt233*gtu33 + 4*gt23L*Gt333*gtu33 + + 2*gt23L*Xt3L) + gt11L*gtu11*SQR(Gt112) + 4* + (Gt112*Gt211*gt22L*gtu11 + Gt112*gt23L*Gt311*gtu11 + Gt111*Gt122*gt12L*gtu21 + Gt122*Gt211*gt22L*gtu21 + + Gt112*Gt212*gt22L*gtu21 + Gt223*gt22L*Gt312*gtu21 + Gt112*gt23L*Gt312*gtu21 + Gt122*Gt212*gt22L*gtu22 + + Gt112*Gt113*gt12L*gtu31 + Gt123*Gt211*gt22L*gtu31 + Gt112*Gt213*gt22L*gtu31 + Gt123*Gt212*gt22L*gtu32 + + Gt123*gt23L*Gt313*gtu33 + gt12L*gtu21*SQR(Gt112)) + gt11L*gtu22*SQR(Gt122) + gt11L*gtu33*SQR(Gt123) + + 5*gt22L*gtu11*SQR(Gt212) + 5*gt22L*gtu22*SQR(Gt222) + 5*gt22L*gtu33*SQR(Gt223) + gt33L*gtu11*SQR(Gt312) + + gt33L*gtu22*SQR(Gt322) + 4*gt23L*gtu32*SQR(Gt323) + gt33L*gtu33*SQR(Gt323); + + Rt23 = gt13L*PDstandard4th2Xt1 + gt33L*PDstandard4th2Xt3 + + khalf*(-(gtu11*PDstandard4th11gt23) - 2*gtu21*PDstandard4th12gt23 - 2*gtu31*PDstandard4th13gt23 - + gtu22*PDstandard4th22gt23 - 2*gtu32*PDstandard4th23gt23 - gtu33*PDstandard4th33gt23) + gt12L*PDstandard4th3Xt1 + + gt22L*PDstandard4th3Xt2 + gt23L*(PDstandard4th2Xt2 + PDstandard4th3Xt3) + + (Gt113*gt12L + Gt112*gt13L + Gt213*gt22L + gt23L*(Gt212 + Gt313) + Gt312*gt33L)*Xt1L + + (Gt123*gt12L + Gt122*gt13L + Gt223*gt22L + gt23L*(Gt222 + Gt323) + Gt322*gt33L)*Xt2L + + (gt12L*Gt133 + Gt123*gt13L + gt22L*Gt233 + gt23L*(Gt223 + Gt333) + Gt323*gt33L)*Xt3L + + gtu21*(gt11L*(Gt113*Gt122 + Gt112*Gt123) + gt12L* + (Gt113*Gt222 + 3*(Gt122*Gt213 + Gt112*Gt223) + Gt123*(Gt212 + 2*Gt313)) + + gt23L*(2*Gt123*Gt311 + Gt222*(4*Gt212 + Gt313) + 5*(Gt223*Gt312 + Gt213*Gt322) + (Gt212 + 4*Gt313)*Gt323) + + gt22L*(Gt212*(2*Gt113 + 3*Gt223) + 2*Gt223*Gt313 + Gt213*(3*Gt222 + 2*Gt323)) + + 3*(Gt313*Gt322 + Gt312*Gt323)*gt33L + 2*(Gt111*(Gt123*gt12L + Gt122*gt13L) + gt13L*(Gt122*Gt212 + Gt112*Gt222) + + Gt211*(Gt123*gt22L + Gt122*gt23L) + Gt113*(gt23L*Gt312 + gt12L*Gt323) + + (Gt122*Gt311 + Gt222*Gt312 + Gt212*Gt322)*gt33L + Gt112*(Gt113*gt12L + Gt212*gt23L + Gt312*gt33L)) + + gt13L*(Gt122*Gt313 + 3*(Gt123*Gt312 + Gt113*Gt322) + Gt112*Gt323 + 2*SQR(Gt112))) + + gtu31*(Gt133*(Gt112*gt11L + gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311)) + + gt23L*(5*Gt233*Gt312 + Gt223*(4*Gt212 + Gt313) + Gt213*(2*Gt112 + 5*Gt323) + Gt212*Gt333) + + Gt113*(gt11L*Gt123 + 2*(Gt112*gt13L + Gt213*gt22L + gt23L*Gt313) + gt13L*Gt323 + gt12L*(Gt223 + 2*Gt333)) + + Gt123*(3*gt12L*Gt213 + gt13L*(2*Gt212 + Gt313) + 2*Gt311*gt33L) + + Gt333*(Gt112*gt13L + 4*gt23L*Gt313 + 3*Gt312*gt33L) + + 3*(Gt112*gt12L*Gt233 + gt22L*(Gt213*Gt223 + Gt212*Gt233) + Gt133*gt13L*Gt312 + Gt313*Gt323*gt33L) + + 2*(Gt111*(gt12L*Gt133 + Gt123*gt13L) + Gt123*Gt211*gt23L + gt13L*(Gt112*Gt223 + Gt113*Gt323) + + Gt213*gt22L*Gt333 + (Gt223*Gt312 + Gt212*Gt323)*gt33L + Gt313*(gt12L*Gt133 + gt22L*Gt233 + Gt112*gt33L) + + gt12L*SQR(Gt113))) + gtu11*(Gt113*(Gt112*gt11L + gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311)) + + (Gt112*gt13L + Gt212*gt23L)*Gt313 + Gt213*(5*gt23L*Gt312 + 2*gt22L*Gt313) + + 3*(Gt213*(Gt112*gt12L + Gt212*gt22L) + Gt312*(Gt113*gt13L + Gt313*gt33L)) + + 2*(Gt111*(Gt113*gt12L + Gt112*gt13L) + Gt113*gt12L*Gt313 + Gt212*Gt312*gt33L + + Gt112*(gt13L*Gt212 + Gt211*gt23L + Gt311*gt33L) + gt23L*(SQR(Gt212) + SQR(Gt313)))) + + gtu32*(Gt133*(gt11L*Gt122 + gt12L*Gt222 + 3*gt13L*Gt322) + gt12L*(4*Gt123*Gt223 + Gt122*Gt233 + 2*Gt133*Gt323) + + Gt233*(3*gt23L*Gt322 + 2*gt22L*Gt323) + gt23L*Gt323*(4*Gt223 + 2*Gt333) + Gt122*(gt13L*Gt333 + 2*Gt313*gt33L) + + Gt222*(gt22L*Gt233 + gt23L*(2*Gt223 + Gt333) + 2*Gt323*gt33L) + gt11L*SQR(Gt123) + + 3*(Gt322*Gt333*gt33L + gt22L*SQR(Gt223)) + gt33L*SQR(Gt323) + + 2*(Gt113*(Gt123*gt12L + Gt122*gt13L) + Gt133*(Gt112*gt12L + Gt212*gt22L + gt23L*Gt312) + + Gt233*(Gt122*gt12L + Gt222*gt22L + gt23L*Gt322) + gt13L*(Gt122*Gt223 + Gt123*(Gt112 + Gt323)) + + Gt223*gt22L*Gt333 + Gt123*(Gt213*gt22L + gt23L*Gt313 + gt13L*(Gt222 + Gt323) + gt12L*Gt333) + + gt23L*(Gt123*Gt212 + Gt122*Gt213 + Gt223*(Gt222 + Gt323) + Gt323*Gt333) + + gt33L*(Gt123*Gt312 + Gt223*Gt322 + SQR(Gt323)))) + + gtu22*(Gt123*(gt11L*Gt122 + gt12L*Gt222 + 2*(Gt212*gt22L + gt23L*Gt312)) + (Gt122*gt13L + Gt222*gt23L)*Gt323 + + Gt223*(5*gt23L*Gt322 + 2*gt22L*Gt323) + 3* + (Gt223*(Gt122*gt12L + Gt222*gt22L) + Gt322*(Gt123*gt13L + Gt323*gt33L)) + + 2*(Gt112*(Gt123*gt12L + Gt122*gt13L) + Gt123*gt12L*Gt323 + Gt222*Gt322*gt33L + + Gt122*(gt13L*Gt222 + Gt212*gt23L + Gt312*gt33L) + gt23L*(SQR(Gt222) + SQR(Gt323)))) + + gtu33*(Gt133*(gt11L*Gt123 + gt12L*Gt223 + 2*(Gt213*gt22L + gt23L*Gt313)) + (Gt123*gt13L + Gt223*gt23L)*Gt333 + + Gt233*(5*gt23L*Gt323 + 2*gt22L*Gt333) + 3* + ((Gt123*gt12L + Gt223*gt22L)*Gt233 + Gt323*(Gt133*gt13L + Gt333*gt33L)) + + 2*(Gt113*(gt12L*Gt133 + Gt123*gt13L) + gt12L*Gt133*Gt333 + Gt223*Gt323*gt33L + + Gt123*(gt13L*Gt223 + Gt213*gt23L + Gt313*gt33L) + gt23L*(SQR(Gt223) + SQR(Gt333)))); + + Rt33 = 6*(Gt133*gt13L*Gt313*gtu31 + Gt233*gt23L*Gt313*gtu31 + Gt113*gt13L*Gt333*gtu31 + Gt213*gt23L*Gt333*gtu31 + + Gt133*gt13L*Gt323*gtu32 + Gt133*gt13L*Gt333*gtu33) + + gtu21*(4*Gt122*gt13L*Gt213 + 2*Gt113*gt12L*Gt223 + 4*Gt112*gt13L*Gt223 + 2*Gt213*Gt223*gt22L + + 4*Gt123*Gt211*gt23L + 4*Gt212*Gt223*gt23L + 6*Gt123*gt13L*Gt313 + 6*Gt223*gt23L*Gt313 + 6*Gt113*gt13L*Gt323 + + 6*Gt213*gt23L*Gt323 + 4*Gt123*Gt311*gt33L - PDstandard4th12gt33) - gtu31*PDstandard4th13gt33 + + gtu22*(4*Gt222*Gt223*gt23L + 6*Gt123*gt13L*Gt323 + 6*Gt223*gt23L*Gt323 + 4*Gt223*Gt322*gt33L - + khalf*PDstandard4th22gt33) + gtu32*(2*Gt223*gt22L*Gt233 + 4*Gt133*Gt212*gt23L + 6*Gt233*gt23L*Gt323 + + 6*Gt123*gt13L*Gt333 + 6*Gt223*gt23L*Gt333 + 4*Gt123*Gt313*gt33L + 10*Gt323*Gt333*gt33L - PDstandard4th23gt33) - + gtu33*khalf*PDstandard4th33gt33 + 2*(gt12L*Gt133*Gt213*gtu31 + Gt113*gt12L*Gt233*gtu31 + gt12L*Gt133*Gt223*gtu32 + + gt13L*PDstandard4th3Xt1) + 2*gt23L*PDstandard4th3Xt2 + + gt33L*(4*Gt213*Gt322*gtu21 + 10*Gt313*Gt323*gtu21 + 4*Gt123*Gt312*gtu22 + 4*Gt133*Gt311*gtu31 + + 4*Gt213*Gt323*gtu31 + 10*Gt313*Gt333*gtu31 + 4*Gt133*Gt312*gtu32 + 4*Gt133*Gt313*gtu33 + 2*PDstandard4th3Xt3) + + 2*Gt213*gt23L*Xt1L + 2*Gt313*gt33L*Xt1L + Gt113* + (4*Gt111*gt13L*gtu11 + 2*gt12L*Gt213*gtu11 + 2*gt11L*Gt123*gtu21 + 2*gt11L*Gt133*gtu31 + 4*Gt123*gt13L*gtu32 + + 4*Gt133*gt13L*gtu33 + 2*gt13L*Xt1L) + 2*Gt223*gt23L*Xt2L + 2*Gt323*gt33L*Xt2L + + Gt123*(4*Gt111*gt13L*gtu21 + 2*gt12L*Gt213*gtu21 + 4*Gt112*gt13L*gtu22 + 2*gt12L*Gt223*gtu22 + + 4*Gt212*gt23L*gtu22 + 4*gt13L*Gt213*gtu31 + 2*gt11L*Gt133*gtu32 + 4*gt13L*Gt233*gtu33 + 2*gt13L*Xt2L) + + 2*Gt133*gt13L*Xt3L + 2*Gt333*gt33L*Xt3L + Gt233* + (4*Gt112*gt13L*gtu31 + 2*Gt213*gt22L*gtu31 + 2*Gt123*gt12L*gtu32 + 2*gt12L*Gt133*gtu33 + 4*Gt223*gt23L*gtu33 + + 6*gt23L*Gt333*gtu33 + 4*Gt323*gt33L*gtu33 + 2*gt23L*Xt3L) + + gtu11*(4*Gt212*Gt213*gt23L + 6*Gt113*gt13L*Gt313 + 6*Gt213*gt23L*Gt313 + 4*Gt113*Gt311*gt33L + + 4*Gt213*Gt312*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt113)) + + 4*(Gt112*gt13L*Gt213*gtu11 + Gt113*Gt211*gt23L*gtu11 + Gt112*Gt113*gt13L*gtu21 + Gt113*Gt212*gt23L*gtu21 + + Gt213*Gt222*gt23L*gtu21 + Gt113*Gt312*gt33L*gtu21 + Gt223*Gt312*gt33L*gtu21 + Gt122*gt13L*Gt223*gtu22 + + Gt111*Gt133*gt13L*gtu31 + Gt133*Gt211*gt23L*gtu31 + Gt113*Gt213*gt23L*gtu31 + Gt213*Gt223*gt23L*gtu31 + + Gt212*Gt233*gt23L*gtu31 + Gt233*Gt312*gt33L*gtu31 + Gt113*Gt313*gt33L*gtu31 + Gt112*Gt133*gt13L*gtu32 + + Gt123*gt13L*Gt223*gtu32 + Gt122*gt13L*Gt233*gtu32 + Gt123*Gt213*gt23L*gtu32 + Gt222*Gt233*gt23L*gtu32 + + Gt233*Gt322*gt33L*gtu32 + Gt223*Gt323*gt33L*gtu32 + Gt133*Gt213*gt23L*gtu33 + gt13L*gtu31*SQR(Gt113)) + + gt11L*gtu22*SQR(Gt123) + gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt213) + gt22L*gtu22*SQR(Gt223) + + 4*gt23L*gtu32*SQR(Gt223) + gt22L*gtu33*SQR(Gt233) + 5*gt33L*gtu11*SQR(Gt313) + 5*gt33L*gtu22*SQR(Gt323) + + 5*gt33L*gtu33*SQR(Gt333); + + Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu21*PDstandard4th12phi - + 2*gt11L*gtu31*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu32*PDstandard4th23phi - gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + - 2*gt11L*Gt321*gtu12*PDstandard4th3phi + 2*gt11L*Gt331*gtu13*PDstandard4th3phi + - gt11L*Gt322*gtu22*PDstandard4th3phi + 2*gt11L*Gt332*gtu23*PDstandard4th3phi + + 2*gt11L*Gt312*gtu21*PDstandard4th3phi + gt11L*Gt322*gtu22*PDstandard4th3phi + + 2*gt11L*Gt313*gtu31*PDstandard4th3phi + 2*gt11L*Gt323*gtu32*PDstandard4th3phi + gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt111 + Gt111*gt11L*gtu11 + 2*gt11L*Gt121*gtu12 + 2*gt11L*Gt131*gtu13 + gt11L*Gt122*gtu22 + - 2*gt11L*Gt132*gtu23 + gt11L*Gt133*gtu33 - 4*gt11L*gtu12*PDstandard4th2phi - 4*gt11L*gtu13*PDstandard4th3phi) + + (Gt111 + Gt111*gt11L*gtu11 + 2*Gt112*gt11L*gtu21 + gt11L*Gt122*gtu22 + 2*Gt113*gt11L*gtu31 + + 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandard4th2phi - 4*gt11L*gtu31*PDstandard4th3phi) + PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + - gt11L*(2*Gt221*gtu12 + 2*Gt231*gtu13 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt11L*gtu23*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - + gt11L*(2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt11L*gtu32*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - 2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi)); - Rphi21 = 2*(-(gt21L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt21L*gtu12*PDstandard4th12phi - - 2*gt21L*gtu13*PDstandard4th13phi - gt21L*gtu22*PDstandard4th22phi - 2*gt21L*gtu23*PDstandard4th23phi - - gt21L*gtu33*PDstandard4th33phi + Gt321*PDstandard4th3phi + gt21L*Gt311*gtu11*PDstandard4th3phi + - 2*gt21L*Gt321*gtu12*PDstandard4th3phi + 2*gt21L*Gt331*gtu13*PDstandard4th3phi + - gt21L*Gt322*gtu22*PDstandard4th3phi + 2*gt21L*Gt332*gtu23*PDstandard4th3phi + - gt21L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt121 + Gt111*gt21L*gtu11 + 2*Gt121*gt21L*gtu12 + 2*Gt131*gt21L*gtu13 + Gt122*gt21L*gtu22 + - 2*Gt132*gt21L*gtu23 + Gt133*gt21L*gtu33 + (2 - 4*gt21L*gtu12)*PDstandard4th2phi - - 4*gt21L*gtu13*PDstandard4th3phi) + PDstandard4th2phi* - (Gt221 + 2*gt21L*Gt221*gtu12 + gt21L*(Gt211*gtu11 + 2*Gt231*gtu13 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt21L*gtu23*PDstandard4th3phi) - 2*gt21L*gtu11*SQR(PDstandard4th1phi) - - 2*gt21L*gtu22*SQR(PDstandard4th2phi) - 2*gt21L*gtu33*SQR(PDstandard4th3phi)); - - Rphi31 = 2*(-PDstandard4th13phi + gt31L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi) - gt31L*gtu22*PDstandard4th22phi - 2*gt31L*gtu23*PDstandard4th23phi - - gt31L*gtu33*PDstandard4th33phi + Gt331*PDstandard4th3phi + Gt311*gt31L*gtu11*PDstandard4th3phi + - 2*gt31L*Gt321*gtu12*PDstandard4th3phi + 2*gt31L*Gt331*gtu13*PDstandard4th3phi + - gt31L*Gt322*gtu22*PDstandard4th3phi + 2*gt31L*Gt332*gtu23*PDstandard4th3phi + - gt31L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt131 + Gt111*gt31L*gtu11 + 2*Gt121*gt31L*gtu12 + 2*Gt131*gt31L*gtu13 + Gt122*gt31L*gtu22 + - 2*Gt132*gt31L*gtu23 + Gt133*gt31L*gtu33 - 4*gt31L*gtu12*PDstandard4th2phi + - (2 - 4*gt31L*gtu13)*PDstandard4th3phi) + - PDstandard4th2phi*(Gt231 + 2*Gt231*gt31L*gtu13 + - gt31L*(Gt211*gtu11 + 2*Gt221*gtu12 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt31L*gtu23*PDstandard4th3phi) - 2*gt31L*gtu11*SQR(PDstandard4th1phi) - - 2*gt31L*gtu22*SQR(PDstandard4th2phi) - 2*gt31L*gtu33*SQR(PDstandard4th3phi)); - - Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu23*PDstandard4th23phi - + Rphi12 = 2*(-(gt12L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt12L*gtu21*PDstandard4th12phi - + 2*gt12L*gtu31*PDstandard4th13phi - gt12L*gtu22*PDstandard4th22phi - 2*gt12L*gtu32*PDstandard4th23phi - + gt12L*gtu33*PDstandard4th33phi + Gt312*PDstandard4th3phi + gt12L*Gt311*gtu11*PDstandard4th3phi + + 2*gt12L*Gt312*gtu21*PDstandard4th3phi + gt12L*Gt322*gtu22*PDstandard4th3phi + + 2*gt12L*Gt313*gtu31*PDstandard4th3phi + 2*gt12L*Gt323*gtu32*PDstandard4th3phi + + gt12L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt112 + Gt111*gt12L*gtu11 + 2*Gt112*gt12L*gtu21 + Gt122*gt12L*gtu22 + 2*Gt113*gt12L*gtu31 + + 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandard4th2phi - + 4*gt12L*gtu31*PDstandard4th3phi) + PDstandard4th2phi* + (Gt212 + 2*gt12L*Gt212*gtu21 + gt12L*(Gt211*gtu11 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt12L*gtu32*PDstandard4th3phi) - 2*gt12L*gtu11*SQR(PDstandard4th1phi) - + 2*gt12L*gtu22*SQR(PDstandard4th2phi) - 2*gt12L*gtu33*SQR(PDstandard4th3phi)); + + Rphi13 = 2*(-PDstandard4th13phi + gt13L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi) - gt13L*gtu22*PDstandard4th22phi - 2*gt13L*gtu32*PDstandard4th23phi - + gt13L*gtu33*PDstandard4th33phi + Gt313*PDstandard4th3phi + gt13L*Gt311*gtu11*PDstandard4th3phi + + 2*gt13L*Gt312*gtu21*PDstandard4th3phi + gt13L*Gt322*gtu22*PDstandard4th3phi + + 2*gt13L*Gt313*gtu31*PDstandard4th3phi + 2*gt13L*Gt323*gtu32*PDstandard4th3phi + + gt13L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt113 + Gt111*gt13L*gtu11 + 2*Gt112*gt13L*gtu21 + Gt122*gt13L*gtu22 + 2*Gt113*gt13L*gtu31 + + 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandard4th2phi + + (2 - 4*gt13L*gtu31)*PDstandard4th3phi) + + PDstandard4th2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + + gt13L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt13L*gtu32*PDstandard4th3phi) - 2*gt13L*gtu11*SQR(PDstandard4th1phi) - + 2*gt13L*gtu22*SQR(PDstandard4th2phi) - 2*gt13L*gtu33*SQR(PDstandard4th3phi)); + + Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu32*PDstandard4th23phi - gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + - 2*gt22L*Gt321*gtu12*PDstandard4th3phi + 2*gt22L*Gt331*gtu13*PDstandard4th3phi + - gt22L*Gt322*gtu22*PDstandard4th3phi + 2*gt22L*Gt332*gtu23*PDstandard4th3phi + + 2*gt22L*Gt312*gtu21*PDstandard4th3phi + gt22L*Gt322*gtu22*PDstandard4th3phi + + 2*gt22L*Gt313*gtu31*PDstandard4th3phi + 2*gt22L*Gt323*gtu32*PDstandard4th3phi + gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt122 + Gt111*gt22L*gtu11 + 2*Gt121*gt22L*gtu12 + 2*Gt131*gt22L*gtu13 + Gt122*gt22L*gtu22 + - 2*Gt132*gt22L*gtu23 + Gt133*gt22L*gtu33 - 4*gt22L*gtu12*PDstandard4th2phi - 4*gt22L*gtu13*PDstandard4th3phi) + + (Gt122 + Gt111*gt22L*gtu11 + 2*Gt112*gt22L*gtu21 + Gt122*gt22L*gtu22 + 2*Gt113*gt22L*gtu31 + + 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandard4th2phi - 4*gt22L*gtu31*PDstandard4th3phi) + PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + - gt22L*(Gt211*gtu11 + 2*Gt221*gtu12 + 2*Gt231*gtu13 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt22L*gtu23*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + + gt22L*(Gt211*gtu11 + 2*Gt212*gtu21 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt22L*gtu32*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi)); - Rphi32 = 2*(-PDstandard4th23phi + gt32L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu23*PDstandard4th23phi) - - gt32L*gtu33*PDstandard4th33phi + Gt332*PDstandard4th3phi + Gt311*gt32L*gtu11*PDstandard4th3phi + - 2*Gt321*gt32L*gtu12*PDstandard4th3phi + 2*gt32L*Gt331*gtu13*PDstandard4th3phi + - Gt322*gt32L*gtu22*PDstandard4th3phi + 2*gt32L*Gt332*gtu23*PDstandard4th3phi + - gt32L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt132 + Gt111*gt32L*gtu11 + 2*Gt121*gt32L*gtu12 + 2*Gt131*gt32L*gtu13 + Gt122*gt32L*gtu22 + - 2*Gt132*gt32L*gtu23 + Gt133*gt32L*gtu33 - 4*gt32L*gtu12*PDstandard4th2phi - 4*gt32L*gtu13*PDstandard4th3phi) + - PDstandard4th2phi*(Gt232 + 2*Gt232*gt32L*gtu23 + - gt32L*(Gt211*gtu11 + 2*Gt221*gtu12 + 2*Gt231*gtu13 + Gt222*gtu22 + Gt233*gtu33) + - (2 - 4*gt32L*gtu23)*PDstandard4th3phi) - 2*gt32L*gtu11*SQR(PDstandard4th1phi) - - 2*gt32L*gtu22*SQR(PDstandard4th2phi) - 2*gt32L*gtu33*SQR(PDstandard4th3phi)); + Rphi23 = 2*(-PDstandard4th23phi + gt23L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi) - + gt23L*gtu33*PDstandard4th33phi + Gt323*PDstandard4th3phi + gt23L*Gt311*gtu11*PDstandard4th3phi + + 2*gt23L*Gt312*gtu21*PDstandard4th3phi + gt23L*Gt322*gtu22*PDstandard4th3phi + + 2*gt23L*Gt313*gtu31*PDstandard4th3phi + 2*gt23L*Gt323*gtu32*PDstandard4th3phi + + gt23L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt123 + Gt111*gt23L*gtu11 + 2*Gt112*gt23L*gtu21 + Gt122*gt23L*gtu22 + 2*Gt113*gt23L*gtu31 + + 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandard4th2phi - 4*gt23L*gtu31*PDstandard4th3phi) + + PDstandard4th2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + + gt23L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + Gt233*gtu33) + + (2 - 4*gt23L*gtu32)*PDstandard4th3phi) - 2*gt23L*gtu11*SQR(PDstandard4th1phi) - + 2*gt23L*gtu22*SQR(PDstandard4th2phi) - 2*gt23L*gtu33*SQR(PDstandard4th3phi)); Rphi33 = 2*(-PDstandard4th33phi + (Gt333 + gt33L* - (Gt322*gtu22 + 2*(Gt321*gtu12 + Gt331*gtu13 + Gt332*gtu23) + Gt333*gtu33))*PDstandard4th3phi + - PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt221*gtu12 + Gt231*gtu13 + Gt232*gtu23) + - Gt233*gtu33 - 4*gtu23*PDstandard4th3phi)) + - PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt121*gtu12 + Gt131*gtu13 + Gt132*gtu23) + - Gt133*gtu33 - 4*(gtu12*PDstandard4th2phi + gtu13*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + - gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - 2*gtu13*PDstandard4th13phi - - gtu22*PDstandard4th22phi - 2*gtu23*PDstandard4th23phi - gtu33*PDstandard4th33phi + + (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandard4th3phi + + PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + + Gt233*gtu33 - 4*gtu32*PDstandard4th3phi)) + + PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + + Gt133*gtu33 - 4*(gtu21*PDstandard4th2phi + gtu31*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + + gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 2*gtu31*PDstandard4th13phi - + gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi - gtu33*PDstandard4th33phi + Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - 2*gtu33*SQR(PDstandard4th3phi))); - R11 = Rphi11 + Rt11; - - R21 = Rphi21 + Rt21; - - R31 = Rphi31 + Rt31; - - R22 = Rphi22 + Rt22; - - R32 = Rphi32 + Rt32; - - R33 = Rphi33 + Rt33; - - Atm11 = At11L*gtu11 + At21L*gtu12 + At31L*gtu13; + Atm11 = At11L*gtu11 + At12L*gtu21 + At13L*gtu31; - Atm21 = At11L*gtu12 + At21L*gtu22 + At31L*gtu23; + Atm21 = At11L*gtu21 + At12L*gtu22 + At13L*gtu32; - Atm31 = At11L*gtu13 + At21L*gtu23 + At31L*gtu33; + Atm31 = At11L*gtu31 + At12L*gtu32 + At13L*gtu33; - Atm12 = At21L*gtu11 + At22L*gtu12 + At32L*gtu13; + Atm12 = At12L*gtu11 + At22L*gtu21 + At23L*gtu31; - Atm22 = At21L*gtu12 + At22L*gtu22 + At32L*gtu23; + Atm22 = At12L*gtu21 + At22L*gtu22 + At23L*gtu32; - Atm32 = At21L*gtu13 + At22L*gtu23 + At32L*gtu33; + Atm32 = At12L*gtu31 + At22L*gtu32 + At23L*gtu33; - Atm13 = At31L*gtu11 + At32L*gtu12 + At33L*gtu13; + Atm13 = At13L*gtu11 + At23L*gtu21 + At33L*gtu31; - Atm23 = At31L*gtu12 + At32L*gtu22 + At33L*gtu23; + Atm23 = At13L*gtu21 + At23L*gtu22 + At33L*gtu32; - Atm33 = At31L*gtu13 + At32L*gtu23 + At33L*gtu33; + Atm33 = At13L*gtu31 + At23L*gtu32 + At33L*gtu33; - Atu11 = Atm11*gtu11 + Atm12*gtu12 + Atm13*gtu13; + Atu11 = Atm11*gtu11 + Atm12*gtu21 + Atm13*gtu31; - Atu12 = Atm11*gtu12 + Atm12*gtu22 + Atm13*gtu23; + Atu21 = Atm11*gtu21 + Atm12*gtu22 + Atm13*gtu32; - Atu13 = Atm11*gtu13 + Atm12*gtu23 + Atm13*gtu33; + Atu31 = Atm11*gtu31 + Atm12*gtu32 + Atm13*gtu33; - Atu22 = Atm21*gtu12 + Atm22*gtu22 + Atm23*gtu23; + Atu22 = Atm21*gtu21 + Atm22*gtu22 + Atm23*gtu32; - Atu23 = Atm21*gtu13 + Atm22*gtu23 + Atm23*gtu33; + Atu32 = Atm21*gtu31 + Atm22*gtu32 + Atm23*gtu33; - Atu33 = Atm31*gtu13 + Atm32*gtu23 + Atm33*gtu33; + Atu33 = Atm31*gtu31 + Atm32*gtu32 + Atm33*gtu33; e4phi = exp(4*phiL); @@ -1187,27 +1177,27 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal g11 = e4phi*gt11L; - g21 = e4phi*gt21L; + g12 = e4phi*gt12L; - g31 = e4phi*gt31L; + g13 = e4phi*gt13L; g22 = e4phi*gt22L; - g32 = e4phi*gt32L; + g23 = e4phi*gt23L; g33 = e4phi*gt33L; - detg = 2*g21*g31*g32 + g33*(g11*g22 - SQR(g21)) - g22*SQR(g31) - g11*SQR(g32); + detg = 2*g12*g13*g23 + g33*(g11*g22 - SQR(g12)) - g22*SQR(g13) - g11*SQR(g23); gu11 = em4phi*gtu11; - gu12 = em4phi*gtu12; + gu21 = em4phi*gtu21; - gu13 = em4phi*gtu13; + gu31 = em4phi*gtu31; gu22 = em4phi*gtu22; - gu23 = em4phi*gtu23; + gu32 = em4phi*gtu32; gu33 = em4phi*gtu33; @@ -1217,216 +1207,228 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal ddetg3 = e4phi*(ddetgt3 + 4*detgt*PDstandard4th3phi); - G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; + G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - G211 = ((6*detg*Gt211 - g11*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; + G211 = ((6*detg*Gt211 - g11*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - G311 = ((6*detg*Gt311 - g11*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; + G311 = ((6*detg*Gt311 - g11*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - G121 = -((-6*detg*Gt121 + ddetg2*(-3 + g21*gu12) + g21*(ddetg1*gu11 + ddetg3*gu13))*INV(detg))/6.; + G112 = -((-6*detg*Gt112 + ddetg2*(-3 + g12*gu21) + g12*(ddetg1*gu11 + ddetg3*gu31))*INV(detg))/6.; - G221 = -((-6*detg*Gt221 + ddetg1*(-3 + g21*gu12) + g21*(ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; + G212 = -((-6*detg*Gt212 + ddetg1*(-3 + g12*gu21) + g12*(ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - G321 = ((6*detg*Gt321 - g21*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; + G312 = ((6*detg*Gt312 - g12*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - G131 = -((-6*detg*Gt131 + g31*(ddetg1*gu11 + ddetg2*gu12) + ddetg3*(-3 + g31*gu13))*INV(detg))/6.; + G113 = -((-6*detg*Gt113 + g13*(ddetg1*gu11 + ddetg2*gu21) + ddetg3*(-3 + g13*gu31))*INV(detg))/6.; - G231 = ((6*detg*Gt231 - g31*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; + G213 = ((6*detg*Gt213 - g13*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - G331 = -((-6*detg*Gt331 + ddetg1*(-3 + g31*gu13) + g31*(ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; + G313 = -((-6*detg*Gt313 + ddetg1*(-3 + g13*gu31) + g13*(ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - G122 = ((6*detg*Gt122 - g22*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; + G122 = ((6*detg*Gt122 - g22*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - G222 = -((-6*detg*Gt222 + ddetg2*(-6 + g22*gu22) + g22*(ddetg1*gu12 + ddetg3*gu23))*INV(detg))/6.; + G222 = -((-6*detg*Gt222 + ddetg2*(-6 + g22*gu22) + g22*(ddetg1*gu21 + ddetg3*gu32))*INV(detg))/6.; - G322 = ((6*detg*Gt322 - g22*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; + G322 = ((6*detg*Gt322 - g22*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - G132 = ((6*detg*Gt132 - g32*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; + G123 = ((6*detg*Gt123 - g23*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - G232 = -((-6*detg*Gt232 + g32*(ddetg1*gu12 + ddetg2*gu22) + ddetg3*(-3 + g32*gu23))*INV(detg))/6.; + G223 = -((-6*detg*Gt223 + g23*(ddetg1*gu21 + ddetg2*gu22) + ddetg3*(-3 + g23*gu32))*INV(detg))/6.; - G332 = -((-6*detg*Gt332 + ddetg2*(-3 + g32*gu23) + g32*(ddetg1*gu13 + ddetg3*gu33))*INV(detg))/6.; + G323 = -((-6*detg*Gt323 + ddetg2*(-3 + g23*gu32) + g23*(ddetg1*gu31 + ddetg3*gu33))*INV(detg))/6.; - G133 = ((6*detg*Gt133 - g33*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; + G133 = ((6*detg*Gt133 - g33*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - G233 = ((6*detg*Gt233 - g33*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; + G233 = ((6*detg*Gt233 - g33*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - G333 = -((-6*detg*Gt333 + g33*(ddetg1*gu13 + ddetg2*gu23) + ddetg3*(-6 + g33*gu33))*INV(detg))/6.; + G333 = -((-6*detg*Gt333 + g33*(ddetg1*gu31 + ddetg2*gu32) + ddetg3*(-6 + g33*gu33))*INV(detg))/6.; + + R11 = Rphi11 + Rt11; + + R12 = Rphi12 + Rt12; + + R13 = Rphi13 + Rt13; + + R22 = Rphi22 + Rt22; + + R23 = Rphi23 + Rt23; + + R33 = Rphi33 + Rt33; phirhsL = beta1L*PDstandard4th1phi + beta2L*PDstandard4th2phi + beta3L*PDstandard4th3phi + ((PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)*phiL)/6. - (alphaL*trKL)/6.; - gt11rhsL = -2*alphaL*At11L + 2*(gt11L*PDstandard4th1beta1 + gt21L*PDstandard4th1beta2 + gt31L*PDstandard4th1beta3) + + gt11rhsL = -2*alphaL*At11L + 2*(gt11L*PDstandard4th1beta1 + gt12L*PDstandard4th1beta2 + gt13L*PDstandard4th1beta3) + beta1L*PDstandard4th1gt11 + beta2L*PDstandard4th2gt11 - gt11L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3gt11; - gt21rhsL = -2*alphaL*At21L + gt22L*PDstandard4th1beta2 + gt32L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt21 + - gt11L*PDstandard4th2beta1 + gt31L*PDstandard4th2beta3 + beta2L*PDstandard4th2gt21 + - gt21L*(kthird*(PDstandard4th1beta1 + PDstandard4th2beta2) - ktwothird*PDstandard4th3beta3) + - beta3L*PDstandard4th3gt21; + gt12rhsL = -2*alphaL*At12L + gt22L*PDstandard4th1beta2 + gt23L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt12 + + gt11L*PDstandard4th2beta1 + gt13L*PDstandard4th2beta3 + beta2L*PDstandard4th2gt12 + + gt12L*(kthird*(PDstandard4th1beta1 + PDstandard4th2beta2) - ktwothird*PDstandard4th3beta3) + + beta3L*PDstandard4th3gt12; - gt31rhsL = -2*alphaL*At31L + gt32L*PDstandard4th1beta2 + gt33L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt31 + - beta2L*PDstandard4th2gt31 + gt11L*PDstandard4th3beta1 + gt21L*PDstandard4th3beta2 + - gt31L*(-(ktwothird*PDstandard4th2beta2) + kthird*(PDstandard4th1beta1 + PDstandard4th3beta3)) + - beta3L*PDstandard4th3gt31; + gt13rhsL = -2*alphaL*At13L + gt23L*PDstandard4th1beta2 + gt33L*PDstandard4th1beta3 + beta1L*PDstandard4th1gt13 + + beta2L*PDstandard4th2gt13 + gt11L*PDstandard4th3beta1 + gt12L*PDstandard4th3beta2 + + gt13L*(-(ktwothird*PDstandard4th2beta2) + kthird*(PDstandard4th1beta1 + PDstandard4th3beta3)) + + beta3L*PDstandard4th3gt13; gt22rhsL = -2*alphaL*At22L + beta1L*PDstandard4th1gt22 + - 2*(gt21L*PDstandard4th2beta1 + gt22L*PDstandard4th2beta2 + gt32L*PDstandard4th2beta3) + beta2L*PDstandard4th2gt22 - + 2*(gt12L*PDstandard4th2beta1 + gt22L*PDstandard4th2beta2 + gt23L*PDstandard4th2beta3) + beta2L*PDstandard4th2gt22 - gt22L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + beta3L*PDstandard4th3gt22; - gt32rhsL = -2*alphaL*At32L + beta1L*PDstandard4th1gt32 + gt31L*PDstandard4th2beta1 + gt33L*PDstandard4th2beta3 + - beta2L*PDstandard4th2gt32 + gt21L*PDstandard4th3beta1 + gt22L*PDstandard4th3beta2 + - gt32L*(-(ktwothird*PDstandard4th1beta1) + kthird*(PDstandard4th2beta2 + PDstandard4th3beta3)) + - beta3L*PDstandard4th3gt32; + gt23rhsL = -2*alphaL*At23L + beta1L*PDstandard4th1gt23 + gt13L*PDstandard4th2beta1 + gt33L*PDstandard4th2beta3 + + beta2L*PDstandard4th2gt23 + gt12L*PDstandard4th3beta1 + gt22L*PDstandard4th3beta2 + + gt23L*(-(ktwothird*PDstandard4th1beta1) + kthird*(PDstandard4th2beta2 + PDstandard4th3beta3)) + + beta3L*PDstandard4th3gt23; gt33rhsL = -2*alphaL*At33L + beta1L*PDstandard4th1gt33 + beta2L*PDstandard4th2gt33 - gt33L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + - 2*(gt31L*PDstandard4th3beta1 + gt32L*PDstandard4th3beta2 + gt33L*PDstandard4th3beta3) + beta3L*PDstandard4th3gt33; + 2*(gt13L*PDstandard4th3beta1 + gt23L*PDstandard4th3beta2 + gt33L*PDstandard4th3beta3) + beta3L*PDstandard4th3gt33; - Xt1rhsL = kthird*(-3*(beta1L*(ddgtu1111 + ddgtu1221 + ddgtu1331) + beta2L*(ddgtu1121 + ddgtu1222 + ddgtu1332) + - beta3L*(ddgtu1131 + ddgtu1232 + ddgtu1333)) + 16*(gtu12*PDstandard4th12beta1 + gtu13*PDstandard4th13beta1) + - (7*dgtu111 + 4*(dgtu122 + dgtu133))*PDstandard4th1beta1 + + Xt1rhsL = kthird*(-3*(beta1L*(ddgtu1111 + ddgtu2112 + ddgtu3113) + beta2L*(ddgtu1112 + ddgtu2122 + ddgtu3123) + + beta3L*(ddgtu1113 + ddgtu2123 + ddgtu3133)) + 16*(gtu21*PDstandard4th12beta1 + gtu31*PDstandard4th13beta1) + + (7*dgtu111 + 4*(dgtu212 + dgtu313))*PDstandard4th1beta1 + gtu11*(10*PDstandard4th11beta1 + 4*(PDstandard4th12beta2 + PDstandard4th13beta3) - 4*alphaL*PDstandard4th1trK) + - 12*gtu23*PDstandard4th23beta1 + (9*dgtu121 + 6*dgtu233)*PDstandard4th2beta1 + - (dgtu122 - 2*(dgtu111 + dgtu133))*PDstandard4th2beta2 + - 4*(gtu12*(PDstandard4th22beta2 + PDstandard4th23beta3) + gtu13*(PDstandard4th23beta2 + PDstandard4th33beta3)) - - 6*(Atu11*PDstandard4th1alpha + Atu12*PDstandard4th2alpha + Atu13*PDstandard4th3alpha) + - (9*dgtu131 + 6*dgtu333)*PDstandard4th3beta1 + + 12*gtu32*PDstandard4th23beta1 + (9*dgtu211 + 6*dgtu323)*PDstandard4th2beta1 + + (dgtu212 - 2*(dgtu111 + dgtu313))*PDstandard4th2beta2 + + 4*(gtu21*(PDstandard4th22beta2 + PDstandard4th23beta3) + gtu31*(PDstandard4th23beta2 + PDstandard4th33beta3)) - + 6*(Atu11*PDstandard4th1alpha + Atu21*PDstandard4th2alpha + Atu31*PDstandard4th3alpha) + + (9*dgtu311 + 6*dgtu333)*PDstandard4th3beta1 + 6*(gtu22*PDstandard4th22beta1 + dgtu222*PDstandard4th2beta1 + gtu33*PDstandard4th33beta1 + - dgtu232*PDstandard4th3beta1) + 3*(dgtu112*PDstandard4th1beta2 + dgtu113*PDstandard4th1beta3 + - dgtu123*PDstandard4th2beta3 + dgtu132*PDstandard4th3beta2) + - (-2*(dgtu111 + dgtu122) + dgtu133)*PDstandard4th3beta3 + - alphaL*(12*(Atu12*Gt121 + Atu13*Gt131 + Atu23*Gt132) + 6*(Atu11*Gt111 + Atu22*Gt122 + Atu33*Gt133) + - 36*(Atu11*PDstandard4th1phi + Atu12*PDstandard4th2phi + Atu13*PDstandard4th3phi) - - 4*(gtu12*PDstandard4th2trK + gtu13*PDstandard4th3trK))); - - Xt2rhsL = kthird*(-3*(beta1L*(ddgtu1211 + ddgtu2221 + ddgtu2331) + beta2L*(ddgtu1221 + ddgtu2222 + ddgtu2332) + - beta3L*(ddgtu1231 + ddgtu2232 + ddgtu2333)) + 12*gtu13*PDstandard4th13beta2 + - (dgtu121 - 2*(dgtu222 + dgtu233))*PDstandard4th1beta1 + (9*dgtu122 + 6*dgtu133)*PDstandard4th1beta2 + - gtu12*(16*PDstandard4th12beta2 + 4*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + - (7*dgtu222 + 4*dgtu233)*PDstandard4th2beta2 + - 4*(gtu12*PDstandard4th11beta1 + gtu23*PDstandard4th13beta1 + - gtu22*(PDstandard4th12beta1 + PDstandard4th23beta3) + dgtu121*PDstandard4th2beta2) + + dgtu322*PDstandard4th3beta1) + 3*(dgtu112*PDstandard4th1beta2 + dgtu113*PDstandard4th1beta3 + + dgtu213*PDstandard4th2beta3 + dgtu312*PDstandard4th3beta2) + + (-2*(dgtu111 + dgtu212) + dgtu313)*PDstandard4th3beta3 + + alphaL*(12*(Atu21*Gt112 + Atu31*Gt113 + Atu32*Gt123) + 6*(Atu11*Gt111 + Atu22*Gt122 + Atu33*Gt133) + + 36*(Atu11*PDstandard4th1phi + Atu21*PDstandard4th2phi + Atu31*PDstandard4th3phi) - + 4*(gtu21*PDstandard4th2trK + gtu31*PDstandard4th3trK))); + + Xt2rhsL = kthird*(-3*(beta1L*(ddgtu2111 + ddgtu2212 + ddgtu3213) + beta2L*(ddgtu2112 + ddgtu2222 + ddgtu3223) + + beta3L*(ddgtu2113 + ddgtu2223 + ddgtu3233)) + 12*gtu31*PDstandard4th13beta2 + + (dgtu211 - 2*(dgtu222 + dgtu323))*PDstandard4th1beta1 + (9*dgtu212 + 6*dgtu313)*PDstandard4th1beta2 + + gtu21*(16*PDstandard4th12beta2 + 4*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + + (7*dgtu222 + 4*dgtu323)*PDstandard4th2beta2 + + 4*(gtu21*PDstandard4th11beta1 + gtu32*PDstandard4th13beta1 + + gtu22*(PDstandard4th12beta1 + PDstandard4th23beta3) + dgtu211*PDstandard4th2beta2) + gtu22*(10*PDstandard4th22beta2 - 4*alphaL*PDstandard4th2trK) - - 6*(Atu12*PDstandard4th1alpha + Atu22*PDstandard4th2alpha + Atu23*PDstandard4th3alpha) + - 3*(dgtu123*PDstandard4th1beta3 + dgtu221*PDstandard4th2beta1 + dgtu223*PDstandard4th2beta3 + - dgtu231*PDstandard4th3beta1) + (9*dgtu232 + 6*dgtu333)*PDstandard4th3beta2 + + 6*(Atu21*PDstandard4th1alpha + Atu22*PDstandard4th2alpha + Atu32*PDstandard4th3alpha) + + 3*(dgtu213*PDstandard4th1beta3 + dgtu221*PDstandard4th2beta1 + dgtu223*PDstandard4th2beta3 + + dgtu321*PDstandard4th3beta1) + (9*dgtu322 + 6*dgtu333)*PDstandard4th3beta2 + 6*(gtu11*PDstandard4th11beta2 + dgtu111*PDstandard4th1beta2 + gtu33*PDstandard4th33beta2 + - dgtu131*PDstandard4th3beta2) + (-2*(dgtu121 + dgtu222) + dgtu233)*PDstandard4th3beta3 + - alphaL*(12*(Atu12*Gt221 + Atu13*Gt231 + Atu23*Gt232) + 6*(Atu11*Gt211 + Atu22*Gt222 + Atu33*Gt233) + - 36*(Atu12*PDstandard4th1phi + Atu22*PDstandard4th2phi + Atu23*PDstandard4th3phi)) + - gtu23*(16*PDstandard4th23beta2 + 4*PDstandard4th33beta3 - 4*alphaL*PDstandard4th3trK)); - - Xt3rhsL = kthird*(-3*(beta1L*(ddgtu1311 + ddgtu2321 + ddgtu3331) + beta2L*(ddgtu1321 + ddgtu2322 + ddgtu3332) + - beta3L*(ddgtu1331 + ddgtu2332 + ddgtu3333)) + 12*gtu12*PDstandard4th12beta3 + - (dgtu131 - 2*(dgtu232 + dgtu333))*PDstandard4th1beta1 + (6*dgtu122 + 9*dgtu133)*PDstandard4th1beta3 + - gtu13*(16*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + - (dgtu232 - 2*(dgtu131 + dgtu333))*PDstandard4th2beta2 + (6*dgtu222 + 9*dgtu233)*PDstandard4th2beta3 + + dgtu311*PDstandard4th3beta2) + (-2*(dgtu211 + dgtu222) + dgtu323)*PDstandard4th3beta3 + + alphaL*(12*(Atu21*Gt212 + Atu31*Gt213 + Atu32*Gt223) + 6*(Atu11*Gt211 + Atu22*Gt222 + Atu33*Gt233) + + 36*(Atu21*PDstandard4th1phi + Atu22*PDstandard4th2phi + Atu32*PDstandard4th3phi)) + + gtu32*(16*PDstandard4th23beta2 + 4*PDstandard4th33beta3 - 4*alphaL*PDstandard4th3trK)); + + Xt3rhsL = kthird*(-3*(beta1L*(ddgtu3111 + ddgtu3212 + ddgtu3313) + beta2L*(ddgtu3112 + ddgtu3222 + ddgtu3323) + + beta3L*(ddgtu3113 + ddgtu3223 + ddgtu3333)) + 12*gtu21*PDstandard4th12beta3 + + (dgtu311 - 2*(dgtu322 + dgtu333))*PDstandard4th1beta1 + (6*dgtu212 + 9*dgtu313)*PDstandard4th1beta3 + + gtu31*(16*PDstandard4th13beta3 - 4*alphaL*PDstandard4th1trK) + + (dgtu322 - 2*(dgtu311 + dgtu333))*PDstandard4th2beta2 + (6*dgtu222 + 9*dgtu323)*PDstandard4th2beta3 + 6*(gtu11*PDstandard4th11beta3 + dgtu111*PDstandard4th1beta3 + gtu22*PDstandard4th22beta3 + - dgtu121*PDstandard4th2beta3) + gtu23*(16*PDstandard4th23beta3 - 4*alphaL*PDstandard4th2trK) - - 6*(Atu13*PDstandard4th1alpha + Atu23*PDstandard4th2alpha + Atu33*PDstandard4th3alpha) + - 3*(dgtu132*PDstandard4th1beta2 + dgtu231*PDstandard4th2beta1 + dgtu331*PDstandard4th3beta1 + - dgtu332*PDstandard4th3beta2) + (4*dgtu232 + 7*dgtu333)*PDstandard4th3beta3 + - 4*(gtu13*(PDstandard4th11beta1 + PDstandard4th12beta2) + gtu23*(PDstandard4th12beta1 + PDstandard4th22beta2) + - gtu33*(PDstandard4th13beta1 + PDstandard4th23beta2) + dgtu131*PDstandard4th3beta3) + - alphaL*(12*(Atu12*Gt321 + Atu13*Gt331 + Atu23*Gt332) + 6*(Atu11*Gt311 + Atu22*Gt322 + Atu33*Gt333) + - 36*(Atu13*PDstandard4th1phi + Atu23*PDstandard4th2phi + Atu33*PDstandard4th3phi)) + + dgtu211*PDstandard4th2beta3) + gtu32*(16*PDstandard4th23beta3 - 4*alphaL*PDstandard4th2trK) - + 6*(Atu31*PDstandard4th1alpha + Atu32*PDstandard4th2alpha + Atu33*PDstandard4th3alpha) + + 3*(dgtu312*PDstandard4th1beta2 + dgtu321*PDstandard4th2beta1 + dgtu331*PDstandard4th3beta1 + + dgtu332*PDstandard4th3beta2) + (4*dgtu322 + 7*dgtu333)*PDstandard4th3beta3 + + 4*(gtu31*(PDstandard4th11beta1 + PDstandard4th12beta2) + gtu32*(PDstandard4th12beta1 + PDstandard4th22beta2) + + gtu33*(PDstandard4th13beta1 + PDstandard4th23beta2) + dgtu311*PDstandard4th3beta3) + + alphaL*(12*(Atu21*Gt312 + Atu31*Gt313 + Atu32*Gt323) + 6*(Atu11*Gt311 + Atu22*Gt322 + Atu33*Gt333) + + 36*(Atu31*PDstandard4th1phi + Atu32*PDstandard4th2phi + Atu33*PDstandard4th3phi)) + gtu33*(10*PDstandard4th33beta3 - 4*alphaL*PDstandard4th3trK)); - trKrhsL = -(gu11*PDstandard4th11alpha) - 2*gu12*PDstandard4th12alpha - 2*gu13*PDstandard4th13alpha + - (G111*gu11 + 2*G121*gu12 + 2*G131*gu13 + G122*gu22 + 2*G132*gu23 + G133*gu33)*PDstandard4th1alpha + - beta1L*PDstandard4th1trK - gu22*PDstandard4th22alpha - 2*gu23*PDstandard4th23alpha + - (G211*gu11 + 2*G221*gu12 + 2*G231*gu13 + G222*gu22 + 2*G232*gu23 + G233*gu33)*PDstandard4th2alpha + + trKrhsL = -(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - 2*gu31*PDstandard4th13alpha + + (G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33)*PDstandard4th1alpha + + beta1L*PDstandard4th1trK - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha + + (G211*gu11 + 2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33)*PDstandard4th2alpha + beta2L*PDstandard4th2trK - gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + - 2*G331*gu13*PDstandard4th3alpha + G322*gu22*PDstandard4th3alpha + 2*G332*gu23*PDstandard4th3alpha + + G322*gu22*PDstandard4th3alpha + 2*G313*gu31*PDstandard4th3alpha + 2*G323*gu32*PDstandard4th3alpha + G333*gu33*PDstandard4th3alpha + 2*(alphaL*Atm12*Atm21 + alphaL*Atm13*Atm31 + alphaL*Atm23*Atm32 + - G321*gu12*PDstandard4th3alpha) + beta3L*PDstandard4th3trK + alphaL*SQR(Atm11) + alphaL*SQR(Atm22) + + G312*gu21*PDstandard4th3alpha) + beta3L*PDstandard4th3trK + alphaL*SQR(Atm11) + alphaL*SQR(Atm22) + alphaL*SQR(Atm33) + alphaL*kthird*SQR(trKL); - At11rhsL = beta1L*PDstandard4th1At11 + 2*(At11L*PDstandard4th1beta1 + At21L*PDstandard4th1beta2 + - At31L*PDstandard4th1beta3) + beta2L*PDstandard4th2At11 + beta3L*PDstandard4th3At11 - + At11rhsL = beta1L*PDstandard4th1At11 + 2*(At11L*PDstandard4th1beta1 + At12L*PDstandard4th1beta2 + + At13L*PDstandard4th1beta3) + beta2L*PDstandard4th2At11 + beta3L*PDstandard4th3At11 - At11L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) - - em4phi*kthird*(3*PDstandard4th11alpha - g11*gu11*PDstandard4th11alpha - 2*g11*gu12*PDstandard4th12alpha - - 2*g11*gu13*PDstandard4th13alpha + (G111*(-3 + g11*gu11) + - g11*(2*G121*gu12 + 2*G131*gu13 + G122*gu22 + 2*G132*gu23 + G133*gu33))*PDstandard4th1alpha - - g11*gu22*PDstandard4th22alpha - 2*g11*gu23*PDstandard4th23alpha + - (G211*(-3 + g11*gu11) + g11*(2*G221*gu12 + 2*G231*gu13 + G222*gu22 + 2*G232*gu23 + G233*gu33))* + em4phi*kthird*(3*PDstandard4th11alpha - g11*gu11*PDstandard4th11alpha - 2*g11*gu21*PDstandard4th12alpha - + 2*g11*gu31*PDstandard4th13alpha + (G111*(-3 + g11*gu11) + + g11*(2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandard4th1alpha - + g11*gu22*PDstandard4th22alpha - 2*g11*gu32*PDstandard4th23alpha + + (G211*(-3 + g11*gu11) + g11*(2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33))* PDstandard4th2alpha - g11*gu33*PDstandard4th33alpha - 3*G311*PDstandard4th3alpha + - g11*G311*gu11*PDstandard4th3alpha + 2*g11*G321*gu12*PDstandard4th3alpha + 2*g11*G331*gu13*PDstandard4th3alpha + - g11*G322*gu22*PDstandard4th3alpha + 2*g11*G332*gu23*PDstandard4th3alpha + g11*G333*gu33*PDstandard4th3alpha - - 3*alphaL*R11 + alphaL*g11*gu11*R11 + 2*alphaL*g11*gu12*R21 + alphaL*g11*gu22*R22 + 2*alphaL*g11*gu13*R31 + - 2*alphaL*g11*gu23*R32 + alphaL*g11*gu33*R33) + alphaL*(-2*(At11L*Atm11 + At21L*Atm21 + At31L*Atm31) + At11L*trKL); - - At21rhsL = beta1L*PDstandard4th1At21 + At22L*PDstandard4th1beta2 + At32L*PDstandard4th1beta3 + - beta2L*PDstandard4th2At21 + At11L*PDstandard4th2beta1 + At31L*PDstandard4th2beta3 + beta3L*PDstandard4th3At21 + - At21L*(PDstandard4th1beta1 + PDstandard4th2beta2 - + g11*G311*gu11*PDstandard4th3alpha + 2*g11*G312*gu21*PDstandard4th3alpha + g11*G322*gu22*PDstandard4th3alpha + + 2*g11*G313*gu31*PDstandard4th3alpha + 2*g11*G323*gu32*PDstandard4th3alpha + g11*G333*gu33*PDstandard4th3alpha - + 3*alphaL*R11 + alphaL*g11*gu11*R11 + 2*alphaL*g11*gu21*R12 + 2*alphaL*g11*gu31*R13 + alphaL*g11*gu22*R22 + + 2*alphaL*g11*gu32*R23 + alphaL*g11*gu33*R33) + alphaL*(-2*(At11L*Atm11 + At12L*Atm21 + At13L*Atm31) + At11L*trKL); + + At12rhsL = beta1L*PDstandard4th1At12 + At22L*PDstandard4th1beta2 + At23L*PDstandard4th1beta3 + + beta2L*PDstandard4th2At12 + At11L*PDstandard4th2beta1 + At13L*PDstandard4th2beta3 + beta3L*PDstandard4th3At12 + + At12L*(PDstandard4th1beta1 + PDstandard4th2beta2 - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - - em4phi*kthird*(3*PDstandard4th12alpha + (G121*(-3 + 2*g21*gu12) + - g21*(G111*gu11 + G122*gu22 + 2*(G131*gu13 + G132*gu23) + G133*gu33))*PDstandard4th1alpha + - (G221*(-3 + 2*g21*gu12) + g21*(G211*gu11 + G222*gu22 + 2*(G231*gu13 + G232*gu23) + G233*gu33))* - PDstandard4th2alpha + G321*(-3 + 2*g21*gu12)*PDstandard4th3alpha + - alphaL*(-3*R21 + g21*(gu22*R22 + 2*gu23*R32)) + - g21*(-(gu11*PDstandard4th11alpha) - 2*gu12*PDstandard4th12alpha - 2*gu13*PDstandard4th13alpha - - gu22*PDstandard4th22alpha - 2*gu23*PDstandard4th23alpha - gu33*PDstandard4th33alpha + - G311*gu11*PDstandard4th3alpha + 2*G331*gu13*PDstandard4th3alpha + G322*gu22*PDstandard4th3alpha + - 2*G332*gu23*PDstandard4th3alpha + G333*gu33*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu12*R21 + - 2*alphaL*gu13*R31 + alphaL*gu33*R33)) + alphaL*(-2*(At11L*Atm12 + At21L*Atm22 + At31L*Atm32) + At21L*trKL); - - At31rhsL = beta1L*PDstandard4th1At31 + At32L*PDstandard4th1beta2 + At33L*PDstandard4th1beta3 + - beta2L*PDstandard4th2At31 + beta3L*PDstandard4th3At31 + At11L*PDstandard4th3beta1 + At21L*PDstandard4th3beta2 + - At31L*(PDstandard4th1beta1 + PDstandard4th3beta3 - + em4phi*kthird*(3*PDstandard4th12alpha + (G112*(-3 + 2*g12*gu21) + + g12*(G111*gu11 + G122*gu22 + 2*(G113*gu31 + G123*gu32) + G133*gu33))*PDstandard4th1alpha + + (G212*(-3 + 2*g12*gu21) + g12*(G211*gu11 + G222*gu22 + 2*(G213*gu31 + G223*gu32) + G233*gu33))* + PDstandard4th2alpha + G312*(-3 + 2*g12*gu21)*PDstandard4th3alpha + + alphaL*(-3*R12 + 2*g12*(gu31*R13 + gu32*R23)) + + g12*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - 2*gu31*PDstandard4th13alpha - + gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - gu33*PDstandard4th33alpha + + G311*gu11*PDstandard4th3alpha + G322*gu22*PDstandard4th3alpha + 2*G313*gu31*PDstandard4th3alpha + + 2*G323*gu32*PDstandard4th3alpha + G333*gu33*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + alphaL*gu22*R22 + alphaL*gu33*R33)) + alphaL*(-2*(At11L*Atm12 + At12L*Atm22 + At13L*Atm32) + At12L*trKL); + + At13rhsL = beta1L*PDstandard4th1At13 + At23L*PDstandard4th1beta2 + At33L*PDstandard4th1beta3 + + beta2L*PDstandard4th2At13 + beta3L*PDstandard4th3At13 + At11L*PDstandard4th3beta1 + At12L*PDstandard4th3beta2 + + At13L*(PDstandard4th1beta1 + PDstandard4th3beta3 - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - - em4phi*kthird*(3*PDstandard4th13alpha + (G131*(-3 + 2*g31*gu13) + - g31*(G111*gu11 + G122*gu22 + 2*(G121*gu12 + G132*gu23) + G133*gu33))*PDstandard4th1alpha + - (G231*(-3 + 2*g31*gu13) + g31*(G211*gu11 + G222*gu22 + 2*(G221*gu12 + G232*gu23) + G233*gu33))* - PDstandard4th2alpha + (G331*(-3 + 2*g31*gu13) + g31*(G322*gu22 + 2*(G321*gu12 + G332*gu23) + G333*gu33))* - PDstandard4th3alpha + alphaL*(-3*R31 + 2*g31*gu23*R32) + - g31*(-(gu11*PDstandard4th11alpha) - 2*gu12*PDstandard4th12alpha - 2*gu13*PDstandard4th13alpha - - gu22*PDstandard4th22alpha - 2*gu23*PDstandard4th23alpha - gu33*PDstandard4th33alpha + - G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu12*R21 + alphaL*gu22*R22 + 2*alphaL*gu13*R31 + - alphaL*gu33*R33)) + alphaL*(-2*(At11L*Atm13 + At21L*Atm23 + At31L*Atm33) + At31L*trKL); + em4phi*kthird*(3*PDstandard4th13alpha + (G113*(-3 + 2*g13*gu31) + + g13*(G111*gu11 + G122*gu22 + 2*(G112*gu21 + G123*gu32) + G133*gu33))*PDstandard4th1alpha + + (G213*(-3 + 2*g13*gu31) + g13*(G211*gu11 + G222*gu22 + 2*(G212*gu21 + G223*gu32) + G233*gu33))* + PDstandard4th2alpha + (G313*(-3 + 2*g13*gu31) + g13*(G322*gu22 + 2*(G312*gu21 + G323*gu32) + G333*gu33))* + PDstandard4th3alpha + g13*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - + 2*gu31*PDstandard4th13alpha - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - + gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + 2*alphaL*gu31*R13 + 2*alphaL*gu32*R23) + alphaL*(-3*R13 + g13*(gu22*R22 + gu33*R33))) + + alphaL*(-2*(At11L*Atm13 + At12L*Atm23 + At13L*Atm33) + At13L*trKL); At22rhsL = beta1L*PDstandard4th1At22 + beta2L*PDstandard4th2At22 + - 2*(At21L*PDstandard4th2beta1 + At22L*PDstandard4th2beta2 + At32L*PDstandard4th2beta3) + beta3L*PDstandard4th3At22 - + 2*(At12L*PDstandard4th2beta1 + At22L*PDstandard4th2beta2 + At23L*PDstandard4th2beta3) + beta3L*PDstandard4th3At22 - At22L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) - - em4phi*kthird*(-(g22*gu11*PDstandard4th11alpha) - 2*g22*gu12*PDstandard4th12alpha - - 2*g22*gu13*PDstandard4th13alpha + (G122*(-3 + g22*gu22) + - g22*(G111*gu11 + 2*G121*gu12 + 2*G131*gu13 + 2*G132*gu23 + G133*gu33))*PDstandard4th1alpha + - 3*PDstandard4th22alpha - g22*gu22*PDstandard4th22alpha - 2*g22*gu23*PDstandard4th23alpha + - (G222*(-3 + g22*gu22) + g22*(G211*gu11 + 2*G221*gu12 + 2*G231*gu13 + 2*G232*gu23 + G233*gu33))* + em4phi*kthird*(-(g22*gu11*PDstandard4th11alpha) - 2*g22*gu21*PDstandard4th12alpha - + 2*g22*gu31*PDstandard4th13alpha + (G122*(-3 + g22*gu22) + + g22*(G111*gu11 + 2*G112*gu21 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33))*PDstandard4th1alpha + + 3*PDstandard4th22alpha - g22*gu22*PDstandard4th22alpha - 2*g22*gu32*PDstandard4th23alpha + + (G222*(-3 + g22*gu22) + g22*(G211*gu11 + 2*G212*gu21 + 2*G213*gu31 + 2*G223*gu32 + G233*gu33))* PDstandard4th2alpha - g22*gu33*PDstandard4th33alpha - 3*G322*PDstandard4th3alpha + - g22*G311*gu11*PDstandard4th3alpha + 2*g22*G321*gu12*PDstandard4th3alpha + 2*g22*G331*gu13*PDstandard4th3alpha + - g22*G322*gu22*PDstandard4th3alpha + 2*g22*G332*gu23*PDstandard4th3alpha + g22*G333*gu33*PDstandard4th3alpha + - alphaL*g22*gu11*R11 + 2*alphaL*g22*gu12*R21 - 3*alphaL*R22 + alphaL*g22*gu22*R22 + 2*alphaL*g22*gu13*R31 + - 2*alphaL*g22*gu23*R32 + alphaL*g22*gu33*R33) + alphaL*(-2*(At21L*Atm12 + At22L*Atm22 + At32L*Atm32) + At22L*trKL); - - At32rhsL = beta1L*PDstandard4th1At32 + beta2L*PDstandard4th2At32 + At31L*PDstandard4th2beta1 + - At33L*PDstandard4th2beta3 + beta3L*PDstandard4th3At32 + At21L*PDstandard4th3beta1 + At22L*PDstandard4th3beta2 + - At32L*(PDstandard4th2beta2 + PDstandard4th3beta3 - + g22*G311*gu11*PDstandard4th3alpha + 2*g22*G312*gu21*PDstandard4th3alpha + g22*G322*gu22*PDstandard4th3alpha + + 2*g22*G313*gu31*PDstandard4th3alpha + 2*g22*G323*gu32*PDstandard4th3alpha + g22*G333*gu33*PDstandard4th3alpha + + alphaL*g22*gu11*R11 + 2*alphaL*g22*gu21*R12 + 2*alphaL*g22*gu31*R13 - 3*alphaL*R22 + alphaL*g22*gu22*R22 + + 2*alphaL*g22*gu32*R23 + alphaL*g22*gu33*R33) + alphaL*(-2*(At12L*Atm12 + At22L*Atm22 + At23L*Atm32) + At22L*trKL); + + At23rhsL = beta1L*PDstandard4th1At23 + beta2L*PDstandard4th2At23 + At13L*PDstandard4th2beta1 + + At33L*PDstandard4th2beta3 + beta3L*PDstandard4th3At23 + At12L*PDstandard4th3beta1 + At22L*PDstandard4th3beta2 + + At23L*(PDstandard4th2beta2 + PDstandard4th3beta3 - ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3)) - - em4phi*kthird*((G132*(-3 + 2*g32*gu23) + g32*(G111*gu11 + 2*(G121*gu12 + G131*gu13) + G122*gu22 + G133*gu33))* + em4phi*kthird*((G123*(-3 + 2*g23*gu32) + g23*(G111*gu11 + G122*gu22 + 2*(G112*gu21 + G113*gu31) + G133*gu33))* PDstandard4th1alpha + 3*PDstandard4th23alpha + - (G232*(-3 + 2*g32*gu23) + g32*(G211*gu11 + 2*(G221*gu12 + G231*gu13) + G222*gu22 + G233*gu33))* - PDstandard4th2alpha + (G332*(-3 + 2*g32*gu23) + g32*(2*(G321*gu12 + G331*gu13) + G322*gu22 + G333*gu33))* - PDstandard4th3alpha + g32*(-(gu11*PDstandard4th11alpha) - 2*gu12*PDstandard4th12alpha - - 2*gu13*PDstandard4th13alpha - gu22*PDstandard4th22alpha - 2*gu23*PDstandard4th23alpha - - gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu12*R21 + - alphaL*gu22*R22 + 2*alphaL*gu13*R31 + 2*alphaL*gu23*R32) + alphaL*(-3*R32 + g32*gu33*R33)) + - alphaL*(-2*(At21L*Atm13 + At22L*Atm23 + At32L*Atm33) + At32L*trKL); + (G223*(-3 + 2*g23*gu32) + g23*(G211*gu11 + G222*gu22 + 2*(G212*gu21 + G213*gu31) + G233*gu33))* + PDstandard4th2alpha + (G323*(-3 + 2*g23*gu32) + g23*(G322*gu22 + 2*(G312*gu21 + G313*gu31) + G333*gu33))* + PDstandard4th3alpha + g23*(-(gu11*PDstandard4th11alpha) - 2*gu21*PDstandard4th12alpha - + 2*gu31*PDstandard4th13alpha - gu22*PDstandard4th22alpha - 2*gu32*PDstandard4th23alpha - + gu33*PDstandard4th33alpha + G311*gu11*PDstandard4th3alpha + alphaL*gu11*R11 + 2*alphaL*gu21*R12 + + 2*alphaL*gu31*R13 + alphaL*gu22*R22 + 2*alphaL*gu32*R23) + alphaL*(-3*R23 + g23*gu33*R33)) + + alphaL*(-2*(At12L*Atm13 + At22L*Atm23 + At23L*Atm33) + At23L*trKL); At33rhsL = beta1L*PDstandard4th1At33 + beta2L*PDstandard4th2At33 + beta3L*PDstandard4th3At33 - At33L*ktwothird*(PDstandard4th1beta1 + PDstandard4th2beta2 + PDstandard4th3beta3) + - 2*(At31L*PDstandard4th3beta1 + At32L*PDstandard4th3beta2 + At33L*PDstandard4th3beta3) - - em4phi*kthird*(-(g33*gu11*PDstandard4th11alpha) - 2*g33*gu12*PDstandard4th12alpha - - 2*g33*gu13*PDstandard4th13alpha + (g33*(G111*gu11 + 2*G121*gu12 + 2*G131*gu13 + G122*gu22 + 2*G132*gu23) + - G133*(-3 + g33*gu33))*PDstandard4th1alpha - g33*gu22*PDstandard4th22alpha - 2*g33*gu23*PDstandard4th23alpha + - (g33*(G211*gu11 + 2*G221*gu12 + 2*G231*gu13 + G222*gu22 + 2*G232*gu23) + G233*(-3 + g33*gu33))* + 2*(At13L*PDstandard4th3beta1 + At23L*PDstandard4th3beta2 + At33L*PDstandard4th3beta3) - + em4phi*kthird*(-(g33*gu11*PDstandard4th11alpha) - 2*g33*gu21*PDstandard4th12alpha - + 2*g33*gu31*PDstandard4th13alpha + (g33*(G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32) + + G133*(-3 + g33*gu33))*PDstandard4th1alpha - g33*gu22*PDstandard4th22alpha - 2*g33*gu32*PDstandard4th23alpha + + (g33*(G211*gu11 + 2*G212*gu21 + G222*gu22 + 2*G213*gu31 + 2*G223*gu32) + G233*(-3 + g33*gu33))* PDstandard4th2alpha + 3*PDstandard4th33alpha - g33*gu33*PDstandard4th33alpha - 3*G333*PDstandard4th3alpha + - G311*g33*gu11*PDstandard4th3alpha + 2*G321*g33*gu12*PDstandard4th3alpha + 2*g33*G331*gu13*PDstandard4th3alpha + - G322*g33*gu22*PDstandard4th3alpha + 2*g33*G332*gu23*PDstandard4th3alpha + g33*G333*gu33*PDstandard4th3alpha + - alphaL*g33*gu11*R11 + 2*alphaL*g33*gu12*R21 + alphaL*g33*gu22*R22 + 2*alphaL*g33*gu13*R31 + - 2*alphaL*g33*gu23*R32 - 3*alphaL*R33 + alphaL*g33*gu33*R33) + - alphaL*(-2*(At31L*Atm13 + At32L*Atm23 + At33L*Atm33) + At33L*trKL); + G311*g33*gu11*PDstandard4th3alpha + 2*G312*g33*gu21*PDstandard4th3alpha + G322*g33*gu22*PDstandard4th3alpha + + 2*G313*g33*gu31*PDstandard4th3alpha + 2*G323*g33*gu32*PDstandard4th3alpha + g33*G333*gu33*PDstandard4th3alpha + + alphaL*g33*gu11*R11 + 2*alphaL*g33*gu21*R12 + 2*alphaL*g33*gu31*R13 + alphaL*g33*gu22*R22 + + 2*alphaL*g33*gu32*R23 - 3*alphaL*R33 + alphaL*g33*gu33*R33) + + alphaL*(-2*(At13L*Atm13 + At23L*Atm23 + At33L*Atm33) + At33L*trKL); alpharhsL = beta1L*PDstandard4th1alpha + beta2L*PDstandard4th2alpha + beta3L*PDstandard4th3alpha - dtalphaL*harmonicF*pow(alphaL,harmonicN); @@ -1449,10 +1451,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal /* Copy local copies back to grid functions */ alpharhs[index] = alpharhsL; At11rhs[index] = At11rhsL; - At21rhs[index] = At21rhsL; + At12rhs[index] = At12rhsL; + At13rhs[index] = At13rhsL; At22rhs[index] = At22rhsL; - At31rhs[index] = At31rhsL; - At32rhs[index] = At32rhsL; + At23rhs[index] = At23rhsL; At33rhs[index] = At33rhsL; beta1rhs[index] = beta1rhsL; beta2rhs[index] = beta2rhsL; @@ -1462,10 +1464,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal dtbeta2rhs[index] = dtbeta2rhsL; dtbeta3rhs[index] = dtbeta3rhsL; gt11rhs[index] = gt11rhsL; - gt21rhs[index] = gt21rhsL; + gt12rhs[index] = gt12rhsL; + gt13rhs[index] = gt13rhsL; gt22rhs[index] = gt22rhsL; - gt31rhs[index] = gt31rhsL; - gt32rhs[index] = gt32rhsL; + gt23rhs[index] = gt23rhsL; gt33rhs[index] = gt33rhsL; phirhs[index] = phirhsL; trKrhs[index] = trKrhsL; diff --git a/ML_BSSN/src/ML_BSSN_constraints.c b/ML_BSSN/src/ML_BSSN_constraints.c index f818a2e..2ee6490 100644 --- a/ML_BSSN/src/ML_BSSN_constraints.c +++ b/ML_BSSN/src/ML_BSSN_constraints.c @@ -94,45 +94,45 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA subblock_index = i - min[0] + (max[0] - min[0]) * (j - min[1] + (max[1]-min[1]) * (k - min[2])); /* Declare shorthands */ + CCTK_REAL Atm11 = INITVALUE, Atm12 = INITVALUE, Atm13 = INITVALUE, Atm21 = INITVALUE, Atm22 = INITVALUE, Atm23 = INITVALUE; + CCTK_REAL Atm31 = INITVALUE, Atm32 = INITVALUE, Atm33 = INITVALUE; CCTK_REAL ddetg1 = INITVALUE, ddetg2 = INITVALUE, ddetg3 = INITVALUE; CCTK_REAL ddetgt1 = INITVALUE, ddetgt2 = INITVALUE, ddetgt3 = INITVALUE; CCTK_REAL detg = INITVALUE; CCTK_REAL detgt = INITVALUE; CCTK_REAL e4phi = INITVALUE; + CCTK_REAL em4phi = INITVALUE; CCTK_REAL g11 = INITVALUE; - CCTK_REAL G111 = INITVALUE, G121 = INITVALUE, G122 = INITVALUE, G131 = INITVALUE, G132 = INITVALUE, G133 = INITVALUE; - CCTK_REAL g21 = INITVALUE; - CCTK_REAL G211 = INITVALUE; + CCTK_REAL G111 = INITVALUE, G112 = INITVALUE, G113 = INITVALUE; + CCTK_REAL g12 = INITVALUE; + CCTK_REAL G122 = INITVALUE, G123 = INITVALUE; + CCTK_REAL g13 = INITVALUE; + CCTK_REAL G133 = INITVALUE, G211 = INITVALUE, G212 = INITVALUE, G213 = INITVALUE; CCTK_REAL g22 = INITVALUE; - CCTK_REAL G221 = INITVALUE, G222 = INITVALUE, G231 = INITVALUE, G232 = INITVALUE, G233 = INITVALUE; - CCTK_REAL g31 = INITVALUE; - CCTK_REAL G311 = INITVALUE; - CCTK_REAL g32 = INITVALUE; - CCTK_REAL G321 = INITVALUE, G322 = INITVALUE; + CCTK_REAL G222 = INITVALUE, G223 = INITVALUE; + CCTK_REAL g23 = INITVALUE; + CCTK_REAL G233 = INITVALUE, G311 = INITVALUE, G312 = INITVALUE, G313 = INITVALUE, G322 = INITVALUE, G323 = INITVALUE; CCTK_REAL g33 = INITVALUE; - CCTK_REAL G331 = INITVALUE, G332 = INITVALUE, G333 = INITVALUE; - CCTK_REAL gK112 = INITVALUE, gK113 = INITVALUE, gK211 = INITVALUE, gK212 = INITVALUE, gK213 = INITVALUE, gK221 = INITVALUE; - CCTK_REAL gK223 = INITVALUE, gK311 = INITVALUE, gK312 = INITVALUE, gK313 = INITVALUE, gK321 = INITVALUE, gK322 = INITVALUE; - CCTK_REAL gK323 = INITVALUE, gK331 = INITVALUE, gK332 = INITVALUE; - CCTK_REAL Gt111 = INITVALUE, Gt121 = INITVALUE, Gt122 = INITVALUE, Gt131 = INITVALUE, Gt132 = INITVALUE, Gt133 = INITVALUE; - CCTK_REAL Gt211 = INITVALUE, Gt221 = INITVALUE, Gt222 = INITVALUE, Gt231 = INITVALUE, Gt232 = INITVALUE, Gt233 = INITVALUE; - CCTK_REAL Gt311 = INITVALUE, Gt321 = INITVALUE, Gt322 = INITVALUE, Gt331 = INITVALUE, Gt332 = INITVALUE, Gt333 = INITVALUE; - CCTK_REAL gtu11 = INITVALUE, gtu12 = INITVALUE, gtu13 = INITVALUE, gtu22 = INITVALUE, gtu23 = INITVALUE, gtu33 = INITVALUE; - CCTK_REAL gu11 = INITVALUE, gu12 = INITVALUE, gu13 = INITVALUE, gu22 = INITVALUE, gu23 = INITVALUE, gu33 = INITVALUE; - CCTK_REAL K11 = INITVALUE, K21 = INITVALUE, K22 = INITVALUE, K31 = INITVALUE, K32 = INITVALUE, K33 = INITVALUE; - CCTK_REAL Km11 = INITVALUE, Km12 = INITVALUE, Km13 = INITVALUE, Km21 = INITVALUE, Km22 = INITVALUE, Km23 = INITVALUE; - CCTK_REAL Km31 = INITVALUE, Km32 = INITVALUE, Km33 = INITVALUE; - CCTK_REAL R11 = INITVALUE, R21 = INITVALUE, R22 = INITVALUE, R31 = INITVALUE, R32 = INITVALUE, R33 = INITVALUE; - CCTK_REAL Rphi11 = INITVALUE, Rphi21 = INITVALUE, Rphi22 = INITVALUE, Rphi31 = INITVALUE, Rphi32 = INITVALUE, Rphi33 = INITVALUE; - CCTK_REAL Rt11 = INITVALUE, Rt21 = INITVALUE, Rt22 = INITVALUE, Rt31 = INITVALUE, Rt32 = INITVALUE, Rt33 = INITVALUE; + CCTK_REAL G333 = INITVALUE; + CCTK_REAL gK112 = INITVALUE, gK113 = INITVALUE, gK121 = INITVALUE, gK122 = INITVALUE, gK123 = INITVALUE, gK131 = INITVALUE; + CCTK_REAL gK132 = INITVALUE, gK133 = INITVALUE, gK221 = INITVALUE, gK223 = INITVALUE, gK231 = INITVALUE, gK232 = INITVALUE; + CCTK_REAL gK233 = INITVALUE, gK331 = INITVALUE, gK332 = INITVALUE; + CCTK_REAL Gt111 = INITVALUE, Gt112 = INITVALUE, Gt113 = INITVALUE, Gt122 = INITVALUE, Gt123 = INITVALUE, Gt133 = INITVALUE; + CCTK_REAL Gt211 = INITVALUE, Gt212 = INITVALUE, Gt213 = INITVALUE, Gt222 = INITVALUE, Gt223 = INITVALUE, Gt233 = INITVALUE; + CCTK_REAL Gt311 = INITVALUE, Gt312 = INITVALUE, Gt313 = INITVALUE, Gt322 = INITVALUE, Gt323 = INITVALUE, Gt333 = INITVALUE; + CCTK_REAL gtu11 = INITVALUE, gtu21 = INITVALUE, gtu22 = INITVALUE, gtu31 = INITVALUE, gtu32 = INITVALUE, gtu33 = INITVALUE; + CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE; + CCTK_REAL R11 = INITVALUE, R12 = INITVALUE, R13 = INITVALUE, R22 = INITVALUE, R23 = INITVALUE, R33 = INITVALUE; + CCTK_REAL Rphi11 = INITVALUE, Rphi12 = INITVALUE, Rphi13 = INITVALUE, Rphi22 = INITVALUE, Rphi23 = INITVALUE, Rphi33 = INITVALUE; + CCTK_REAL Rt11 = INITVALUE, Rt12 = INITVALUE, Rt13 = INITVALUE, Rt22 = INITVALUE, Rt23 = INITVALUE, Rt33 = INITVALUE; CCTK_REAL trR = INITVALUE; /* Declare local copies of grid functions */ - CCTK_REAL At11L = INITVALUE, At21L = INITVALUE, At22L = INITVALUE, At31L = INITVALUE, At32L = INITVALUE, At33L = INITVALUE; + CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE; CCTK_REAL cAL = INITVALUE; CCTK_REAL cSL = INITVALUE; CCTK_REAL cXt1L = INITVALUE, cXt2L = INITVALUE, cXt3L = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; CCTK_REAL HL = INITVALUE; CCTK_REAL M1L = INITVALUE, M2L = INITVALUE, M3L = INITVALUE; CCTK_REAL phiL = INITVALUE; @@ -143,17 +143,17 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Declare derivatives */ CCTK_REAL PDstandard4th2At11 = INITVALUE; CCTK_REAL PDstandard4th3At11 = INITVALUE; - CCTK_REAL PDstandard4th1At21 = INITVALUE; - CCTK_REAL PDstandard4th2At21 = INITVALUE; - CCTK_REAL PDstandard4th3At21 = INITVALUE; + CCTK_REAL PDstandard4th1At12 = INITVALUE; + CCTK_REAL PDstandard4th2At12 = INITVALUE; + CCTK_REAL PDstandard4th3At12 = INITVALUE; + CCTK_REAL PDstandard4th1At13 = INITVALUE; + CCTK_REAL PDstandard4th2At13 = INITVALUE; + CCTK_REAL PDstandard4th3At13 = INITVALUE; CCTK_REAL PDstandard4th1At22 = INITVALUE; CCTK_REAL PDstandard4th3At22 = INITVALUE; - CCTK_REAL PDstandard4th1At31 = INITVALUE; - CCTK_REAL PDstandard4th2At31 = INITVALUE; - CCTK_REAL PDstandard4th3At31 = INITVALUE; - CCTK_REAL PDstandard4th1At32 = INITVALUE; - CCTK_REAL PDstandard4th2At32 = INITVALUE; - CCTK_REAL PDstandard4th3At32 = INITVALUE; + CCTK_REAL PDstandard4th1At23 = INITVALUE; + CCTK_REAL PDstandard4th2At23 = INITVALUE; + CCTK_REAL PDstandard4th3At23 = INITVALUE; CCTK_REAL PDstandard4th1At33 = INITVALUE; CCTK_REAL PDstandard4th2At33 = INITVALUE; CCTK_REAL PDstandard4th1gt11 = INITVALUE; @@ -168,18 +168,30 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA CCTK_REAL PDstandard4th23gt11 = INITVALUE; CCTK_REAL PDstandard4th31gt11 = INITVALUE; CCTK_REAL PDstandard4th32gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt21 = INITVALUE; - CCTK_REAL PDstandard4th2gt21 = INITVALUE; - CCTK_REAL PDstandard4th3gt21 = INITVALUE; - CCTK_REAL PDstandard4th11gt21 = INITVALUE; - CCTK_REAL PDstandard4th22gt21 = INITVALUE; - CCTK_REAL PDstandard4th33gt21 = INITVALUE; - CCTK_REAL PDstandard4th12gt21 = INITVALUE; - CCTK_REAL PDstandard4th13gt21 = INITVALUE; - CCTK_REAL PDstandard4th21gt21 = INITVALUE; - CCTK_REAL PDstandard4th23gt21 = INITVALUE; - CCTK_REAL PDstandard4th31gt21 = INITVALUE; - CCTK_REAL PDstandard4th32gt21 = INITVALUE; + CCTK_REAL PDstandard4th1gt12 = INITVALUE; + CCTK_REAL PDstandard4th2gt12 = INITVALUE; + CCTK_REAL PDstandard4th3gt12 = INITVALUE; + CCTK_REAL PDstandard4th11gt12 = INITVALUE; + CCTK_REAL PDstandard4th22gt12 = INITVALUE; + CCTK_REAL PDstandard4th33gt12 = INITVALUE; + CCTK_REAL PDstandard4th12gt12 = INITVALUE; + CCTK_REAL PDstandard4th13gt12 = INITVALUE; + CCTK_REAL PDstandard4th21gt12 = INITVALUE; + CCTK_REAL PDstandard4th23gt12 = INITVALUE; + CCTK_REAL PDstandard4th31gt12 = INITVALUE; + CCTK_REAL PDstandard4th32gt12 = INITVALUE; + CCTK_REAL PDstandard4th1gt13 = INITVALUE; + CCTK_REAL PDstandard4th2gt13 = INITVALUE; + CCTK_REAL PDstandard4th3gt13 = INITVALUE; + CCTK_REAL PDstandard4th11gt13 = INITVALUE; + CCTK_REAL PDstandard4th22gt13 = INITVALUE; + CCTK_REAL PDstandard4th33gt13 = INITVALUE; + CCTK_REAL PDstandard4th12gt13 = INITVALUE; + CCTK_REAL PDstandard4th13gt13 = INITVALUE; + CCTK_REAL PDstandard4th21gt13 = INITVALUE; + CCTK_REAL PDstandard4th23gt13 = INITVALUE; + CCTK_REAL PDstandard4th31gt13 = INITVALUE; + CCTK_REAL PDstandard4th32gt13 = INITVALUE; CCTK_REAL PDstandard4th1gt22 = INITVALUE; CCTK_REAL PDstandard4th2gt22 = INITVALUE; CCTK_REAL PDstandard4th3gt22 = INITVALUE; @@ -192,30 +204,18 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA CCTK_REAL PDstandard4th23gt22 = INITVALUE; CCTK_REAL PDstandard4th31gt22 = INITVALUE; CCTK_REAL PDstandard4th32gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt31 = INITVALUE; - CCTK_REAL PDstandard4th2gt31 = INITVALUE; - CCTK_REAL PDstandard4th3gt31 = INITVALUE; - CCTK_REAL PDstandard4th11gt31 = INITVALUE; - CCTK_REAL PDstandard4th22gt31 = INITVALUE; - CCTK_REAL PDstandard4th33gt31 = INITVALUE; - CCTK_REAL PDstandard4th12gt31 = INITVALUE; - CCTK_REAL PDstandard4th13gt31 = INITVALUE; - CCTK_REAL PDstandard4th21gt31 = INITVALUE; - CCTK_REAL PDstandard4th23gt31 = INITVALUE; - CCTK_REAL PDstandard4th31gt31 = INITVALUE; - CCTK_REAL PDstandard4th32gt31 = INITVALUE; - CCTK_REAL PDstandard4th1gt32 = INITVALUE; - CCTK_REAL PDstandard4th2gt32 = INITVALUE; - CCTK_REAL PDstandard4th3gt32 = INITVALUE; - CCTK_REAL PDstandard4th11gt32 = INITVALUE; - CCTK_REAL PDstandard4th22gt32 = INITVALUE; - CCTK_REAL PDstandard4th33gt32 = INITVALUE; - CCTK_REAL PDstandard4th12gt32 = INITVALUE; - CCTK_REAL PDstandard4th13gt32 = INITVALUE; - CCTK_REAL PDstandard4th21gt32 = INITVALUE; - CCTK_REAL PDstandard4th23gt32 = INITVALUE; - CCTK_REAL PDstandard4th31gt32 = INITVALUE; - CCTK_REAL PDstandard4th32gt32 = INITVALUE; + CCTK_REAL PDstandard4th1gt23 = INITVALUE; + CCTK_REAL PDstandard4th2gt23 = INITVALUE; + CCTK_REAL PDstandard4th3gt23 = INITVALUE; + CCTK_REAL PDstandard4th11gt23 = INITVALUE; + CCTK_REAL PDstandard4th22gt23 = INITVALUE; + CCTK_REAL PDstandard4th33gt23 = INITVALUE; + CCTK_REAL PDstandard4th12gt23 = INITVALUE; + CCTK_REAL PDstandard4th13gt23 = INITVALUE; + CCTK_REAL PDstandard4th21gt23 = INITVALUE; + CCTK_REAL PDstandard4th23gt23 = INITVALUE; + CCTK_REAL PDstandard4th31gt23 = INITVALUE; + CCTK_REAL PDstandard4th32gt23 = INITVALUE; CCTK_REAL PDstandard4th1gt33 = INITVALUE; CCTK_REAL PDstandard4th2gt33 = INITVALUE; CCTK_REAL PDstandard4th3gt33 = INITVALUE; @@ -255,16 +255,16 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Assign local copies of grid functions */ At11L = At11[index]; - At21L = At21[index]; + At12L = At12[index]; + At13L = At13[index]; At22L = At22[index]; - At31L = At31[index]; - At32L = At32[index]; + At23L = At23[index]; At33L = At33[index]; gt11L = gt11[index]; - gt21L = gt21[index]; + gt12L = gt12[index]; + gt13L = gt13[index]; gt22L = gt22[index]; - gt31L = gt31[index]; - gt32L = gt32[index]; + gt23L = gt23[index]; gt33L = gt33[index]; phiL = phi[index]; trKL = trK[index]; @@ -279,17 +279,17 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Precompute derivatives (new style) */ PDstandard4th2At11 = PDstandard4th2(At11, i, j, k); PDstandard4th3At11 = PDstandard4th3(At11, i, j, k); - PDstandard4th1At21 = PDstandard4th1(At21, i, j, k); - PDstandard4th2At21 = PDstandard4th2(At21, i, j, k); - PDstandard4th3At21 = PDstandard4th3(At21, i, j, k); + PDstandard4th1At12 = PDstandard4th1(At12, i, j, k); + PDstandard4th2At12 = PDstandard4th2(At12, i, j, k); + PDstandard4th3At12 = PDstandard4th3(At12, i, j, k); + PDstandard4th1At13 = PDstandard4th1(At13, i, j, k); + PDstandard4th2At13 = PDstandard4th2(At13, i, j, k); + PDstandard4th3At13 = PDstandard4th3(At13, i, j, k); PDstandard4th1At22 = PDstandard4th1(At22, i, j, k); PDstandard4th3At22 = PDstandard4th3(At22, i, j, k); - PDstandard4th1At31 = PDstandard4th1(At31, i, j, k); - PDstandard4th2At31 = PDstandard4th2(At31, i, j, k); - PDstandard4th3At31 = PDstandard4th3(At31, i, j, k); - PDstandard4th1At32 = PDstandard4th1(At32, i, j, k); - PDstandard4th2At32 = PDstandard4th2(At32, i, j, k); - PDstandard4th3At32 = PDstandard4th3(At32, i, j, k); + PDstandard4th1At23 = PDstandard4th1(At23, i, j, k); + PDstandard4th2At23 = PDstandard4th2(At23, i, j, k); + PDstandard4th3At23 = PDstandard4th3(At23, i, j, k); PDstandard4th1At33 = PDstandard4th1(At33, i, j, k); PDstandard4th2At33 = PDstandard4th2(At33, i, j, k); PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); @@ -301,15 +301,24 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA PDstandard4th12gt11 = PDstandard4th12(gt11, i, j, k); PDstandard4th13gt11 = PDstandard4th13(gt11, i, j, k); PDstandard4th23gt11 = PDstandard4th23(gt11, i, j, k); - PDstandard4th1gt21 = PDstandard4th1(gt21, i, j, k); - PDstandard4th2gt21 = PDstandard4th2(gt21, i, j, k); - PDstandard4th3gt21 = PDstandard4th3(gt21, i, j, k); - PDstandard4th11gt21 = PDstandard4th11(gt21, i, j, k); - PDstandard4th22gt21 = PDstandard4th22(gt21, i, j, k); - PDstandard4th33gt21 = PDstandard4th33(gt21, i, j, k); - PDstandard4th12gt21 = PDstandard4th12(gt21, i, j, k); - PDstandard4th13gt21 = PDstandard4th13(gt21, i, j, k); - PDstandard4th23gt21 = PDstandard4th23(gt21, i, j, k); + PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); + PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); + PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); + PDstandard4th11gt12 = PDstandard4th11(gt12, i, j, k); + PDstandard4th22gt12 = PDstandard4th22(gt12, i, j, k); + PDstandard4th33gt12 = PDstandard4th33(gt12, i, j, k); + PDstandard4th12gt12 = PDstandard4th12(gt12, i, j, k); + PDstandard4th13gt12 = PDstandard4th13(gt12, i, j, k); + PDstandard4th23gt12 = PDstandard4th23(gt12, i, j, k); + PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); + PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); + PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); + PDstandard4th11gt13 = PDstandard4th11(gt13, i, j, k); + PDstandard4th22gt13 = PDstandard4th22(gt13, i, j, k); + PDstandard4th33gt13 = PDstandard4th33(gt13, i, j, k); + PDstandard4th12gt13 = PDstandard4th12(gt13, i, j, k); + PDstandard4th13gt13 = PDstandard4th13(gt13, i, j, k); + PDstandard4th23gt13 = PDstandard4th23(gt13, i, j, k); PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); @@ -319,24 +328,15 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA PDstandard4th12gt22 = PDstandard4th12(gt22, i, j, k); PDstandard4th13gt22 = PDstandard4th13(gt22, i, j, k); PDstandard4th23gt22 = PDstandard4th23(gt22, i, j, k); - PDstandard4th1gt31 = PDstandard4th1(gt31, i, j, k); - PDstandard4th2gt31 = PDstandard4th2(gt31, i, j, k); - PDstandard4th3gt31 = PDstandard4th3(gt31, i, j, k); - PDstandard4th11gt31 = PDstandard4th11(gt31, i, j, k); - PDstandard4th22gt31 = PDstandard4th22(gt31, i, j, k); - PDstandard4th33gt31 = PDstandard4th33(gt31, i, j, k); - PDstandard4th12gt31 = PDstandard4th12(gt31, i, j, k); - PDstandard4th13gt31 = PDstandard4th13(gt31, i, j, k); - PDstandard4th23gt31 = PDstandard4th23(gt31, i, j, k); - PDstandard4th1gt32 = PDstandard4th1(gt32, i, j, k); - PDstandard4th2gt32 = PDstandard4th2(gt32, i, j, k); - PDstandard4th3gt32 = PDstandard4th3(gt32, i, j, k); - PDstandard4th11gt32 = PDstandard4th11(gt32, i, j, k); - PDstandard4th22gt32 = PDstandard4th22(gt32, i, j, k); - PDstandard4th33gt32 = PDstandard4th33(gt32, i, j, k); - PDstandard4th12gt32 = PDstandard4th12(gt32, i, j, k); - PDstandard4th13gt32 = PDstandard4th13(gt32, i, j, k); - PDstandard4th23gt32 = PDstandard4th23(gt32, i, j, k); + PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); + PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); + PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); + PDstandard4th11gt23 = PDstandard4th11(gt23, i, j, k); + PDstandard4th22gt23 = PDstandard4th22(gt23, i, j, k); + PDstandard4th33gt23 = PDstandard4th33(gt23, i, j, k); + PDstandard4th12gt23 = PDstandard4th12(gt23, i, j, k); + PDstandard4th13gt23 = PDstandard4th13(gt23, i, j, k); + PDstandard4th23gt23 = PDstandard4th23(gt23, i, j, k); PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); @@ -379,99 +379,423 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA ddetgt3 = 0; - gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt32L)); + gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); - gtu12 = (gt31L*gt32L - gt21L*gt33L)*INV(detgt); + gtu21 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); - gtu13 = (-(gt22L*gt31L) + gt21L*gt32L)*INV(detgt); + gtu31 = (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt); - gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt31L)); + gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt13L)); - gtu23 = (gt21L*gt31L - gt11L*gt32L)*INV(detgt); + gtu32 = (gt12L*gt13L - gt11L*gt23L)*INV(detgt); - gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt21L)); + gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu12*PDstandard4th1gt21 + gtu13*PDstandard4th1gt31) - - gtu12*PDstandard4th2gt11 - gtu13*PDstandard4th3gt11); + Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - + gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); - Gt211 = khalf*(gtu12*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt21 + gtu23*PDstandard4th1gt31) - - gtu22*PDstandard4th2gt11 - gtu23*PDstandard4th3gt11); + Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - + gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); - Gt311 = khalf*(gtu13*PDstandard4th1gt11 + 2*(gtu23*PDstandard4th1gt21 + gtu33*PDstandard4th1gt31) - - gtu23*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); + Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - + gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); - Gt121 = khalf*(gtu12*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu13*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + + gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt221 = khalf*(gtu22*PDstandard4th1gt22 + gtu12*PDstandard4th2gt11 + - gtu23*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + + gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt321 = khalf*(gtu23*PDstandard4th1gt22 + gtu13*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + + gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt131 = khalf*(gtu13*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu12*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + + gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt231 = khalf*(gtu23*PDstandard4th1gt33 + gtu12*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + + gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt331 = khalf*(gtu33*PDstandard4th1gt33 + gtu13*PDstandard4th3gt11 + - gtu23*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + + gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu12*PDstandard4th2gt22 + - gtu13*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + + gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt222 = khalf*(gtu12*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu22*PDstandard4th2gt22 + - gtu23*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + + gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt322 = khalf*(gtu13*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu23*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + + gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt132 = khalf*(gtu13*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu12*PDstandard4th3gt22); + Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu21*PDstandard4th3gt22); - Gt232 = khalf*(gtu23*PDstandard4th2gt33 + gtu12*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + + Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + gtu22*PDstandard4th3gt22); - Gt332 = khalf*(gtu33*PDstandard4th2gt33 + gtu13*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu23*PDstandard4th3gt22); + Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu32*PDstandard4th3gt22); + + Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + + 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); + + Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + + 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); + + Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + + 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); + + Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu21* + (2*Gt211*Gt212*gt22L + 6*Gt112*gt13L*Gt311 + 4*Gt113*gt11L*Gt312 + 4*gt13L*Gt312*Gt313 + 4*gt13L*Gt211*Gt322 + + 4*gt13L*Gt311*Gt323 + 2*Gt311*Gt312*gt33L - PDstandard4th12gt11) - gtu31*PDstandard4th13gt11 + + 2*gt11L*PDstandard4th1Xt1 + gt12L*(6*Gt111*Gt212*gtu21 + 4*Gt211*Gt222*gtu21 + 4*Gt212*Gt222*gtu22 + + 6*Gt113*Gt211*gtu31 + 6*Gt113*Gt212*gtu32 + 6*Gt113*Gt213*gtu33 + 2*PDstandard4th1Xt2) + + gt13L*(6*Gt111*Gt312*gtu21 + 4*Gt212*Gt312*gtu21 + 6*Gt112*Gt312*gtu22 + 6*Gt113*Gt311*gtu31 + + 6*Gt113*Gt312*gtu32 + 6*Gt113*Gt313*gtu33 + 2*PDstandard4th1Xt3) - gtu22*khalf*PDstandard4th22gt11 + + gtu32*(2*Gt212*Gt213*gt22L + 4*gt12L*Gt233*Gt312 + 2*Gt213*gt23L*Gt312 + 6*Gt112*gt13L*Gt313 + + 4*gt13L*Gt213*Gt322 + 4*gt13L*Gt212*Gt323 + 4*gt13L*Gt313*Gt323 + 4*gt13L*Gt312*Gt333 + 2*Gt312*Gt313*gt33L - + PDstandard4th23gt11) - gtu33*khalf*PDstandard4th33gt11 + + Gt111*(10*Gt113*gt11L*gtu31 + 6*gt12L*Gt213*gtu31 + 2*gt11L*Xt1L) + + Gt211*(4*Gt112*gt11L*gtu11 + 6*Gt111*gt12L*gtu11 + 2*gt23L*Gt311*gtu11 + 4*gt13L*Gt312*gtu11 + + 6*Gt112*gt12L*gtu21 + 4*gt11L*Gt123*gtu31 + 4*gt12L*Gt223*gtu31 + 2*Gt213*gt22L*gtu31 + 2*gt12L*Xt1L) + + Gt311*(6*Gt111*gt13L*gtu11 + 4*gt12L*Gt213*gtu11 + 4*gt13L*Gt313*gtu11 + 4*gt11L*Gt123*gtu21 + + 4*gt12L*Gt223*gtu21 + 2*Gt212*gt23L*gtu21 + 4*gt11L*Gt133*gtu31 + 4*gt12L*Gt233*gtu31 + 2*Gt213*gt23L*gtu31 + + 2*Gt313*gt33L*gtu31 + 2*gt13L*Xt1L) + 2*gt12L*Gt212*Xt2L + + Gt112*(10*Gt111*gt11L*gtu21 + 4*gt11L*Gt212*gtu21 + 6*gt12L*Gt212*gtu22 + 4*gt11L*Gt213*gtu31 + + 10*Gt113*gt11L*gtu32 + 2*gt11L*Xt2L) + Gt312* + (4*gt12L*Gt213*gtu21 + 2*Gt211*gt23L*gtu21 + 4*gt11L*Gt123*gtu22 + 4*gt12L*Gt223*gtu22 + 2*Gt212*gt23L*gtu22 + + 4*gt13L*Gt213*gtu31 + 4*gt11L*Gt133*gtu32 + 2*gt13L*Xt2L) + 2*Gt113*gt11L*Xt3L + + Gt213*(4*gt11L*Gt122*gtu32 + 6*Gt112*gt12L*gtu32 + 4*gt11L*Gt123*gtu33 + 2*gt12L*Xt3L) + + Gt313*(4*Gt113*gt11L*gtu31 + 6*Gt111*gt13L*gtu31 + 4*gt12L*Gt213*gtu31 + 2*Gt211*gt23L*gtu31 + + 4*gt11L*Gt123*gtu32 + 4*gt12L*Gt223*gtu32 + 2*Gt212*gt23L*gtu32 + 4*gt11L*Gt133*gtu33 + 4*gt12L*Gt233*gtu33 + + 2*Gt213*gt23L*gtu33 + 2*gt13L*Xt3L) + 5*gt11L*gtu11*SQR(Gt111) + 5*gt11L*gtu22*SQR(Gt112) + + 5*gt11L*gtu33*SQR(Gt113) + gt22L*gtu11*SQR(Gt211) + gt22L*gtu22*SQR(Gt212) + + 4*(gt12L*Gt211*Gt212*gtu11 + Gt113*gt11L*Gt311*gtu11 + gt11L*Gt122*Gt211*gtu21 + gt11L*Gt122*Gt212*gtu22 + + gt13L*Gt212*Gt322*gtu22 + gt13L*Gt312*Gt323*gtu22 + gt12L*Gt212*Gt213*gtu31 + gt13L*Gt211*Gt323*gtu31 + + gt13L*Gt311*Gt333*gtu31 + gt11L*Gt123*Gt212*gtu32 + gt12L*Gt213*Gt222*gtu32 + gt12L*Gt212*Gt223*gtu32 + + gt12L*Gt213*Gt223*gtu33 + gt13L*Gt213*Gt323*gtu33 + gt13L*Gt313*Gt333*gtu33 + gt12L*gtu21*SQR(Gt212)) + + gt22L*gtu33*SQR(Gt213) + gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt312) + 4*gt13L*gtu31*SQR(Gt313) + + gt33L*gtu33*SQR(Gt313); + + Rt12 = gt22L*PDstandard4th1Xt2 + gt23L*PDstandard4th1Xt3 + gt11L*PDstandard4th2Xt1 + + gt12L*(PDstandard4th1Xt1 + PDstandard4th2Xt2) + gt13L*PDstandard4th2Xt3 + + khalf*(-(gtu11*PDstandard4th11gt12) - 2*gtu21*PDstandard4th12gt12 - 2*gtu31*PDstandard4th13gt12 - + gtu22*PDstandard4th22gt12 - 2*gtu32*PDstandard4th23gt12 - gtu33*PDstandard4th33gt12) + + (Gt112*gt11L + gt12L*(Gt111 + Gt212) + Gt211*gt22L + gt23L*Gt311 + gt13L*Gt312)*Xt1L + + (gt11L*Gt122 + gt12L*(Gt112 + Gt222) + Gt212*gt22L + gt23L*Gt312 + gt13L*Gt322)*Xt2L + + (gt11L*Gt123 + gt12L*(Gt113 + Gt223) + Gt213*gt22L + gt23L*Gt313 + gt13L*Gt323)*Xt3L + + gtu11*(gt11L*(Gt112*(3*Gt111 + 2*Gt212) + 2*Gt113*Gt312) + + Gt111*(gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311) + gt13L*Gt312) + + Gt211*(5*Gt112*gt12L + 3*(Gt212*gt22L + gt23L*Gt312)) + + Gt311*(3*Gt112*gt13L + Gt212*gt23L + 2*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + Gt312*gt33L) + + 2*(Gt312*(gt12L*Gt213 + gt13L*(Gt212 + Gt313)) + gt12L*(SQR(Gt111) + SQR(Gt212)))) + + gtu22*(Gt112*(3*gt11L*Gt122 + gt12L*Gt222 + 2*(Gt212*gt22L + gt23L*Gt312) + gt13L*Gt322) + + Gt222*(3*Gt212*gt22L + gt23L*Gt312 + 2*(gt11L*Gt122 + gt13L*Gt322)) + + Gt312*(3*Gt122*gt13L + 2*(Gt223*gt22L + gt23L*Gt323)) + + Gt322*(3*Gt212*gt23L + 2*(gt11L*Gt123 + gt13L*Gt323) + Gt312*gt33L) + + gt12L*(5*Gt122*Gt212 + 2*(Gt123*Gt312 + Gt223*Gt322 + SQR(Gt112) + SQR(Gt222)))) + + gtu33*(Gt113*(3*gt11L*Gt123 + gt12L*Gt223 + 2*(Gt213*gt22L + gt23L*Gt313) + gt13L*Gt323) + + Gt223*(3*Gt213*gt22L + gt23L*Gt313 + 2*(gt11L*Gt123 + gt13L*Gt323)) + + Gt313*(3*Gt123*gt13L + 2*(gt22L*Gt233 + gt23L*Gt333)) + + Gt323*(3*Gt213*gt23L + 2*(gt11L*Gt133 + gt13L*Gt333) + Gt313*gt33L) + + gt12L*(5*Gt123*Gt213 + 2*(Gt133*Gt313 + Gt233*Gt323 + SQR(Gt113) + SQR(Gt223)))) + + gtu21*(Gt111*(3*gt11L*Gt122 + gt12L*(2*Gt112 + Gt222) + gt13L*Gt322) + + 2*(Gt112*(gt11L*Gt222 + Gt211*gt22L) + Gt223*gt22L*Gt311 + Gt111*(Gt112*gt12L + Gt212*gt22L + gt23L*Gt312) + + (Gt113*gt11L + gt13L*Gt313)*Gt322 + gt13L*(Gt222*Gt312 + Gt212*Gt322)) + + gt12L*(5*Gt122*Gt211 + Gt212*(4*Gt112 + 2*Gt222) + + 2*(Gt212*(Gt112 + Gt222) + Gt123*Gt311 + (Gt113 + Gt223)*Gt312 + Gt213*Gt322)) + + Gt312*(2*(Gt213*gt22L + gt23L*Gt313) + gt13L*(4*Gt112 + 2*Gt323)) + + gt23L*(4*Gt212*Gt312 + Gt311*(Gt222 + 2*(Gt112 + Gt323))) + + gt11L*(2*(Gt122*Gt212 + Gt123*Gt312) + 3*SQR(Gt112)) + + 3*(Gt122*gt13L*Gt311 + Gt211*(Gt222*gt22L + gt23L*Gt322) + gt22L*SQR(Gt212)) + gt33L*(Gt311*Gt322 + SQR(Gt312)))\ + + gtu31*(Gt111*(3*gt11L*Gt123 + gt12L*(2*Gt113 + Gt223) + gt13L*Gt323) + + gt11L*(2*(Gt123*Gt212 + Gt133*Gt312) + Gt113*(3*Gt112 + 2*Gt323)) + + 3*((Gt212*Gt213 + Gt211*Gt223)*gt22L + Gt123*gt13L*Gt311 + gt23L*(Gt213*Gt312 + Gt211*Gt323)) + + gt12L*(5*Gt123*Gt211 + 3*Gt112*Gt213 + Gt212*(Gt113 + 2*Gt223) + + 2*(Gt212*Gt223 + Gt133*Gt311 + Gt233*Gt312 + Gt113*Gt313 + Gt213*(Gt112 + Gt323))) + + gt13L*(3*Gt112*Gt313 + 2*Gt212*Gt323 + Gt312*(Gt113 + 2*Gt333)) + + gt23L*(Gt212*Gt313 + Gt311*(Gt223 + 2*(Gt113 + Gt333))) + (Gt312*Gt313 + Gt311*Gt323)*gt33L + + 2*(Gt223*(Gt112*gt11L + gt13L*Gt312) + gt22L*(Gt113*Gt211 + Gt233*Gt311 + Gt213*Gt313) + + Gt111*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + gt13L*Gt313*Gt323 + gt23L*SQR(Gt313))) + + gtu32*(3*((Gt213*Gt222 + Gt212*Gt223)*gt22L + gt13L*(Gt123*Gt312 + Gt122*Gt313) + Gt213*gt23L*Gt322) + + Gt112*(3*gt11L*Gt123 + gt12L*(2*Gt113 + Gt223) + gt13L*Gt323) + + gt12L*(5*(Gt123*Gt212 + Gt122*Gt213) + Gt222*(Gt113 + 4*Gt223) + + 2*(Gt133*Gt312 + Gt123*Gt313 + Gt233*Gt322 + Gt223*Gt323)) + + gt11L*(3*Gt113*Gt122 + 2*(Gt133*Gt322 + Gt123*(Gt222 + Gt323))) + + gt13L*(2*Gt222*Gt323 + Gt322*(Gt113 + 2*Gt333)) + + gt23L*(Gt222*Gt313 + 3*Gt212*Gt323 + Gt312*(Gt223 + 2*(Gt113 + Gt333))) + (Gt313*Gt322 + Gt312*Gt323)*gt33L + + 2*(gt22L*(Gt113*Gt212 + Gt233*Gt312) + Gt112*(Gt113*gt12L + Gt213*gt22L + gt23L*Gt313) + + Gt223*(gt11L*Gt122 + gt22L*Gt313 + gt13L*Gt322) + gt23L*Gt313*Gt323 + gt13L*SQR(Gt323))); + + Rt13 = gt23L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 + + khalf*(-(gtu11*PDstandard4th11gt13) - 2*gtu21*PDstandard4th12gt13 - 2*gtu31*PDstandard4th13gt13 - + gtu22*PDstandard4th22gt13 - 2*gtu32*PDstandard4th23gt13 - gtu33*PDstandard4th33gt13) + gt11L*PDstandard4th3Xt1 + + gt12L*PDstandard4th3Xt2 + gt13L*(PDstandard4th1Xt1 + PDstandard4th3Xt3) + + (Gt113*gt11L + gt12L*Gt213 + Gt211*gt23L + gt13L*(Gt111 + Gt313) + Gt311*gt33L)*Xt1L + + (gt11L*Gt123 + gt12L*Gt223 + Gt212*gt23L + gt13L*(Gt112 + Gt323) + Gt312*gt33L)*Xt2L + + (gt11L*Gt133 + gt12L*Gt233 + Gt213*gt23L + gt13L*(Gt113 + Gt333) + Gt313*gt33L)*Xt3L + + gtu21*((Gt212*Gt213 + Gt211*Gt223)*gt22L + Gt123*(Gt111*gt11L + gt12L*Gt211 + 3*gt13L*Gt311) + + gt12L*(3*Gt113*Gt212 + Gt112*Gt213 + Gt223*(Gt111 + 2*Gt313)) + + gt11L*(3*Gt112*Gt113 + 2*(Gt122*Gt213 + Gt123*Gt313)) + gt13L*(Gt112*Gt313 + Gt111*Gt323) + + gt23L*(Gt213*Gt312 + Gt212*Gt313 + Gt211*Gt323) + Gt312*Gt313*gt33L + + 3*(Gt113*gt13L*Gt312 + Gt311*(Gt223*gt23L + Gt323*gt33L)) + + 2*(Gt213*(gt12L*Gt222 + gt13L*Gt322) + gt11L*(Gt111*Gt123 + Gt112*Gt223 + Gt113*Gt323) + + gt12L*(Gt123*Gt211 + Gt212*Gt223 + Gt213*Gt323) + + gt13L*(Gt112*(Gt111 + Gt212) + Gt123*Gt311 + (Gt113 + Gt223)*Gt312 + 2*Gt313*Gt323) + + (Gt112*Gt311 + Gt312*(Gt212 + Gt313))*gt33L + Gt111*(Gt112*gt13L + Gt212*gt23L + Gt312*gt33L) + + Gt211*(Gt122*gt13L + Gt222*gt23L + Gt322*gt33L) + gt23L*(Gt112*Gt211 + Gt213*Gt312 + SQR(Gt212)))) + + gtu32*(gt11L*(Gt123*(3*Gt113 + 2*Gt223) + 2*Gt133*Gt323) + Gt223*(gt23L*(2*Gt212 + 3*Gt313) + 2*gt13L*Gt323) + + Gt233*(Gt212*gt22L + 3*gt23L*Gt312 + 2*(gt11L*Gt122 + gt12L*Gt323)) + + Gt123*(3*gt12L*Gt213 + gt13L*(2*Gt212 + 5*Gt313) + 2*gt11L*Gt333) + + gt13L*(5*Gt133*Gt312 + 2*Gt233*Gt322 + 4*Gt323*Gt333) + 3*(Gt313*Gt323 + Gt312*Gt333)*gt33L + + Gt212*(gt23L*Gt333 + 2*Gt323*gt33L) + Gt113*(gt12L*Gt223 + gt13L*Gt323 + 2*(Gt212*gt23L + Gt312*gt33L)) + + Gt112*(3*gt11L*Gt133 + gt12L*Gt233 + gt13L*(2*Gt113 + Gt333) + 2*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L)) + + Gt213*(Gt223*gt22L + gt23L*Gt323 + 2*(Gt122*gt13L + Gt222*gt23L + Gt322*gt33L)) + + gt12L*(3*Gt133*Gt212 + 2*(Gt222*Gt233 + Gt223*Gt333 + SQR(Gt223)))) + + gtu31*(Gt133*(Gt111*gt11L + gt12L*Gt211 + 3*gt13L*Gt311) + Gt233*(Gt211*gt22L + 3*gt23L*Gt311) + + gt12L*(4*Gt113*Gt213 + Gt233*(Gt111 + 2*Gt313)) + gt13L*(4*Gt113*Gt313 + 2*Gt213*Gt323 + Gt111*Gt333) + + Gt211*(gt23L*Gt333 + 2*Gt323*gt33L) + gt11L*(2*(Gt123*Gt213 + Gt133*Gt313) + 3*SQR(Gt113)) + gt22L*SQR(Gt213) + + gt33L*(3*Gt311*Gt333 + SQR(Gt313)) + 2*(Gt211*(Gt123*gt13L + Gt223*gt23L) + Gt213*(gt12L*Gt223 + gt23L*Gt313) + + gt23L*(Gt113*Gt211 + Gt213*(Gt212 + Gt313)) + gt11L*(Gt111*Gt133 + Gt112*Gt233 + Gt113*Gt333) + + gt12L*(Gt133*Gt211 + Gt212*Gt233 + Gt213*Gt333) + + gt13L*(Gt112*Gt213 + Gt133*Gt311 + Gt233*Gt312 + Gt113*(Gt111 + Gt313) + 2*Gt313*Gt333) + + Gt111*(Gt113*gt13L + Gt213*gt23L + Gt313*gt33L) + gt33L*(Gt113*Gt311 + Gt213*Gt312 + SQR(Gt313)))) + + gtu11*(Gt211*(3*Gt113*gt12L + 2*Gt112*gt13L + Gt213*gt22L + gt23L*Gt313) + + gt11L*(2*Gt112*Gt213 + Gt113*(3*Gt111 + 2*Gt313)) + + Gt111*(gt12L*Gt213 + gt13L*Gt313 + 2*(Gt211*gt23L + Gt311*gt33L)) + + Gt311*(5*Gt113*gt13L + 3*(Gt213*gt23L + Gt313*gt33L)) + + 2*(Gt212*(gt12L*Gt213 + Gt211*gt23L) + Gt213*(gt13L*Gt312 + gt12L*Gt313) + Gt211*Gt312*gt33L + + gt13L*(SQR(Gt111) + SQR(Gt313)))) + gtu22* + (Gt212*(3*Gt123*gt12L + 2*Gt122*gt13L + Gt223*gt22L + gt23L*Gt323) + + gt11L*(2*Gt122*Gt223 + Gt123*(3*Gt112 + 2*Gt323)) + + Gt112*(gt12L*Gt223 + gt13L*Gt323 + 2*(Gt212*gt23L + Gt312*gt33L)) + + Gt312*(5*Gt123*gt13L + 3*(Gt223*gt23L + Gt323*gt33L)) + + 2*(Gt222*(gt12L*Gt223 + Gt212*gt23L) + Gt223*(gt13L*Gt322 + gt12L*Gt323) + Gt212*Gt322*gt33L + + gt13L*(SQR(Gt112) + SQR(Gt323)))) + gtu33* + (gt12L*(3*Gt133*Gt213 + 2*Gt233*(Gt223 + Gt333)) + Gt213*(gt22L*Gt233 + gt23L*(2*Gt223 + Gt333)) + + Gt113*(3*gt11L*Gt133 + gt12L*Gt233 + gt13L*Gt333 + 2*(Gt213*gt23L + Gt313*gt33L)) + + Gt313*(5*Gt133*gt13L + 3*(Gt233*gt23L + Gt333*gt33L)) + + 2*(Gt123*(gt13L*Gt213 + gt11L*Gt233) + gt11L*Gt133*Gt333 + Gt323*(gt13L*Gt233 + Gt213*gt33L) + + gt13L*(SQR(Gt113) + SQR(Gt333)))); + + Rt22 = 6*(Gt122*gt12L*Gt212*gtu21 + Gt112*gt12L*Gt222*gtu21 + Gt122*gt12L*Gt222*gtu22 + Gt123*gt12L*Gt212*gtu31 + + Gt123*gt12L*Gt222*gtu32 + Gt123*gt12L*Gt223*gtu33) - gtu11*khalf*PDstandard4th11gt22 + + gtu21*(10*Gt212*Gt222*gt22L + 4*Gt122*gt23L*Gt311 + 2*Gt122*gt13L*Gt312 + 6*Gt222*gt23L*Gt312 + + 4*Gt113*gt12L*Gt322 + 4*gt23L*Gt312*Gt323 + 2*Gt312*Gt322*gt33L - PDstandard4th12gt22) + + gtu31*(10*Gt212*Gt223*gt22L + 2*Gt123*gt13L*Gt312 + 4*Gt112*gt23L*Gt313 + 4*Gt113*gt12L*Gt323 + + 4*gt23L*Gt312*Gt333 + 2*Gt312*Gt323*gt33L - PDstandard4th13gt22) - gtu22*khalf*PDstandard4th22gt22 + + gtu32*(6*Gt223*gt23L*Gt322 + 2*Gt122*gt13L*Gt323 + 4*gt23L*Gt322*Gt333 + 2*Gt322*Gt323*gt33L - + PDstandard4th23gt22) + gt12L*(4*Gt111*Gt123*gtu31 + 6*Gt112*Gt223*gtu31 + 4*Gt113*Gt122*gtu32 + + 4*Gt113*Gt123*gtu33 + 2*PDstandard4th2Xt1) + + gt22L*(4*Gt122*Gt213*gtu32 + 10*Gt222*Gt223*gtu32 + 4*Gt123*Gt213*gtu33 + 2*PDstandard4th2Xt2) + + gt23L*(6*Gt212*Gt322*gtu21 + 4*Gt313*Gt322*gtu21 + 6*Gt222*Gt322*gtu22 + 4*Gt123*Gt311*gtu31 + + 6*Gt212*Gt323*gtu31 + 4*Gt313*Gt323*gtu31 + 4*Gt122*Gt313*gtu32 + 6*Gt223*Gt323*gtu33 + 2*PDstandard4th2Xt3) - + gtu33*khalf*PDstandard4th33gt22 + 2*Gt212*gt22L*Xt1L + + Gt112*(4*Gt111*gt12L*gtu11 + 6*gt12L*Gt212*gtu11 + 2*gt11L*Gt122*gtu21 + 4*Gt122*gt12L*gtu22 + + 2*gt11L*Gt123*gtu31 + 4*Gt123*gt12L*gtu32 + 2*gt12L*Xt1L) + + Gt312*(4*Gt113*gt12L*gtu11 + 2*Gt112*gt13L*gtu11 + 4*Gt213*gt22L*gtu11 + 6*Gt212*gt23L*gtu11 + + 4*gt23L*Gt313*gtu11 + 4*Gt123*gt12L*gtu21 + 4*Gt122*gt23L*gtu22 + 4*gt12L*Gt133*gtu31 + 4*gt22L*Gt233*gtu31 + + 6*Gt223*gt23L*gtu31 + 4*Gt123*gt23L*gtu32 + 2*gt23L*Xt1L) + 2*Gt222*gt22L*Xt2L + + Gt122*(2*gt11L*Gt123*gtu32 + 6*gt12L*Gt223*gtu32 + 2*gt12L*Xt2L) + + Gt322*(2*Gt112*gt13L*gtu21 + 4*Gt213*gt22L*gtu21 + 4*Gt123*gt12L*gtu22 + 2*Gt122*gt13L*gtu22 + + 4*Gt223*gt22L*gtu22 + 4*gt23L*Gt323*gtu22 + 4*gt12L*Gt133*gtu32 + 2*Gt123*gt13L*gtu32 + 4*gt22L*Gt233*gtu32 + + 2*gt23L*Xt2L) + 2*Gt123*gt12L*Xt3L + 2*Gt223*gt22L*Xt3L + + Gt323*(2*Gt112*gt13L*gtu31 + 4*Gt213*gt22L*gtu31 + 4*Gt123*gt12L*gtu32 + 4*Gt223*gt22L*gtu32 + + 6*Gt222*gt23L*gtu32 + 4*gt12L*Gt133*gtu33 + 2*Gt123*gt13L*gtu33 + 4*gt22L*Gt233*gtu33 + 4*gt23L*Gt333*gtu33 + + 2*gt23L*Xt3L) + gt11L*gtu11*SQR(Gt112) + 4* + (Gt112*Gt211*gt22L*gtu11 + Gt112*gt23L*Gt311*gtu11 + Gt111*Gt122*gt12L*gtu21 + Gt122*Gt211*gt22L*gtu21 + + Gt112*Gt212*gt22L*gtu21 + Gt223*gt22L*Gt312*gtu21 + Gt112*gt23L*Gt312*gtu21 + Gt122*Gt212*gt22L*gtu22 + + Gt112*Gt113*gt12L*gtu31 + Gt123*Gt211*gt22L*gtu31 + Gt112*Gt213*gt22L*gtu31 + Gt123*Gt212*gt22L*gtu32 + + Gt123*gt23L*Gt313*gtu33 + gt12L*gtu21*SQR(Gt112)) + gt11L*gtu22*SQR(Gt122) + gt11L*gtu33*SQR(Gt123) + + 5*gt22L*gtu11*SQR(Gt212) + 5*gt22L*gtu22*SQR(Gt222) + 5*gt22L*gtu33*SQR(Gt223) + gt33L*gtu11*SQR(Gt312) + + gt33L*gtu22*SQR(Gt322) + 4*gt23L*gtu32*SQR(Gt323) + gt33L*gtu33*SQR(Gt323); + + Rt23 = gt13L*PDstandard4th2Xt1 + gt33L*PDstandard4th2Xt3 + + khalf*(-(gtu11*PDstandard4th11gt23) - 2*gtu21*PDstandard4th12gt23 - 2*gtu31*PDstandard4th13gt23 - + gtu22*PDstandard4th22gt23 - 2*gtu32*PDstandard4th23gt23 - gtu33*PDstandard4th33gt23) + gt12L*PDstandard4th3Xt1 + + gt22L*PDstandard4th3Xt2 + gt23L*(PDstandard4th2Xt2 + PDstandard4th3Xt3) + + (Gt113*gt12L + Gt112*gt13L + Gt213*gt22L + gt23L*(Gt212 + Gt313) + Gt312*gt33L)*Xt1L + + (Gt123*gt12L + Gt122*gt13L + Gt223*gt22L + gt23L*(Gt222 + Gt323) + Gt322*gt33L)*Xt2L + + (gt12L*Gt133 + Gt123*gt13L + gt22L*Gt233 + gt23L*(Gt223 + Gt333) + Gt323*gt33L)*Xt3L + + gtu21*(gt11L*(Gt113*Gt122 + Gt112*Gt123) + gt12L* + (Gt113*Gt222 + 3*(Gt122*Gt213 + Gt112*Gt223) + Gt123*(Gt212 + 2*Gt313)) + + gt23L*(2*Gt123*Gt311 + Gt222*(4*Gt212 + Gt313) + 5*(Gt223*Gt312 + Gt213*Gt322) + (Gt212 + 4*Gt313)*Gt323) + + gt22L*(Gt212*(2*Gt113 + 3*Gt223) + 2*Gt223*Gt313 + Gt213*(3*Gt222 + 2*Gt323)) + + 3*(Gt313*Gt322 + Gt312*Gt323)*gt33L + 2*(Gt111*(Gt123*gt12L + Gt122*gt13L) + gt13L*(Gt122*Gt212 + Gt112*Gt222) + + Gt211*(Gt123*gt22L + Gt122*gt23L) + Gt113*(gt23L*Gt312 + gt12L*Gt323) + + (Gt122*Gt311 + Gt222*Gt312 + Gt212*Gt322)*gt33L + Gt112*(Gt113*gt12L + Gt212*gt23L + Gt312*gt33L)) + + gt13L*(Gt122*Gt313 + 3*(Gt123*Gt312 + Gt113*Gt322) + Gt112*Gt323 + 2*SQR(Gt112))) + + gtu31*(Gt133*(Gt112*gt11L + gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311)) + + gt23L*(5*Gt233*Gt312 + Gt223*(4*Gt212 + Gt313) + Gt213*(2*Gt112 + 5*Gt323) + Gt212*Gt333) + + Gt113*(gt11L*Gt123 + 2*(Gt112*gt13L + Gt213*gt22L + gt23L*Gt313) + gt13L*Gt323 + gt12L*(Gt223 + 2*Gt333)) + + Gt123*(3*gt12L*Gt213 + gt13L*(2*Gt212 + Gt313) + 2*Gt311*gt33L) + + Gt333*(Gt112*gt13L + 4*gt23L*Gt313 + 3*Gt312*gt33L) + + 3*(Gt112*gt12L*Gt233 + gt22L*(Gt213*Gt223 + Gt212*Gt233) + Gt133*gt13L*Gt312 + Gt313*Gt323*gt33L) + + 2*(Gt111*(gt12L*Gt133 + Gt123*gt13L) + Gt123*Gt211*gt23L + gt13L*(Gt112*Gt223 + Gt113*Gt323) + + Gt213*gt22L*Gt333 + (Gt223*Gt312 + Gt212*Gt323)*gt33L + Gt313*(gt12L*Gt133 + gt22L*Gt233 + Gt112*gt33L) + + gt12L*SQR(Gt113))) + gtu11*(Gt113*(Gt112*gt11L + gt12L*Gt212 + 2*(Gt211*gt22L + gt23L*Gt311)) + + (Gt112*gt13L + Gt212*gt23L)*Gt313 + Gt213*(5*gt23L*Gt312 + 2*gt22L*Gt313) + + 3*(Gt213*(Gt112*gt12L + Gt212*gt22L) + Gt312*(Gt113*gt13L + Gt313*gt33L)) + + 2*(Gt111*(Gt113*gt12L + Gt112*gt13L) + Gt113*gt12L*Gt313 + Gt212*Gt312*gt33L + + Gt112*(gt13L*Gt212 + Gt211*gt23L + Gt311*gt33L) + gt23L*(SQR(Gt212) + SQR(Gt313)))) + + gtu32*(Gt133*(gt11L*Gt122 + gt12L*Gt222 + 3*gt13L*Gt322) + gt12L*(4*Gt123*Gt223 + Gt122*Gt233 + 2*Gt133*Gt323) + + Gt233*(3*gt23L*Gt322 + 2*gt22L*Gt323) + gt23L*Gt323*(4*Gt223 + 2*Gt333) + Gt122*(gt13L*Gt333 + 2*Gt313*gt33L) + + Gt222*(gt22L*Gt233 + gt23L*(2*Gt223 + Gt333) + 2*Gt323*gt33L) + gt11L*SQR(Gt123) + + 3*(Gt322*Gt333*gt33L + gt22L*SQR(Gt223)) + gt33L*SQR(Gt323) + + 2*(Gt113*(Gt123*gt12L + Gt122*gt13L) + Gt133*(Gt112*gt12L + Gt212*gt22L + gt23L*Gt312) + + Gt233*(Gt122*gt12L + Gt222*gt22L + gt23L*Gt322) + gt13L*(Gt122*Gt223 + Gt123*(Gt112 + Gt323)) + + Gt223*gt22L*Gt333 + Gt123*(Gt213*gt22L + gt23L*Gt313 + gt13L*(Gt222 + Gt323) + gt12L*Gt333) + + gt23L*(Gt123*Gt212 + Gt122*Gt213 + Gt223*(Gt222 + Gt323) + Gt323*Gt333) + + gt33L*(Gt123*Gt312 + Gt223*Gt322 + SQR(Gt323)))) + + gtu22*(Gt123*(gt11L*Gt122 + gt12L*Gt222 + 2*(Gt212*gt22L + gt23L*Gt312)) + (Gt122*gt13L + Gt222*gt23L)*Gt323 + + Gt223*(5*gt23L*Gt322 + 2*gt22L*Gt323) + 3* + (Gt223*(Gt122*gt12L + Gt222*gt22L) + Gt322*(Gt123*gt13L + Gt323*gt33L)) + + 2*(Gt112*(Gt123*gt12L + Gt122*gt13L) + Gt123*gt12L*Gt323 + Gt222*Gt322*gt33L + + Gt122*(gt13L*Gt222 + Gt212*gt23L + Gt312*gt33L) + gt23L*(SQR(Gt222) + SQR(Gt323)))) + + gtu33*(Gt133*(gt11L*Gt123 + gt12L*Gt223 + 2*(Gt213*gt22L + gt23L*Gt313)) + (Gt123*gt13L + Gt223*gt23L)*Gt333 + + Gt233*(5*gt23L*Gt323 + 2*gt22L*Gt333) + 3* + ((Gt123*gt12L + Gt223*gt22L)*Gt233 + Gt323*(Gt133*gt13L + Gt333*gt33L)) + + 2*(Gt113*(gt12L*Gt133 + Gt123*gt13L) + gt12L*Gt133*Gt333 + Gt223*Gt323*gt33L + + Gt123*(gt13L*Gt223 + Gt213*gt23L + Gt313*gt33L) + gt23L*(SQR(Gt223) + SQR(Gt333)))); + + Rt33 = 6*(Gt133*gt13L*Gt313*gtu31 + Gt233*gt23L*Gt313*gtu31 + Gt113*gt13L*Gt333*gtu31 + Gt213*gt23L*Gt333*gtu31 + + Gt133*gt13L*Gt323*gtu32 + Gt133*gt13L*Gt333*gtu33) + + gtu21*(4*Gt122*gt13L*Gt213 + 2*Gt113*gt12L*Gt223 + 4*Gt112*gt13L*Gt223 + 2*Gt213*Gt223*gt22L + + 4*Gt123*Gt211*gt23L + 4*Gt212*Gt223*gt23L + 6*Gt123*gt13L*Gt313 + 6*Gt223*gt23L*Gt313 + 6*Gt113*gt13L*Gt323 + + 6*Gt213*gt23L*Gt323 + 4*Gt123*Gt311*gt33L - PDstandard4th12gt33) - gtu31*PDstandard4th13gt33 + + gtu22*(4*Gt222*Gt223*gt23L + 6*Gt123*gt13L*Gt323 + 6*Gt223*gt23L*Gt323 + 4*Gt223*Gt322*gt33L - + khalf*PDstandard4th22gt33) + gtu32*(2*Gt223*gt22L*Gt233 + 4*Gt133*Gt212*gt23L + 6*Gt233*gt23L*Gt323 + + 6*Gt123*gt13L*Gt333 + 6*Gt223*gt23L*Gt333 + 4*Gt123*Gt313*gt33L + 10*Gt323*Gt333*gt33L - PDstandard4th23gt33) - + gtu33*khalf*PDstandard4th33gt33 + 2*(gt12L*Gt133*Gt213*gtu31 + Gt113*gt12L*Gt233*gtu31 + gt12L*Gt133*Gt223*gtu32 + + gt13L*PDstandard4th3Xt1) + 2*gt23L*PDstandard4th3Xt2 + + gt33L*(4*Gt213*Gt322*gtu21 + 10*Gt313*Gt323*gtu21 + 4*Gt123*Gt312*gtu22 + 4*Gt133*Gt311*gtu31 + + 4*Gt213*Gt323*gtu31 + 10*Gt313*Gt333*gtu31 + 4*Gt133*Gt312*gtu32 + 4*Gt133*Gt313*gtu33 + 2*PDstandard4th3Xt3) + + 2*Gt213*gt23L*Xt1L + 2*Gt313*gt33L*Xt1L + Gt113* + (4*Gt111*gt13L*gtu11 + 2*gt12L*Gt213*gtu11 + 2*gt11L*Gt123*gtu21 + 2*gt11L*Gt133*gtu31 + 4*Gt123*gt13L*gtu32 + + 4*Gt133*gt13L*gtu33 + 2*gt13L*Xt1L) + 2*Gt223*gt23L*Xt2L + 2*Gt323*gt33L*Xt2L + + Gt123*(4*Gt111*gt13L*gtu21 + 2*gt12L*Gt213*gtu21 + 4*Gt112*gt13L*gtu22 + 2*gt12L*Gt223*gtu22 + + 4*Gt212*gt23L*gtu22 + 4*gt13L*Gt213*gtu31 + 2*gt11L*Gt133*gtu32 + 4*gt13L*Gt233*gtu33 + 2*gt13L*Xt2L) + + 2*Gt133*gt13L*Xt3L + 2*Gt333*gt33L*Xt3L + Gt233* + (4*Gt112*gt13L*gtu31 + 2*Gt213*gt22L*gtu31 + 2*Gt123*gt12L*gtu32 + 2*gt12L*Gt133*gtu33 + 4*Gt223*gt23L*gtu33 + + 6*gt23L*Gt333*gtu33 + 4*Gt323*gt33L*gtu33 + 2*gt23L*Xt3L) + + gtu11*(4*Gt212*Gt213*gt23L + 6*Gt113*gt13L*Gt313 + 6*Gt213*gt23L*Gt313 + 4*Gt113*Gt311*gt33L + + 4*Gt213*Gt312*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt113)) + + 4*(Gt112*gt13L*Gt213*gtu11 + Gt113*Gt211*gt23L*gtu11 + Gt112*Gt113*gt13L*gtu21 + Gt113*Gt212*gt23L*gtu21 + + Gt213*Gt222*gt23L*gtu21 + Gt113*Gt312*gt33L*gtu21 + Gt223*Gt312*gt33L*gtu21 + Gt122*gt13L*Gt223*gtu22 + + Gt111*Gt133*gt13L*gtu31 + Gt133*Gt211*gt23L*gtu31 + Gt113*Gt213*gt23L*gtu31 + Gt213*Gt223*gt23L*gtu31 + + Gt212*Gt233*gt23L*gtu31 + Gt233*Gt312*gt33L*gtu31 + Gt113*Gt313*gt33L*gtu31 + Gt112*Gt133*gt13L*gtu32 + + Gt123*gt13L*Gt223*gtu32 + Gt122*gt13L*Gt233*gtu32 + Gt123*Gt213*gt23L*gtu32 + Gt222*Gt233*gt23L*gtu32 + + Gt233*Gt322*gt33L*gtu32 + Gt223*Gt323*gt33L*gtu32 + Gt133*Gt213*gt23L*gtu33 + gt13L*gtu31*SQR(Gt113)) + + gt11L*gtu22*SQR(Gt123) + gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt213) + gt22L*gtu22*SQR(Gt223) + + 4*gt23L*gtu32*SQR(Gt223) + gt22L*gtu33*SQR(Gt233) + 5*gt33L*gtu11*SQR(Gt313) + 5*gt33L*gtu22*SQR(Gt323) + + 5*gt33L*gtu33*SQR(Gt333); + + Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu21*PDstandard4th12phi - + 2*gt11L*gtu31*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu32*PDstandard4th23phi - + gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + + 2*gt11L*Gt312*gtu21*PDstandard4th3phi + gt11L*Gt322*gtu22*PDstandard4th3phi + + 2*gt11L*Gt313*gtu31*PDstandard4th3phi + 2*gt11L*Gt323*gtu32*PDstandard4th3phi + + gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt111 + Gt111*gt11L*gtu11 + 2*Gt112*gt11L*gtu21 + gt11L*Gt122*gtu22 + 2*Gt113*gt11L*gtu31 + + 2*gt11L*Gt123*gtu32 + gt11L*Gt133*gtu33 - 4*gt11L*gtu21*PDstandard4th2phi - 4*gt11L*gtu31*PDstandard4th3phi) + + PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + + gt11L*(2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt11L*gtu32*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - + 2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi)); - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu12*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt31 + - 2*gtu12*PDstandard4th3gt32 + gtu13*PDstandard4th3gt33); + Rphi12 = 2*(-(gt12L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt12L*gtu21*PDstandard4th12phi - + 2*gt12L*gtu31*PDstandard4th13phi - gt12L*gtu22*PDstandard4th22phi - 2*gt12L*gtu32*PDstandard4th23phi - + gt12L*gtu33*PDstandard4th33phi + Gt312*PDstandard4th3phi + gt12L*Gt311*gtu11*PDstandard4th3phi + + 2*gt12L*Gt312*gtu21*PDstandard4th3phi + gt12L*Gt322*gtu22*PDstandard4th3phi + + 2*gt12L*Gt313*gtu31*PDstandard4th3phi + 2*gt12L*Gt323*gtu32*PDstandard4th3phi + + gt12L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt112 + Gt111*gt12L*gtu11 + 2*Gt112*gt12L*gtu21 + Gt122*gt12L*gtu22 + 2*Gt113*gt12L*gtu31 + + 2*Gt123*gt12L*gtu32 + gt12L*Gt133*gtu33 + (2 - 4*gt12L*gtu21)*PDstandard4th2phi - + 4*gt12L*gtu31*PDstandard4th3phi) + PDstandard4th2phi* + (Gt212 + 2*gt12L*Gt212*gtu21 + gt12L*(Gt211*gtu11 + Gt222*gtu22 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt12L*gtu32*PDstandard4th3phi) - 2*gt12L*gtu11*SQR(PDstandard4th1phi) - + 2*gt12L*gtu22*SQR(PDstandard4th2phi) - 2*gt12L*gtu33*SQR(PDstandard4th3phi)); + + Rphi13 = 2*(-PDstandard4th13phi + gt13L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi) - gt13L*gtu22*PDstandard4th22phi - 2*gt13L*gtu32*PDstandard4th23phi - + gt13L*gtu33*PDstandard4th33phi + Gt313*PDstandard4th3phi + gt13L*Gt311*gtu11*PDstandard4th3phi + + 2*gt13L*Gt312*gtu21*PDstandard4th3phi + gt13L*Gt322*gtu22*PDstandard4th3phi + + 2*gt13L*Gt313*gtu31*PDstandard4th3phi + 2*gt13L*Gt323*gtu32*PDstandard4th3phi + + gt13L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt113 + Gt111*gt13L*gtu11 + 2*Gt112*gt13L*gtu21 + Gt122*gt13L*gtu22 + 2*Gt113*gt13L*gtu31 + + 2*Gt123*gt13L*gtu32 + Gt133*gt13L*gtu33 - 4*gt13L*gtu21*PDstandard4th2phi + + (2 - 4*gt13L*gtu31)*PDstandard4th3phi) + + PDstandard4th2phi*(Gt213 + 2*gt13L*Gt213*gtu31 + + gt13L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt13L*gtu32*PDstandard4th3phi) - 2*gt13L*gtu11*SQR(PDstandard4th1phi) - + 2*gt13L*gtu22*SQR(PDstandard4th2phi) - 2*gt13L*gtu33*SQR(PDstandard4th3phi)); + + Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu32*PDstandard4th23phi - + gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + + 2*gt22L*Gt312*gtu21*PDstandard4th3phi + gt22L*Gt322*gtu22*PDstandard4th3phi + + 2*gt22L*Gt313*gtu31*PDstandard4th3phi + 2*gt22L*Gt323*gtu32*PDstandard4th3phi + + gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt122 + Gt111*gt22L*gtu11 + 2*Gt112*gt22L*gtu21 + Gt122*gt22L*gtu22 + 2*Gt113*gt22L*gtu31 + + 2*Gt123*gt22L*gtu32 + Gt133*gt22L*gtu33 - 4*gt22L*gtu21*PDstandard4th2phi - 4*gt22L*gtu31*PDstandard4th3phi) + + PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + + gt22L*(Gt211*gtu11 + 2*Gt212*gtu21 + 2*Gt213*gtu31 + 2*Gt223*gtu32 + Gt233*gtu33) - + 4*gt22L*gtu32*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + + (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi)); - Gt233 = khalf*(-(gtu12*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu12*PDstandard4th3gt31 + - 2*gtu22*PDstandard4th3gt32 + gtu23*PDstandard4th3gt33); + Rphi23 = 2*(-PDstandard4th23phi + gt23L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - + 2*gtu31*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi) - + gt23L*gtu33*PDstandard4th33phi + Gt323*PDstandard4th3phi + gt23L*Gt311*gtu11*PDstandard4th3phi + + 2*gt23L*Gt312*gtu21*PDstandard4th3phi + gt23L*Gt322*gtu22*PDstandard4th3phi + + 2*gt23L*Gt313*gtu31*PDstandard4th3phi + 2*gt23L*Gt323*gtu32*PDstandard4th3phi + + gt23L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* + (Gt123 + Gt111*gt23L*gtu11 + 2*Gt112*gt23L*gtu21 + Gt122*gt23L*gtu22 + 2*Gt113*gt23L*gtu31 + + 2*Gt123*gt23L*gtu32 + Gt133*gt23L*gtu33 - 4*gt23L*gtu21*PDstandard4th2phi - 4*gt23L*gtu31*PDstandard4th3phi) + + PDstandard4th2phi*(Gt223 + 2*Gt223*gt23L*gtu32 + + gt23L*(Gt211*gtu11 + 2*Gt212*gtu21 + Gt222*gtu22 + 2*Gt213*gtu31 + Gt233*gtu33) + + (2 - 4*gt23L*gtu32)*PDstandard4th3phi) - 2*gt23L*gtu11*SQR(PDstandard4th1phi) - + 2*gt23L*gtu22*SQR(PDstandard4th2phi) - 2*gt23L*gtu33*SQR(PDstandard4th3phi)); - Gt333 = khalf*(-(gtu13*PDstandard4th1gt33) - gtu23*PDstandard4th2gt33 + 2*gtu13*PDstandard4th3gt31 + - 2*gtu23*PDstandard4th3gt32 + gtu33*PDstandard4th3gt33); + Rphi33 = 2*(-PDstandard4th33phi + (Gt333 + gt33L* + (Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33))*PDstandard4th3phi + + PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + + Gt233*gtu33 - 4*gtu32*PDstandard4th3phi)) + + PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + + Gt133*gtu33 - 4*(gtu21*PDstandard4th2phi + gtu31*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + + gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu21*PDstandard4th12phi - 2*gtu31*PDstandard4th13phi - + gtu22*PDstandard4th22phi - 2*gtu32*PDstandard4th23phi - gtu33*PDstandard4th33phi + + Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - + 2*gtu33*SQR(PDstandard4th3phi))); e4phi = exp(4*phiL); + em4phi = INV(e4phi); + g11 = e4phi*gt11L; - g21 = e4phi*gt21L; + g12 = e4phi*gt12L; - g31 = e4phi*gt31L; + g13 = e4phi*gt13L; g22 = e4phi*gt22L; - g32 = e4phi*gt32L; + g23 = e4phi*gt23L; g33 = e4phi*gt33L; - detg = 2*g21*g31*g32 + g33*(g11*g22 - SQR(g21)) - g22*SQR(g31) - g11*SQR(g32); + detg = CUB(e4phi); - gu11 = INV(detg)*(g22*g33 - SQR(g32)); + gu11 = em4phi*gtu11; - gu12 = (g31*g32 - g21*g33)*INV(detg); + gu21 = em4phi*gtu21; - gu13 = (-(g22*g31) + g21*g32)*INV(detg); + gu31 = em4phi*gtu31; - gu22 = INV(detg)*(g11*g33 - SQR(g31)); + gu22 = em4phi*gtu22; - gu23 = (g21*g31 - g11*g32)*INV(detg); + gu32 = em4phi*gtu32; - gu33 = INV(detg)*(g11*g22 - SQR(g21)); + gu33 = em4phi*gtu33; ddetg1 = e4phi*(ddetgt1 + 4*detgt*PDstandard4th1phi); @@ -479,471 +803,139 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA ddetg3 = e4phi*(ddetgt3 + 4*detgt*PDstandard4th3phi); - G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; - - G211 = ((6*detg*Gt211 - g11*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; - - G311 = ((6*detg*Gt311 - g11*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; - - G121 = -((-6*detg*Gt121 + ddetg2*(-3 + g21*gu12) + g21*(ddetg1*gu11 + ddetg3*gu13))*INV(detg))/6.; - - G221 = -((-6*detg*Gt221 + ddetg1*(-3 + g21*gu12) + g21*(ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; - - G321 = ((6*detg*Gt321 - g21*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; - - G131 = -((-6*detg*Gt131 + g31*(ddetg1*gu11 + ddetg2*gu12) + ddetg3*(-3 + g31*gu13))*INV(detg))/6.; - - G231 = ((6*detg*Gt231 - g31*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; - - G331 = -((-6*detg*Gt331 + ddetg1*(-3 + g31*gu13) + g31*(ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; - - G122 = ((6*detg*Gt122 - g22*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; - - G222 = -((-6*detg*Gt222 + ddetg2*(-6 + g22*gu22) + g22*(ddetg1*gu12 + ddetg3*gu23))*INV(detg))/6.; - - G322 = ((6*detg*Gt322 - g22*(ddetg1*gu13 + ddetg2*gu23 + ddetg3*gu33))*INV(detg))/6.; - - G132 = ((6*detg*Gt132 - g32*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; - - G232 = -((-6*detg*Gt232 + g32*(ddetg1*gu12 + ddetg2*gu22) + ddetg3*(-3 + g32*gu23))*INV(detg))/6.; - - G332 = -((-6*detg*Gt332 + ddetg2*(-3 + g32*gu23) + g32*(ddetg1*gu13 + ddetg3*gu33))*INV(detg))/6.; - - G133 = ((6*detg*Gt133 - g33*(ddetg1*gu11 + ddetg2*gu12 + ddetg3*gu13))*INV(detg))/6.; - - G233 = ((6*detg*Gt233 - g33*(ddetg1*gu12 + ddetg2*gu22 + ddetg3*gu23))*INV(detg))/6.; - - G333 = -((-6*detg*Gt333 + g33*(ddetg1*gu13 + ddetg2*gu23) + ddetg3*(-6 + g33*gu33))*INV(detg))/6.; - - Rt11 = -(gtu11*khalf*PDstandard4th11gt11) + gtu12* - (2*Gt211*Gt221*gt22L + 4*gt21L*Gt232*Gt311 + 6*Gt121*Gt311*gt31L + 4*gt11L*Gt131*Gt321 + 4*Gt221*gt31L*Gt321 + - 4*Gt211*gt31L*Gt322 + 2*Gt221*Gt311*gt32L + 2*Gt211*Gt321*gt32L + 4*gt31L*Gt321*Gt331 + 4*Gt311*gt31L*Gt332 + - 2*Gt311*Gt321*gt33L - PDstandard4th12gt11) + - gtu13*(2*Gt231*Gt311*gt32L + 4*gt11L*Gt131*Gt331 + 2*Gt211*gt32L*Gt331 + 4*Gt211*gt31L*Gt332 + - 4*Gt311*gt31L*Gt333 + 2*Gt311*Gt331*gt33L - PDstandard4th13gt11) + 2*gt11L*PDstandard4th1Xt1 + - gt21L*(6*Gt111*Gt221*gtu12 + 4*Gt211*Gt222*gtu12 + 6*Gt131*Gt211*gtu13 + 6*Gt121*Gt221*gtu22 + - 6*Gt131*Gt221*gtu23 + 6*Gt131*Gt231*gtu33 + 2*PDstandard4th1Xt2) + 2*gt31L*PDstandard4th1Xt3 - - gtu22*khalf*PDstandard4th22gt11 - gtu23*PDstandard4th23gt11 - gtu33*khalf*PDstandard4th33gt11 + - Gt111*(10*gt11L*Gt131*gtu13 + 6*gt21L*Gt231*gtu13 + 2*gt11L*Xt1L) + - Gt211*(4*gt11L*Gt121*gtu11 + 6*Gt111*gt21L*gtu11 + 4*gt31L*Gt321*gtu11 + 2*Gt311*gt32L*gtu11 + - 4*gt11L*Gt122*gtu12 + 4*gt11L*Gt132*gtu13 + 2*gt22L*Gt231*gtu13 + 4*gt21L*Gt232*gtu13 + 2*gt21L*Xt1L) + - Gt311*(4*gt21L*Gt231*gtu11 + 6*Gt111*gt31L*gtu11 + 4*gt11L*Gt132*gtu12 + 4*gt11L*Gt133*gtu13 + - 4*gt21L*Gt233*gtu13 + 6*Gt131*gt31L*gtu13 + 2*gt31L*Xt1L) + - Gt121*(10*Gt111*gt11L*gtu12 + 6*Gt211*gt21L*gtu12 + 4*gt11L*Gt231*gtu13 + 6*gt31L*Gt321*gtu22 + - 10*gt11L*Gt131*gtu23 + 2*gt11L*Xt2L) + Gt221* - (4*gt31L*Gt322*gtu22 + 2*Gt321*gt32L*gtu22 + 2*gt22L*Gt231*gtu23 + 2*gt32L*Gt331*gtu23 + 4*gt31L*Gt332*gtu23 + - 2*gt21L*Xt2L) + Gt321*(4*gt21L*Gt231*gtu12 + 6*Gt111*gt31L*gtu12 + 4*Gt231*gt31L*gtu13 + 4*gt11L*Gt132*gtu22 + - 4*gt31L*Gt332*gtu22 + 4*gt11L*Gt133*gtu23 + 4*gt21L*Gt233*gtu23 + 6*Gt131*gt31L*gtu23 + 2*gt31L*Xt2L) + - 2*gt11L*Gt131*Xt3L + Gt231*(4*gt11L*Gt122*gtu23 + 6*Gt121*gt21L*gtu23 + 4*gt31L*Gt322*gtu23 + 2*Gt321*gt32L*gtu23 + - 4*gt11L*Gt132*gtu33 + 2*gt32L*Gt331*gtu33 + 4*gt31L*Gt332*gtu33 + 2*gt21L*Xt3L) + - Gt331*(4*gt21L*Gt231*gtu13 + 6*Gt111*gt31L*gtu13 + 4*gt11L*Gt132*gtu23 + 4*gt21L*Gt232*gtu23 + - 6*Gt121*gt31L*gtu23 + 2*Gt321*gt33L*gtu23 + 4*gt11L*Gt133*gtu33 + 4*gt21L*Gt233*gtu33 + 6*Gt131*gt31L*gtu33 + - 4*gt31L*Gt333*gtu33 + 2*gt31L*Xt3L) + 5*gt11L*gtu11*SQR(Gt111) + 5*gt11L*gtu22*SQR(Gt121) + - 5*gt11L*gtu33*SQR(Gt131) + gt22L*gtu11*SQR(Gt211) + gt22L*gtu22*SQR(Gt221) + - 4*(Gt211*gt21L*Gt221*gtu11 + gt11L*Gt131*Gt311*gtu11 + Gt311*gt31L*Gt331*gtu11 + gt11L*Gt121*Gt221*gtu12 + - gt21L*Gt221*Gt231*gtu13 + gt11L*Gt122*Gt221*gtu22 + gt21L*Gt221*Gt222*gtu22 + gt21L*Gt232*Gt321*gtu22 + - gt11L*Gt132*Gt221*gtu23 + gt21L*Gt222*Gt231*gtu23 + gt21L*Gt221*Gt232*gtu23 + gt31L*Gt331*Gt332*gtu23 + - gt31L*Gt321*Gt333*gtu23 + gt21L*Gt231*Gt232*gtu33 + gt21L*gtu12*SQR(Gt221)) + gt22L*gtu33*SQR(Gt231) + - gt33L*gtu11*SQR(Gt311) + gt33L*gtu22*SQR(Gt321) + 4*gt31L*gtu13*SQR(Gt331) + gt33L*gtu33*SQR(Gt331); - - Rt21 = gt22L*PDstandard4th1Xt2 + gt32L*PDstandard4th1Xt3 + gt11L*PDstandard4th2Xt1 + - gt21L*(PDstandard4th1Xt1 + PDstandard4th2Xt2) + gt31L*PDstandard4th2Xt3 + - khalf*(-(gtu11*PDstandard4th11gt21) - 2*gtu12*PDstandard4th12gt21 - 2*gtu13*PDstandard4th13gt21 - - gtu22*PDstandard4th22gt21 - 2*gtu23*PDstandard4th23gt21 - gtu33*PDstandard4th33gt21) + - (gt11L*Gt121 + gt21L*(Gt111 + Gt221) + Gt211*gt22L + gt31L*Gt321 + Gt311*gt32L)*Xt1L + - (gt11L*Gt122 + gt21L*(Gt121 + Gt222) + Gt221*gt22L + gt31L*Gt322 + Gt321*gt32L)*Xt2L + - (gt11L*Gt132 + gt22L*Gt231 + gt21L*(Gt131 + Gt232) + gt32L*Gt331 + gt31L*Gt332)*Xt3L + - gtu11*(gt11L*(Gt121*(3*Gt111 + 2*Gt221) + 2*Gt131*Gt321) + - Gt111*(gt21L*Gt221 + gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - Gt211*(5*Gt121*gt21L + 3*(Gt221*gt22L + Gt321*gt32L)) + gt31L*(3*Gt121*Gt311 + 2*Gt321*(Gt221 + Gt331)) + - Gt311*(Gt221*gt32L + Gt321*gt33L) + 2*(Gt311*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + - gt21L*(Gt231*Gt321 + SQR(Gt111) + SQR(Gt221)))) + - gtu22*(gt11L*(Gt122*(3*Gt121 + 2*Gt222) + 2*Gt132*Gt322) + - Gt121*(gt21L*Gt222 + gt31L*Gt322 + 2*(Gt221*gt22L + Gt321*gt32L)) + - Gt221*(5*Gt122*gt21L + 3*(Gt222*gt22L + Gt322*gt32L)) + gt31L*(3*Gt122*Gt321 + 2*Gt322*(Gt222 + Gt332)) + - Gt321*(Gt222*gt32L + Gt322*gt33L) + 2*(Gt321*(Gt132*gt21L + gt22L*Gt232 + gt32L*Gt332) + - gt21L*(Gt232*Gt322 + SQR(Gt121) + SQR(Gt222)))) + - gtu33*(gt11L*(Gt132*(3*Gt131 + 2*Gt232) + 2*Gt133*Gt332) + - Gt131*(gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331) + gt31L*Gt332) + - Gt231*(5*Gt132*gt21L + 3*(gt22L*Gt232 + gt32L*Gt332)) + - Gt331*(3*Gt132*gt31L + gt32L*(Gt232 + 2*Gt333) + Gt332*gt33L) + - 2*((Gt133*gt21L + gt22L*Gt233)*Gt331 + Gt332*(gt21L*Gt233 + gt31L*(Gt232 + Gt333)) + - gt21L*(SQR(Gt131) + SQR(Gt232)))) + gtu12* - (Gt122*(Gt111*gt11L + 3*Gt211*gt21L + Gt311*gt31L) + - gt21L*(Gt111*Gt222 + Gt221*(4*Gt121 + 2*Gt222) + 2*(Gt132*Gt311 + Gt232*Gt321)) + - gt31L*((Gt111 + 2*Gt221)*Gt322 + Gt321*(4*Gt121 + 2*Gt332)) + - gt32L*(2*Gt221*Gt321 + 3*Gt211*Gt322 + Gt311*(Gt222 + 2*Gt332)) + - gt11L*(2*(Gt122*Gt221 + Gt132*Gt321) + 3*SQR(Gt121)) + gt22L*(3*Gt211*Gt222 + 2*Gt232*Gt311 + SQR(Gt221)) + - 2*(gt11L*(Gt111*Gt122 + Gt121*Gt222 + Gt131*Gt322) + - gt21L*(Gt122*Gt211 + Gt121*(Gt111 + Gt221) + Gt221*Gt222 + Gt131*Gt321 + Gt231*Gt322) + - Gt111*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + gt31L*(Gt122*Gt311 + Gt222*Gt321 + Gt322*Gt331) + - gt32L*(Gt121*Gt311 + Gt321*(Gt221 + Gt331)) + gt22L*(Gt121*Gt211 + Gt231*Gt321 + SQR(Gt221))) + - gt33L*(Gt311*Gt322 + SQR(Gt321))) + gtu13* - (gt22L*(3*Gt211*Gt232 + 2*Gt233*Gt311) + Gt132*(Gt111*gt11L + 3*Gt211*gt21L + Gt311*gt31L) + - gt11L*(3*Gt121*Gt131 + 2*(Gt132*Gt221 + Gt133*Gt321)) + - gt21L*(Gt131*Gt221 + 3*Gt121*Gt231 + Gt111*Gt232 + 2*(Gt133*Gt311 + Gt233*Gt321)) + - Gt221*(gt22L*Gt231 + 2*gt21L*Gt232 + gt32L*Gt331) + gt31L*(3*Gt121*Gt331 + Gt111*Gt332) + - gt32L*(3*Gt211*Gt332 + Gt311*(Gt232 + 2*Gt333)) + Gt311*Gt332*gt33L + - Gt321*(Gt231*gt32L + gt31L*(Gt131 + 2*Gt333) + Gt331*gt33L) + - 2*(Gt111*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + gt22L*(Gt131*Gt211 + Gt231*(Gt221 + Gt331)) + - gt11L*(Gt111*Gt132 + Gt121*Gt232 + Gt131*Gt332) + gt31L*(Gt132*Gt311 + Gt232*Gt321 + (Gt221 + Gt331)*Gt332) + - gt21L*(Gt132*Gt211 + Gt221*Gt232 + Gt131*(Gt111 + Gt331) + Gt231*(Gt121 + Gt332)) + - gt32L*(Gt131*Gt311 + Gt231*Gt321 + SQR(Gt331)))) + - gtu23*(gt22L*(3*Gt221*Gt232 + 2*Gt233*Gt321) + Gt132*(gt11L*Gt121 + 3*gt21L*Gt221 + gt31L*Gt321) + - gt11L*(3*Gt122*Gt131 + 2*(Gt132*Gt222 + Gt133*Gt322)) + - gt21L*(Gt131*Gt222 + 3*Gt122*Gt231 + Gt121*Gt232 + 2*(Gt133*Gt321 + Gt233*Gt322)) + - Gt222*(gt22L*Gt231 + 2*gt21L*Gt232 + gt32L*Gt331) + gt31L*(3*Gt122*Gt331 + Gt121*Gt332) + - gt32L*(3*Gt221*Gt332 + Gt321*(Gt232 + 2*Gt333)) + Gt321*Gt332*gt33L + - Gt322*(Gt231*gt32L + gt31L*(Gt131 + 2*Gt333) + Gt331*gt33L) + - 2*(Gt131*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + Gt231*(Gt122*gt21L + Gt222*gt22L + Gt322*gt32L) + - Gt121*(Gt131*gt21L + gt22L*Gt231 + gt32L*Gt331) + Gt331*(Gt132*gt21L + gt22L*Gt232 + gt32L*Gt332) + - gt11L*(Gt122*Gt232 + Gt132*(Gt121 + Gt332)) + gt21L*(Gt132*Gt221 + Gt232*(Gt222 + Gt332)) + - gt31L*(Gt132*Gt321 + Gt232*Gt322 + Gt222*Gt332 + SQR(Gt332)))); - - Rt31 = gt32L*PDstandard4th1Xt2 + gt33L*PDstandard4th1Xt3 + - khalf*(-(gtu11*PDstandard4th11gt31) - 2*gtu12*PDstandard4th12gt31 - 2*gtu13*PDstandard4th13gt31 - - gtu22*PDstandard4th22gt31 - 2*gtu23*PDstandard4th23gt31 - gtu33*PDstandard4th33gt31) + gt11L*PDstandard4th3Xt1 + - gt21L*PDstandard4th3Xt2 + gt31L*(PDstandard4th1Xt1 + PDstandard4th3Xt3) + - (gt11L*Gt131 + gt21L*Gt231 + Gt211*gt32L + gt31L*(Gt111 + Gt331) + Gt311*gt33L)*Xt1L + - (gt11L*Gt132 + gt21L*Gt232 + Gt221*gt32L + gt31L*(Gt121 + Gt332) + Gt321*gt33L)*Xt2L + - (gt11L*Gt133 + gt21L*Gt233 + Gt231*gt32L + gt31L*(Gt131 + Gt333) + Gt331*gt33L)*Xt3L + - gtu12*(gt22L*(Gt221*Gt231 + Gt211*Gt232) + Gt132*(Gt111*gt11L + Gt211*gt21L + 3*Gt311*gt31L) + - gt21L*((Gt121 + 2*Gt222)*Gt231 + Gt232*(Gt111 + 2*Gt331)) + - gt11L*(3*Gt121*Gt131 + 2*(Gt122*Gt231 + Gt132*Gt331)) + gt31L*(Gt121*Gt331 + Gt111*Gt332) + - gt32L*(Gt231*Gt321 + Gt221*Gt331 + Gt211*(2*Gt222 + Gt332)) + (2*Gt211*Gt322 + Gt321*Gt331)*gt33L + - 3*(Gt131*(gt21L*Gt221 + gt31L*Gt321) + Gt311*(Gt232*gt32L + Gt332*gt33L)) + - 2*(gt11L*(Gt111*Gt132 + Gt121*Gt232 + Gt131*Gt332) + gt21L*(Gt132*Gt211 + Gt221*Gt232 + Gt231*Gt332) + - gt31L*(Gt122*Gt211 + Gt121*(2*Gt111 + Gt221) + Gt132*Gt311 + (Gt131 + Gt232)*Gt321 + Gt231*Gt322 + - 2*Gt331*Gt332) + (Gt121*Gt311 + Gt321*(Gt221 + Gt331))*gt33L + Gt111*(Gt221*gt32L + Gt321*gt33L) + - gt32L*(Gt121*Gt211 + Gt231*Gt321 + SQR(Gt221)))) + - gtu23*(Gt233*(Gt221*gt22L + 2*gt31L*Gt322 + Gt321*gt32L) + Gt132*(gt11L*Gt131 + gt21L*Gt231 + 3*gt31L*Gt331) + - Gt232*(Gt131*gt21L + gt22L*Gt231 + 3*gt32L*Gt331) + (Gt131*gt31L + Gt231*gt32L)*Gt332 + - gt21L*((Gt121 + 2*Gt222)*Gt233 + 2*Gt232*Gt333) + gt11L*(3*Gt121*Gt133 + 2*(Gt122*Gt233 + Gt132*Gt333)) + - Gt333*(Gt121*gt31L + Gt221*gt32L + Gt321*gt33L) + 3*(Gt133*(gt21L*Gt221 + gt31L*Gt321) + Gt331*Gt332*gt33L) + - 2*((Gt222*Gt231 + Gt221*(Gt131 + Gt232) + Gt233*Gt321)*gt32L + gt11L*(Gt132*(Gt131 + Gt232) + Gt133*Gt332) + - gt31L*(Gt121*Gt131 + Gt122*Gt231 + Gt133*Gt321 + Gt132*(Gt221 + Gt331) + Gt332*(Gt232 + 2*Gt333)) + - (Gt231*Gt322 + Gt221*Gt332 + Gt321*(Gt131 + Gt333))*gt33L + Gt121*(Gt131*gt31L + Gt231*gt32L + Gt331*gt33L) + - gt21L*(Gt132*Gt231 + Gt233*Gt332 + SQR(Gt232)))) + - gtu11*(Gt231*(Gt211*gt22L + 2*(gt21L*Gt221 + gt31L*Gt321) + 3*Gt311*gt32L) + - gt21L*(3*Gt131*Gt211 + Gt231*(Gt111 + 2*Gt331)) + gt11L*(2*Gt121*Gt231 + Gt131*(3*Gt111 + 2*Gt331)) + - 3*Gt311*Gt331*gt33L + Gt211*(gt32L*Gt331 + 2*Gt321*gt33L) + - gt31L*(5*Gt131*Gt311 + Gt111*Gt331 + 2*(Gt121*Gt211 + SQR(Gt111))) + - 2*(Gt211*(Gt111 + Gt221)*gt32L + Gt111*Gt311*gt33L + gt31L*SQR(Gt331))) + - gtu13*(Gt133*(Gt111*gt11L + Gt211*gt21L + 3*Gt311*gt31L) + gt32L*(3*Gt233*Gt311 + 2*Gt231*(Gt111 + Gt331)) + - gt21L*(Gt111*Gt233 + 2*(Gt231*Gt232 + Gt233*Gt331)) + Gt111*(gt31L*Gt333 + 2*Gt331*gt33L) + - Gt211*(gt22L*Gt233 + gt32L*Gt333 + 2*(Gt132*gt31L + Gt232*gt32L + Gt332*gt33L)) + - gt11L*(2*(Gt132*Gt231 + Gt133*Gt331) + 3*SQR(Gt131)) + gt22L*SQR(Gt231) + gt33L*(3*Gt311*Gt333 + SQR(Gt331)) + - 2*(gt32L*(Gt131*Gt211 + Gt231*(Gt221 + Gt331)) + Gt131*(Gt111*gt31L + 2*(gt21L*Gt231 + gt31L*Gt331)) + - gt11L*(Gt111*Gt133 + Gt121*Gt233 + Gt131*Gt333) + gt21L*(Gt133*Gt211 + Gt221*Gt233 + Gt231*Gt333) + - gt31L*(Gt133*Gt311 + Gt233*Gt321 + Gt131*(Gt111 + Gt331) + Gt231*(Gt121 + Gt332) + 2*Gt331*Gt333) + - gt33L*(Gt131*Gt311 + Gt231*Gt321 + SQR(Gt331)))) + - gtu22*(Gt232*(Gt221*gt22L + 2*(gt21L*Gt222 + gt31L*Gt322) + 3*Gt321*gt32L) + - gt21L*(3*Gt132*Gt221 + Gt232*(Gt121 + 2*Gt332)) + gt11L*(2*Gt122*Gt232 + Gt132*(3*Gt121 + 2*Gt332)) + - 3*Gt321*Gt332*gt33L + Gt221*(gt32L*Gt332 + 2*Gt322*gt33L) + - gt31L*(5*Gt132*Gt321 + Gt121*Gt332 + 2*(Gt122*Gt221 + SQR(Gt121))) + - 2*(Gt221*(Gt121 + Gt222)*gt32L + Gt121*Gt321*gt33L + gt31L*SQR(Gt332))) + - gtu33*(Gt233*(gt22L*Gt231 + 2*gt21L*Gt232 + 3*gt32L*Gt331) + gt21L*(3*Gt133*Gt231 + Gt233*(Gt131 + 2*Gt333)) + - gt11L*(2*Gt132*Gt233 + Gt133*(3*Gt131 + 2*Gt333)) + 3*Gt331*Gt333*gt33L + Gt231*(gt32L*Gt333 + 2*Gt332*gt33L) + - gt31L*(5*Gt133*Gt331 + Gt131*Gt333 + 2*SQR(Gt131)) + - 2*(Gt231*(Gt132*gt31L + (Gt131 + Gt232)*gt32L) + Gt131*Gt331*gt33L + gt31L*(Gt233*Gt332 + SQR(Gt333)))); - - Rt22 = 6*(Gt122*gt21L*Gt221*gtu12 + Gt121*gt21L*Gt222*gtu12 + Gt222*Gt321*gt32L*gtu12 + Gt221*Gt322*gt32L*gtu12 + - Gt132*gt21L*Gt221*gtu13 + Gt122*gt21L*Gt222*gtu22 + Gt132*gt21L*Gt222*gtu23 + Gt232*gt32L*Gt332*gtu33) - - gtu11*khalf*PDstandard4th11gt22 + gtu12*(2*Gt122*gt31L*Gt321 + 4*Gt131*gt21L*Gt322 + 4*Gt121*Gt321*gt32L + - 4*Gt322*gt32L*Gt331 + 4*Gt321*gt32L*Gt332 + 2*Gt321*Gt322*gt33L - PDstandard4th12gt22) - - gtu13*PDstandard4th13gt22 - gtu22*khalf*PDstandard4th22gt22 + - gtu23*(2*Gt132*gt31L*Gt322 + 4*Gt122*gt32L*Gt331 + 4*gt22L*Gt232*Gt332 + 4*Gt322*gt32L*Gt333 + - 2*Gt322*Gt332*gt33L - PDstandard4th23gt22) + 2*gt21L*PDstandard4th2Xt1 + - gt22L*(10*Gt221*Gt222*gtu12 + 4*Gt232*Gt321*gtu12 + 4*Gt132*Gt211*gtu13 + 4*Gt122*Gt221*gtu22 + - 4*Gt132*Gt221*gtu23 + 10*Gt222*Gt232*gtu23 + 4*Gt233*Gt322*gtu23 + 4*Gt132*Gt231*gtu33 + 2*PDstandard4th2Xt2) + - gt32L*(4*Gt121*Gt311*gtu11 + 6*Gt221*Gt321*gtu11 + 4*Gt122*Gt311*gtu12 + 4*Gt132*Gt311*gtu13 + - 6*Gt232*Gt321*gtu13 + 4*Gt121*Gt331*gtu13 + 4*Gt122*Gt321*gtu22 + 6*Gt232*Gt322*gtu23 + 4*Gt132*Gt331*gtu33 + - 2*PDstandard4th2Xt3) - gtu33*khalf*PDstandard4th33gt22 + 2*Gt221*gt22L*Xt1L + - Gt121*(4*Gt111*gt21L*gtu11 + 6*gt21L*Gt221*gtu11 + 2*gt11L*Gt122*gtu12 + 2*gt11L*Gt132*gtu13 + - 4*Gt122*gt21L*gtu22 + 4*Gt132*gt21L*gtu23 + 2*gt21L*Xt1L) + - Gt321*(4*gt22L*Gt231*gtu11 + 2*Gt121*gt31L*gtu11 + 4*gt32L*Gt331*gtu11 + 4*Gt132*gt21L*gtu12 + - 4*Gt133*gt21L*gtu13 + 4*gt22L*Gt233*gtu13 + 2*Gt132*gt31L*gtu13 + 2*Gt332*gt33L*gtu13 + 4*Gt132*gt32L*gtu23 + - 2*gt32L*Xt1L) + 2*Gt222*gt22L*Xt2L + Gt122*(2*gt11L*Gt132*gtu23 + 4*gt22L*Gt231*gtu23 + 2*gt21L*Xt2L) + - Gt322*(4*gt22L*Gt231*gtu12 + 2*Gt121*gt31L*gtu12 + 4*Gt132*gt21L*gtu22 + 2*Gt122*gt31L*gtu22 + - 6*Gt222*gt32L*gtu22 + 4*Gt133*gt21L*gtu23 + 2*gt32L*Xt2L) + 2*Gt132*gt21L*Xt3L + - Gt232*(6*Gt121*gt21L*gtu13 + 10*Gt221*gt22L*gtu13 + 4*gt22L*Gt322*gtu22 + 6*Gt122*gt21L*gtu23 + - 6*Gt132*gt21L*gtu33 + 2*gt22L*Xt3L) + Gt332* - (2*Gt121*gt31L*gtu13 + 6*Gt221*gt32L*gtu13 + 4*Gt322*gt32L*gtu22 + 4*Gt132*gt21L*gtu23 + 2*Gt122*gt31L*gtu23 + - 6*Gt222*gt32L*gtu23 + 4*Gt133*gt21L*gtu33 + 4*gt22L*Gt233*gtu33 + 2*Gt132*gt31L*gtu33 + 2*gt32L*Xt3L) + - gt11L*gtu11*SQR(Gt121) + 4*(Gt121*Gt211*gt22L*gtu11 + Gt131*gt21L*Gt321*gtu11 + Gt111*Gt122*gt21L*gtu12 + - Gt122*Gt211*gt22L*gtu12 + Gt121*Gt221*gt22L*gtu12 + Gt121*Gt131*gt21L*gtu13 + Gt111*Gt132*gt21L*gtu13 + - Gt121*gt22L*Gt231*gtu13 + Gt131*gt21L*Gt332*gtu13 + gt22L*Gt231*Gt332*gtu13 + gt32L*Gt331*Gt332*gtu13 + - Gt321*gt32L*Gt333*gtu13 + Gt122*Gt131*gt21L*gtu23 + Gt131*Gt132*gt21L*gtu33 + gt32L*Gt332*Gt333*gtu33 + - gt21L*gtu12*SQR(Gt121)) + gt11L*gtu22*SQR(Gt122) + gt11L*gtu33*SQR(Gt132) + 5*gt22L*gtu11*SQR(Gt221) + - 5*gt22L*gtu22*SQR(Gt222) + 5*gt22L*gtu33*SQR(Gt232) + gt33L*gtu11*SQR(Gt321) + gt33L*gtu22*SQR(Gt322) + - 4*gt32L*gtu23*SQR(Gt332) + gt33L*gtu33*SQR(Gt332); - - Rt32 = gt31L*PDstandard4th2Xt1 + gt33L*PDstandard4th2Xt3 + - khalf*(-(gtu11*PDstandard4th11gt32) - 2*gtu12*PDstandard4th12gt32 - 2*gtu13*PDstandard4th13gt32 - - gtu22*PDstandard4th22gt32 - 2*gtu23*PDstandard4th23gt32 - gtu33*PDstandard4th33gt32) + gt21L*PDstandard4th3Xt1 + - gt22L*PDstandard4th3Xt2 + gt32L*(PDstandard4th2Xt2 + PDstandard4th3Xt3) + - (Gt131*gt21L + gt22L*Gt231 + Gt121*gt31L + gt32L*(Gt221 + Gt331) + Gt321*gt33L)*Xt1L + - (Gt132*gt21L + gt22L*Gt232 + Gt122*gt31L + gt32L*(Gt222 + Gt332) + Gt322*gt33L)*Xt2L + - (Gt133*gt21L + gt22L*Gt233 + Gt132*gt31L + gt32L*(Gt232 + Gt333) + Gt332*gt33L)*Xt3L + - gtu12*(gt11L*(Gt122*Gt131 + Gt121*Gt132) + gt32L* - (2*(Gt132*Gt311 + Gt131*Gt321) + 5*(Gt232*Gt321 + Gt231*Gt322) + Gt222*(4*Gt221 + Gt331) + - (Gt221 + 4*Gt331)*Gt332) + gt21L*(3*Gt122*Gt231 + Gt132*(Gt221 + 2*Gt331) + Gt131*(Gt222 + 2*Gt332)) + - 3*(Gt121*gt21L*Gt232 + gt22L*(Gt222*Gt231 + Gt221*Gt232) + gt31L*(Gt132*Gt321 + Gt131*Gt322) + - (Gt322*Gt331 + Gt321*Gt332)*gt33L) + 2* - ((Gt122*Gt221 + Gt121*Gt222)*gt31L + Gt111*(Gt132*gt21L + Gt122*gt31L) + - gt22L*(Gt132*Gt211 + Gt131*Gt221 + Gt232*Gt331 + Gt231*Gt332) + (Gt222*Gt321 + Gt221*Gt322)*gt33L + - Gt122*(Gt211*gt32L + Gt311*gt33L) + Gt121*(Gt131*gt21L + Gt221*gt32L + Gt321*gt33L)) + - gt31L*(Gt122*Gt331 + Gt121*Gt332 + 2*SQR(Gt121))) + - gtu13*(gt11L*(Gt131*Gt132 + Gt121*Gt133) + Gt133*(gt21L*Gt221 + 3*gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - gt32L*(5*Gt233*Gt321 + Gt232*(4*Gt221 + Gt331) + Gt231*(2*Gt121 + 5*Gt332) + Gt221*Gt333) + - Gt331*(2*gt22L*Gt233 + Gt132*gt31L + 4*gt32L*Gt333) + - Gt131*(2*(gt22L*Gt231 + Gt121*gt31L + gt32L*Gt331) + gt31L*Gt332 + gt21L*(Gt232 + 2*Gt333)) + - Gt121*(gt31L*Gt333 + 2*Gt331*gt33L) + 3*(Gt231*(Gt132*gt21L + gt22L*Gt232) + (Gt121*gt21L + Gt221*gt22L)*Gt233 + - (Gt331*Gt332 + Gt321*Gt333)*gt33L) + 2* - (Gt111*(Gt133*gt21L + Gt132*gt31L) + gt31L*(Gt132*Gt221 + Gt121*Gt232 + Gt131*Gt332) + gt22L*Gt231*Gt333 + - (Gt232*Gt321 + Gt221*Gt332)*gt33L + Gt132*(Gt211*gt32L + Gt311*gt33L) + gt21L*(Gt133*Gt331 + SQR(Gt131)))) + - gtu11*(Gt131*(gt11L*Gt121 + gt21L*Gt221 + 3*gt31L*Gt321 + 2*(Gt211*gt22L + Gt311*gt32L)) + - (Gt121*gt31L + Gt221*gt32L)*Gt331 + Gt231*(5*Gt321*gt32L + 2*gt22L*Gt331) + - 3*((Gt121*gt21L + Gt221*gt22L)*Gt231 + Gt321*Gt331*gt33L) + - 2*(Gt111*(Gt131*gt21L + Gt121*gt31L) + Gt131*gt21L*Gt331 + Gt221*Gt321*gt33L + - Gt121*(Gt221*gt31L + Gt211*gt32L + Gt311*gt33L) + gt32L*(SQR(Gt221) + SQR(Gt331)))) + - gtu23*(Gt233*(Gt122*gt21L + Gt222*gt22L + 3*Gt322*gt32L) + - Gt133*(gt11L*Gt122 + 3*gt31L*Gt322 + gt21L*(Gt222 + 2*Gt332)) + - Gt132*(4*gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331 + gt31L*(Gt222 + Gt332))) + - gt32L*(4*Gt232*Gt332 + Gt222*Gt333) + Gt122*(gt31L*Gt333 + 2*Gt331*gt33L) + gt11L*SQR(Gt132) + - 3*(Gt322*Gt333*gt33L + gt22L*SQR(Gt232)) + gt33L*SQR(Gt332) + - 2*(Gt131*(Gt132*gt21L + Gt122*gt31L) + Gt133*(Gt121*gt21L + Gt221*gt22L + Gt321*gt32L) + - gt31L*(Gt122*Gt232 + Gt132*(Gt121 + Gt332)) + Gt233*(Gt122*gt21L + Gt322*gt32L + gt22L*(Gt222 + Gt332)) + - (Gt132*gt21L + gt22L*Gt232)*Gt333 + gt32L* - (Gt132*Gt221 + Gt122*Gt231 + Gt232*(2*Gt222 + Gt332) + 2*Gt332*Gt333) + - gt33L*(Gt132*Gt321 + Gt232*Gt322 + Gt222*Gt332 + SQR(Gt332)))) + - gtu22*(Gt132*(gt11L*Gt122 + gt21L*Gt222 + 3*gt31L*Gt322 + 2*(Gt221*gt22L + Gt321*gt32L)) + - (Gt122*gt31L + Gt222*gt32L)*Gt332 + Gt232*(5*Gt322*gt32L + 2*gt22L*Gt332) + - 3*((Gt122*gt21L + Gt222*gt22L)*Gt232 + Gt322*Gt332*gt33L) + - 2*(Gt121*(Gt132*gt21L + Gt122*gt31L) + Gt132*gt21L*Gt332 + Gt222*Gt322*gt33L + - Gt122*(Gt222*gt31L + Gt221*gt32L + Gt321*gt33L) + gt32L*(SQR(Gt222) + SQR(Gt332)))) + - gtu33*(Gt133*(gt11L*Gt132 + gt21L*Gt232 + 2*(gt22L*Gt231 + gt32L*Gt331)) + (Gt132*gt31L + Gt232*gt32L)*Gt333 + - Gt233*(5*gt32L*Gt332 + 2*gt22L*Gt333) + 3* - ((Gt132*gt21L + gt22L*Gt232)*Gt233 + Gt332*(Gt133*gt31L + Gt333*gt33L)) + - 2*(Gt131*(Gt133*gt21L + Gt132*gt31L) + Gt133*gt21L*Gt333 + Gt232*Gt332*gt33L + - Gt132*(Gt232*gt31L + Gt231*gt32L + Gt331*gt33L) + gt32L*(SQR(Gt232) + SQR(Gt333)))); - - Rt33 = 6*(Gt133*gt31L*Gt331*gtu13 + Gt233*gt32L*Gt331*gtu13 + Gt131*gt31L*Gt333*gtu13 + Gt231*gt32L*Gt333*gtu13 + - Gt132*gt31L*Gt332*gtu22 + Gt133*gt31L*Gt332*gtu23 + Gt132*gt31L*Gt333*gtu23 + Gt232*gt32L*Gt333*gtu23 + - Gt133*gt31L*Gt333*gtu33) + gtu12*(2*gt22L*Gt231*Gt232 + 4*Gt111*Gt132*gt31L + 4*Gt132*Gt211*gt32L + - 4*Gt221*Gt232*gt32L + 6*Gt132*gt31L*Gt331 + 6*Gt232*gt32L*Gt331 + 6*Gt131*gt31L*Gt332 + 6*Gt231*gt32L*Gt332 + - 4*Gt132*Gt311*gt33L - PDstandard4th12gt33) - gtu13*PDstandard4th13gt33 - gtu22*khalf*PDstandard4th22gt33 - - gtu23*PDstandard4th23gt33 - gtu33*khalf*PDstandard4th33gt33 + - 2*(Gt132*gt21L*Gt231*gtu12 + Gt131*gt21L*Gt232*gtu12 + Gt133*gt21L*Gt231*gtu13 + Gt131*gt21L*Gt233*gtu13 + - gt22L*Gt231*Gt233*gtu13 + Gt132*gt21L*Gt232*gtu22 + gt11L*Gt132*Gt133*gtu23 + Gt132*gt21L*Gt233*gtu23 + - gt22L*Gt232*Gt233*gtu23 + Gt133*gt21L*Gt233*gtu33 + gt31L*PDstandard4th3Xt1) + 2*gt32L*PDstandard4th3Xt2 + - gt33L*(4*Gt231*Gt322*gtu12 + 10*Gt331*Gt332*gtu12 + 4*Gt133*Gt311*gtu13 + 4*Gt231*Gt332*gtu13 + - 10*Gt331*Gt333*gtu13 + 4*Gt132*Gt321*gtu22 + 4*Gt133*Gt321*gtu23 + 4*Gt133*Gt331*gtu33 + 2*PDstandard4th3Xt3) + - 2*Gt231*gt32L*Xt1L + 2*Gt331*gt33L*Xt1L + Gt131* - (2*gt21L*Gt231*gtu11 + 4*Gt111*gt31L*gtu11 + 2*gt11L*Gt132*gtu12 + 2*gt11L*Gt133*gtu13 + 4*Gt132*gt31L*gtu23 + - 4*Gt133*gt31L*gtu33 + 2*gt31L*Xt1L) + 2*Gt132*gt31L*Xt2L + - Gt232*(4*Gt222*gt32L*gtu22 + 6*gt32L*Gt332*gtu22 + 2*Gt133*gt21L*gtu23 + 4*Gt233*gt32L*gtu33 + 2*gt32L*Xt2L) + - Gt332*(4*Gt232*gt33L*gtu23 + 10*Gt333*gt33L*gtu23 + 4*Gt233*gt33L*gtu33 + 2*gt33L*Xt2L) + 2*Gt133*gt31L*Xt3L + - 2*Gt333*gt33L*Xt3L + Gt233*(4*Gt222*gt32L*gtu23 + 6*gt32L*Gt332*gtu23 + 4*Gt132*gt31L*gtu33 + 6*gt32L*Gt333*gtu33 + - 2*gt32L*Xt3L) + gtu11*(4*Gt221*Gt231*gt32L + 6*Gt131*gt31L*Gt331 + 6*Gt231*gt32L*Gt331 + 4*Gt131*Gt311*gt33L + - 4*Gt231*Gt321*gt33L - khalf*PDstandard4th11gt33 + gt11L*SQR(Gt131)) + - 4*(Gt121*Gt231*gt31L*gtu11 + Gt131*Gt211*gt32L*gtu11 + Gt121*Gt131*gt31L*gtu12 + Gt122*Gt231*gt31L*gtu12 + - Gt121*Gt232*gt31L*gtu12 + Gt131*Gt221*gt32L*gtu12 + Gt222*Gt231*gt32L*gtu12 + Gt131*Gt321*gt33L*gtu12 + - Gt232*Gt321*gt33L*gtu12 + Gt111*Gt133*gt31L*gtu13 + Gt132*Gt231*gt31L*gtu13 + Gt121*Gt233*gt31L*gtu13 + - Gt133*Gt211*gt32L*gtu13 + Gt131*Gt231*gt32L*gtu13 + Gt231*Gt232*gt32L*gtu13 + Gt221*Gt233*gt32L*gtu13 + - Gt233*Gt321*gt33L*gtu13 + Gt131*Gt331*gt33L*gtu13 + Gt121*Gt132*gt31L*gtu22 + Gt122*Gt232*gt31L*gtu22 + - Gt132*Gt221*gt32L*gtu22 + Gt232*Gt322*gt33L*gtu22 + Gt121*Gt133*gt31L*gtu23 + Gt132*Gt232*gt31L*gtu23 + - Gt122*Gt233*gt31L*gtu23 + Gt133*Gt221*gt32L*gtu23 + Gt132*Gt231*gt32L*gtu23 + Gt233*Gt322*gt33L*gtu23 + - Gt132*Gt331*gt33L*gtu23 + Gt133*Gt231*gt32L*gtu33 + gt31L*gtu13*SQR(Gt131)) + gt11L*gtu22*SQR(Gt132) + - gt11L*gtu33*SQR(Gt133) + gt22L*gtu11*SQR(Gt231) + gt22L*gtu22*SQR(Gt232) + 4*gt32L*gtu23*SQR(Gt232) + - gt22L*gtu33*SQR(Gt233) + 5*gt33L*gtu11*SQR(Gt331) + 5*gt33L*gtu22*SQR(Gt332) + 5*gt33L*gtu33*SQR(Gt333); - - Rphi11 = 2*(-PDstandard4th11phi - gt11L*gtu11*PDstandard4th11phi - 2*gt11L*gtu12*PDstandard4th12phi - - 2*gt11L*gtu13*PDstandard4th13phi - gt11L*gtu22*PDstandard4th22phi - 2*gt11L*gtu23*PDstandard4th23phi - - gt11L*gtu33*PDstandard4th33phi + Gt311*PDstandard4th3phi + gt11L*Gt311*gtu11*PDstandard4th3phi + - 2*gt11L*Gt321*gtu12*PDstandard4th3phi + 2*gt11L*Gt331*gtu13*PDstandard4th3phi + - gt11L*Gt322*gtu22*PDstandard4th3phi + 2*gt11L*Gt332*gtu23*PDstandard4th3phi + - gt11L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt111 + Gt111*gt11L*gtu11 + 2*gt11L*Gt121*gtu12 + 2*gt11L*Gt131*gtu13 + gt11L*Gt122*gtu22 + - 2*gt11L*Gt132*gtu23 + gt11L*Gt133*gtu33 - 4*gt11L*gtu12*PDstandard4th2phi - 4*gt11L*gtu13*PDstandard4th3phi) + - PDstandard4th2phi*(Gt211 + gt11L*Gt211*gtu11 + - gt11L*(2*Gt221*gtu12 + 2*Gt231*gtu13 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt11L*gtu23*PDstandard4th3phi) + (2 - 2*gt11L*gtu11)*SQR(PDstandard4th1phi) - - 2*gt11L*gtu22*SQR(PDstandard4th2phi) - 2*gt11L*gtu33*SQR(PDstandard4th3phi)); + G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - Rphi21 = 2*(-(gt21L*gtu11*PDstandard4th11phi) - PDstandard4th12phi - 2*gt21L*gtu12*PDstandard4th12phi - - 2*gt21L*gtu13*PDstandard4th13phi - gt21L*gtu22*PDstandard4th22phi - 2*gt21L*gtu23*PDstandard4th23phi - - gt21L*gtu33*PDstandard4th33phi + Gt321*PDstandard4th3phi + gt21L*Gt311*gtu11*PDstandard4th3phi + - 2*gt21L*Gt321*gtu12*PDstandard4th3phi + 2*gt21L*Gt331*gtu13*PDstandard4th3phi + - gt21L*Gt322*gtu22*PDstandard4th3phi + 2*gt21L*Gt332*gtu23*PDstandard4th3phi + - gt21L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt121 + Gt111*gt21L*gtu11 + 2*Gt121*gt21L*gtu12 + 2*Gt131*gt21L*gtu13 + Gt122*gt21L*gtu22 + - 2*Gt132*gt21L*gtu23 + Gt133*gt21L*gtu33 + (2 - 4*gt21L*gtu12)*PDstandard4th2phi - - 4*gt21L*gtu13*PDstandard4th3phi) + PDstandard4th2phi* - (Gt221 + 2*gt21L*Gt221*gtu12 + gt21L*(Gt211*gtu11 + 2*Gt231*gtu13 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt21L*gtu23*PDstandard4th3phi) - 2*gt21L*gtu11*SQR(PDstandard4th1phi) - - 2*gt21L*gtu22*SQR(PDstandard4th2phi) - 2*gt21L*gtu33*SQR(PDstandard4th3phi)); - - Rphi31 = 2*(-PDstandard4th13phi + gt31L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi) - gt31L*gtu22*PDstandard4th22phi - 2*gt31L*gtu23*PDstandard4th23phi - - gt31L*gtu33*PDstandard4th33phi + Gt331*PDstandard4th3phi + Gt311*gt31L*gtu11*PDstandard4th3phi + - 2*gt31L*Gt321*gtu12*PDstandard4th3phi + 2*gt31L*Gt331*gtu13*PDstandard4th3phi + - gt31L*Gt322*gtu22*PDstandard4th3phi + 2*gt31L*Gt332*gtu23*PDstandard4th3phi + - gt31L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt131 + Gt111*gt31L*gtu11 + 2*Gt121*gt31L*gtu12 + 2*Gt131*gt31L*gtu13 + Gt122*gt31L*gtu22 + - 2*Gt132*gt31L*gtu23 + Gt133*gt31L*gtu33 - 4*gt31L*gtu12*PDstandard4th2phi + - (2 - 4*gt31L*gtu13)*PDstandard4th3phi) + - PDstandard4th2phi*(Gt231 + 2*Gt231*gt31L*gtu13 + - gt31L*(Gt211*gtu11 + 2*Gt221*gtu12 + Gt222*gtu22 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt31L*gtu23*PDstandard4th3phi) - 2*gt31L*gtu11*SQR(PDstandard4th1phi) - - 2*gt31L*gtu22*SQR(PDstandard4th2phi) - 2*gt31L*gtu33*SQR(PDstandard4th3phi)); - - Rphi22 = 2*(-PDstandard4th22phi + gt22L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi - gtu22*PDstandard4th22phi) - 2*gt22L*gtu23*PDstandard4th23phi - - gt22L*gtu33*PDstandard4th33phi + Gt322*PDstandard4th3phi + gt22L*Gt311*gtu11*PDstandard4th3phi + - 2*gt22L*Gt321*gtu12*PDstandard4th3phi + 2*gt22L*Gt331*gtu13*PDstandard4th3phi + - gt22L*Gt322*gtu22*PDstandard4th3phi + 2*gt22L*Gt332*gtu23*PDstandard4th3phi + - gt22L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt122 + Gt111*gt22L*gtu11 + 2*Gt121*gt22L*gtu12 + 2*Gt131*gt22L*gtu13 + Gt122*gt22L*gtu22 + - 2*Gt132*gt22L*gtu23 + Gt133*gt22L*gtu33 - 4*gt22L*gtu12*PDstandard4th2phi - 4*gt22L*gtu13*PDstandard4th3phi) + - PDstandard4th2phi*(Gt222 + Gt222*gt22L*gtu22 + - gt22L*(Gt211*gtu11 + 2*Gt221*gtu12 + 2*Gt231*gtu13 + 2*Gt232*gtu23 + Gt233*gtu33) - - 4*gt22L*gtu23*PDstandard4th3phi) - 2*gt22L*gtu11*SQR(PDstandard4th1phi) + - (2 - 2*gt22L*gtu22)*SQR(PDstandard4th2phi) - 2*gt22L*gtu33*SQR(PDstandard4th3phi)); + G211 = ((6*detg*Gt211 - g11*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - Rphi32 = 2*(-PDstandard4th23phi + gt32L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - - 2*gtu13*PDstandard4th13phi - gtu22*PDstandard4th22phi - 2*gtu23*PDstandard4th23phi) - - gt32L*gtu33*PDstandard4th33phi + Gt332*PDstandard4th3phi + Gt311*gt32L*gtu11*PDstandard4th3phi + - 2*Gt321*gt32L*gtu12*PDstandard4th3phi + 2*gt32L*Gt331*gtu13*PDstandard4th3phi + - Gt322*gt32L*gtu22*PDstandard4th3phi + 2*gt32L*Gt332*gtu23*PDstandard4th3phi + - gt32L*Gt333*gtu33*PDstandard4th3phi + PDstandard4th1phi* - (Gt132 + Gt111*gt32L*gtu11 + 2*Gt121*gt32L*gtu12 + 2*Gt131*gt32L*gtu13 + Gt122*gt32L*gtu22 + - 2*Gt132*gt32L*gtu23 + Gt133*gt32L*gtu33 - 4*gt32L*gtu12*PDstandard4th2phi - 4*gt32L*gtu13*PDstandard4th3phi) + - PDstandard4th2phi*(Gt232 + 2*Gt232*gt32L*gtu23 + - gt32L*(Gt211*gtu11 + 2*Gt221*gtu12 + 2*Gt231*gtu13 + Gt222*gtu22 + Gt233*gtu33) + - (2 - 4*gt32L*gtu23)*PDstandard4th3phi) - 2*gt32L*gtu11*SQR(PDstandard4th1phi) - - 2*gt32L*gtu22*SQR(PDstandard4th2phi) - 2*gt32L*gtu33*SQR(PDstandard4th3phi)); + G311 = ((6*detg*Gt311 - g11*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - Rphi33 = 2*(-PDstandard4th33phi + (Gt333 + gt33L* - (Gt322*gtu22 + 2*(Gt321*gtu12 + Gt331*gtu13 + Gt332*gtu23) + Gt333*gtu33))*PDstandard4th3phi + - PDstandard4th2phi*(Gt233 + gt33L*(Gt211*gtu11 + Gt222*gtu22 + 2*(Gt221*gtu12 + Gt231*gtu13 + Gt232*gtu23) + - Gt233*gtu33 - 4*gtu23*PDstandard4th3phi)) + - PDstandard4th1phi*(Gt133 + gt33L*(Gt111*gtu11 + Gt122*gtu22 + 2*(Gt121*gtu12 + Gt131*gtu13 + Gt132*gtu23) + - Gt133*gtu33 - 4*(gtu12*PDstandard4th2phi + gtu13*PDstandard4th3phi))) + 2*SQR(PDstandard4th3phi) + - gt33L*(-(gtu11*PDstandard4th11phi) - 2*gtu12*PDstandard4th12phi - 2*gtu13*PDstandard4th13phi - - gtu22*PDstandard4th22phi - 2*gtu23*PDstandard4th23phi - gtu33*PDstandard4th33phi + - Gt311*gtu11*PDstandard4th3phi - 2*gtu11*SQR(PDstandard4th1phi) - 2*gtu22*SQR(PDstandard4th2phi) - - 2*gtu33*SQR(PDstandard4th3phi))); + G112 = -((-6*detg*Gt112 + ddetg2*(-3 + g12*gu21) + g12*(ddetg1*gu11 + ddetg3*gu31))*INV(detg))/6.; - R11 = Rphi11 + Rt11; + G212 = -((-6*detg*Gt212 + ddetg1*(-3 + g12*gu21) + g12*(ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - R21 = Rphi21 + Rt21; + G312 = ((6*detg*Gt312 - g12*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - R31 = Rphi31 + Rt31; + G113 = -((-6*detg*Gt113 + g13*(ddetg1*gu11 + ddetg2*gu21) + ddetg3*(-3 + g13*gu31))*INV(detg))/6.; - R22 = Rphi22 + Rt22; + G213 = ((6*detg*Gt213 - g13*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - R32 = Rphi32 + Rt32; + G313 = -((-6*detg*Gt313 + ddetg1*(-3 + g13*gu31) + g13*(ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - R33 = Rphi33 + Rt33; + G122 = ((6*detg*Gt122 - g22*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; + + G222 = -((-6*detg*Gt222 + ddetg2*(-6 + g22*gu22) + g22*(ddetg1*gu21 + ddetg3*gu32))*INV(detg))/6.; + + G322 = ((6*detg*Gt322 - g22*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - trR = gu11*R11 + gu22*R22 + 2*(gu12*R21 + gu13*R31 + gu23*R32) + gu33*R33; + G123 = ((6*detg*Gt123 - g23*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - K11 = At11L*e4phi + g11*kthird*trKL; + G223 = -((-6*detg*Gt223 + g23*(ddetg1*gu21 + ddetg2*gu22) + ddetg3*(-3 + g23*gu32))*INV(detg))/6.; - K21 = At21L*e4phi + g21*kthird*trKL; + G323 = -((-6*detg*Gt323 + ddetg2*(-3 + g23*gu32) + g23*(ddetg1*gu31 + ddetg3*gu33))*INV(detg))/6.; - K31 = At31L*e4phi + g31*kthird*trKL; + G133 = ((6*detg*Gt133 - g33*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - K22 = At22L*e4phi + g22*kthird*trKL; + G233 = ((6*detg*Gt233 - g33*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - K32 = At32L*e4phi + g32*kthird*trKL; + G333 = -((-6*detg*Gt333 + g33*(ddetg1*gu31 + ddetg2*gu32) + ddetg3*(-6 + g33*gu33))*INV(detg))/6.; + + R11 = Rphi11 + Rt11; + + R12 = Rphi12 + Rt12; + + R13 = Rphi13 + Rt13; + + R22 = Rphi22 + Rt22; + + R23 = Rphi23 + Rt23; + + R33 = Rphi33 + Rt33; - K33 = At33L*e4phi + g33*kthird*trKL; + trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; - Km11 = gu11*K11 + gu12*K21 + gu13*K31; + Atm11 = At11L*gtu11 + At12L*gtu21 + At13L*gtu31; - Km21 = gu12*K11 + gu22*K21 + gu23*K31; + Atm21 = At11L*gtu21 + At12L*gtu22 + At13L*gtu32; - Km31 = gu13*K11 + gu23*K21 + gu33*K31; + Atm31 = At11L*gtu31 + At12L*gtu32 + At13L*gtu33; - Km12 = gu11*K21 + gu12*K22 + gu13*K32; + Atm12 = At12L*gtu11 + At22L*gtu21 + At23L*gtu31; - Km22 = gu12*K21 + gu22*K22 + gu23*K32; + Atm22 = At12L*gtu21 + At22L*gtu22 + At23L*gtu32; - Km32 = gu13*K21 + gu23*K22 + gu33*K32; + Atm32 = At12L*gtu31 + At22L*gtu32 + At23L*gtu33; - Km13 = gu11*K31 + gu12*K32 + gu13*K33; + Atm13 = At13L*gtu11 + At23L*gtu21 + At33L*gtu31; - Km23 = gu12*K31 + gu22*K32 + gu23*K33; + Atm23 = At13L*gtu21 + At23L*gtu22 + At33L*gtu32; - Km33 = gu13*K31 + gu23*K32 + gu33*K33; + Atm33 = At13L*gtu31 + At23L*gtu32 + At33L*gtu33; - HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR - SQR(Km11) - SQR(Km22) - SQR(Km33) + SQR(trKL); + HL = -2*(Atm12*Atm21 + Atm13*Atm31 + Atm23*Atm32) + trR - SQR(Atm11) - SQR(Atm22) - SQR(Atm33) + ktwothird*SQR(trKL); - gK112 = e4phi*(-2*(At11L*G121 + At21L*G221 + At31L*G321) + PDstandard4th2At11 + 4*At11L*PDstandard4th2phi) + + gK112 = e4phi*(-2*(At11L*G112 + At12L*G212 + At13L*G312) + PDstandard4th2At11 + 4*At11L*PDstandard4th2phi) + g11*kthird*PDstandard4th2trK; - gK113 = e4phi*(-2*(At11L*G131 + At21L*G231 + At31L*G331) + PDstandard4th3At11 + 4*At11L*PDstandard4th3phi) + + gK113 = e4phi*(-2*(At11L*G113 + At12L*G213 + At13L*G313) + PDstandard4th3At11 + 4*At11L*PDstandard4th3phi) + g11*kthird*PDstandard4th3trK; - gK211 = e4phi*(-(At11L*G121) - At22L*G211 - At21L*(G111 + G221) - At32L*G311 - At31L*G321 + PDstandard4th1At21 + - 4*At21L*PDstandard4th1phi) + g21*kthird*PDstandard4th1trK; + gK121 = e4phi*(-(At11L*G112) - At22L*G211 - At12L*(G111 + G212) - At23L*G311 - At13L*G312 + PDstandard4th1At12 + + 4*At12L*PDstandard4th1phi) + g12*kthird*PDstandard4th1trK; - gK212 = e4phi*(-(At11L*G122) - At22L*G221 - At21L*(G121 + G222) - At32L*G321 - At31L*G322 + PDstandard4th2At21 + - 4*At21L*PDstandard4th2phi) + g21*kthird*PDstandard4th2trK; + gK122 = e4phi*(-(At11L*G122) - At22L*G212 - At12L*(G112 + G222) - At23L*G312 - At13L*G322 + PDstandard4th2At12 + + 4*At12L*PDstandard4th2phi) + g12*kthird*PDstandard4th2trK; - gK213 = e4phi*(-(At11L*G132) - At22L*G231 - At21L*(G131 + G232) - At32L*G331 - At31L*G332 + PDstandard4th3At21 + - 4*At21L*PDstandard4th3phi) + g21*kthird*PDstandard4th3trK; + gK123 = e4phi*(-(At11L*G123) - At22L*G213 - At12L*(G113 + G223) - At23L*G313 - At13L*G323 + PDstandard4th3At12 + + 4*At12L*PDstandard4th3phi) + g12*kthird*PDstandard4th3trK; - gK311 = e4phi*(-(At11L*G131) - At32L*G211 - At21L*G231 - At33L*G311 - At31L*(G111 + G331) + PDstandard4th1At31 + - 4*At31L*PDstandard4th1phi) + g31*kthird*PDstandard4th1trK; + gK131 = e4phi*(-(At11L*G113) - At23L*G211 - At12L*G213 - At33L*G311 - At13L*(G111 + G313) + PDstandard4th1At13 + + 4*At13L*PDstandard4th1phi) + g13*kthird*PDstandard4th1trK; - gK312 = e4phi*(-(At11L*G132) - At32L*G221 - At21L*G232 - At33L*G321 - At31L*(G121 + G332) + PDstandard4th2At31 + - 4*At31L*PDstandard4th2phi) + g31*kthird*PDstandard4th2trK; + gK132 = e4phi*(-(At11L*G123) - At23L*G212 - At12L*G223 - At33L*G312 - At13L*(G112 + G323) + PDstandard4th2At13 + + 4*At13L*PDstandard4th2phi) + g13*kthird*PDstandard4th2trK; - gK313 = e4phi*(-(At11L*G133) - At32L*G231 - At21L*G233 - At33L*G331 - At31L*(G131 + G333) + PDstandard4th3At31 + - 4*At31L*PDstandard4th3phi) + g31*kthird*PDstandard4th3trK; + gK133 = e4phi*(-(At11L*G133) - At23L*G213 - At12L*G233 - At33L*G313 - At13L*(G113 + G333) + PDstandard4th3At13 + + 4*At13L*PDstandard4th3phi) + g13*kthird*PDstandard4th3trK; - gK221 = e4phi*(-2*(At21L*G121 + At22L*G221 + At32L*G321) + PDstandard4th1At22 + 4*At22L*PDstandard4th1phi) + + gK221 = e4phi*(-2*(At12L*G112 + At22L*G212 + At23L*G312) + PDstandard4th1At22 + 4*At22L*PDstandard4th1phi) + g22*kthird*PDstandard4th1trK; - gK223 = e4phi*(-2*(At21L*G132 + At22L*G232 + At32L*G332) + PDstandard4th3At22 + 4*At22L*PDstandard4th3phi) + + gK223 = e4phi*(-2*(At12L*G123 + At22L*G223 + At23L*G323) + PDstandard4th3At22 + 4*At22L*PDstandard4th3phi) + g22*kthird*PDstandard4th3trK; - gK321 = e4phi*(-(At31L*G121) - At21L*G131 - At32L*G221 - At22L*G231 - At33L*G321 - At32L*G331 + PDstandard4th1At32 + - 4*At32L*PDstandard4th1phi) + g32*kthird*PDstandard4th1trK; + gK231 = e4phi*(-(At13L*G112) - At12L*G113 - At23L*G212 - At22L*G213 - At33L*G312 - At23L*G313 + PDstandard4th1At23 + + 4*At23L*PDstandard4th1phi) + g23*kthird*PDstandard4th1trK; - gK322 = e4phi*(-(At31L*G122) - At21L*G132 - At32L*G222 - At22L*G232 - At33L*G322 - At32L*G332 + PDstandard4th2At32 + - 4*At32L*PDstandard4th2phi) + g32*kthird*PDstandard4th2trK; + gK232 = e4phi*(-(At13L*G122) - At12L*G123 - At23L*G222 - At22L*G223 - At33L*G322 - At23L*G323 + PDstandard4th2At23 + + 4*At23L*PDstandard4th2phi) + g23*kthird*PDstandard4th2trK; - gK323 = e4phi*(-(At31L*G132) - At21L*G133 - At32L*G232 - At22L*G233 - At33L*G332 - At32L*G333 + PDstandard4th3At32 + - 4*At32L*PDstandard4th3phi) + g32*kthird*PDstandard4th3trK; + gK233 = e4phi*(-(At13L*G123) - At12L*G133 - At23L*G223 - At22L*G233 - At33L*G323 - At23L*G333 + PDstandard4th3At23 + + 4*At23L*PDstandard4th3phi) + g23*kthird*PDstandard4th3trK; - gK331 = e4phi*(-2*(At31L*G131 + At32L*G231 + At33L*G331) + PDstandard4th1At33 + 4*At33L*PDstandard4th1phi) + + gK331 = e4phi*(-2*(At13L*G113 + At23L*G213 + At33L*G313) + PDstandard4th1At33 + 4*At33L*PDstandard4th1phi) + g33*kthird*PDstandard4th1trK; - gK332 = e4phi*(-2*(At31L*G132 + At32L*G232 + At33L*G332) + PDstandard4th2At33 + 4*At33L*PDstandard4th2phi) + + gK332 = e4phi*(-2*(At13L*G123 + At23L*G223 + At33L*G323) + PDstandard4th2At33 + 4*At33L*PDstandard4th2phi) + g33*kthird*PDstandard4th2trK; - M1L = (gK112 - gK211)*gu12 + (gK113 - gK311)*gu13 + (gK212 - gK221)*gu22 + (gK213 + gK312 - 2*gK321)*gu23 + - (gK313 - gK331)*gu33; + M1L = (gK112 - gK121)*gu21 + (gK122 - gK221)*gu22 + (gK113 - gK131)*gu31 + (gK123 + gK132 - 2*gK231)*gu32 + + (gK133 - gK331)*gu33; - M2L = (-gK112 + gK211)*gu11 + (-gK212 + gK221)*gu12 + (gK213 - 2*gK312 + gK321)*gu13 + (gK223 - gK322)*gu23 + - (gK323 - gK332)*gu33; + M2L = (-gK112 + gK121)*gu11 + (-gK122 + gK221)*gu21 + (gK123 - 2*gK132 + gK231)*gu31 + (gK223 - gK232)*gu32 + + (gK233 - gK332)*gu33; - M3L = (-gK113 + gK311)*gu11 + (-2*gK213 + gK312 + gK321)*gu12 + (-gK313 + gK331)*gu13 + (-gK223 + gK322)*gu22 + - (-gK323 + gK332)*gu23; + M3L = (-gK113 + gK131)*gu11 + (-2*gK123 + gK132 + gK231)*gu21 + (-gK223 + gK232)*gu22 + (-gK133 + gK331)*gu31 + + (-gK233 + gK332)*gu32; - cSL = Log(detgt); + cSL = trR; - cXt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt121*gtu12 + Gt131*gtu13 + Gt132*gtu23) + Gt133*gtu33 - Xt1L; + cXt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + Gt133*gtu33 - Xt1L; - cXt2L = Gt211*gtu11 + Gt222*gtu22 + 2*(Gt221*gtu12 + Gt231*gtu13 + Gt232*gtu23) + Gt233*gtu33 - Xt2L; + cXt2L = Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + Gt233*gtu33 - Xt2L; - cXt3L = Gt311*gtu11 + Gt322*gtu22 + 2*(Gt321*gtu12 + Gt331*gtu13 + Gt332*gtu23) + Gt333*gtu33 - Xt3L; + cXt3L = Gt311*gtu11 + Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33 - Xt3L; - cAL = At11L*gtu11 + At22L*gtu22 + 2*(At21L*gtu12 + At31L*gtu13 + At32L*gtu23) + At33L*gtu33; + cAL = At11L*gtu11 + At22L*gtu22 + 2*(At12L*gtu21 + At13L*gtu31 + At23L*gtu32) + At33L*gtu33; /* Copy local copies back to grid functions */ diff --git a/ML_BSSN/src/ML_BSSN_convertFromADMBase.c b/ML_BSSN/src/ML_BSSN_convertFromADMBase.c index 24c57f9..973cf21 100644 --- a/ML_BSSN/src/ML_BSSN_convertFromADMBase.c +++ b/ML_BSSN/src/ML_BSSN_convertFromADMBase.c @@ -96,15 +96,14 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C /* Declare shorthands */ CCTK_REAL detg = INITVALUE; CCTK_REAL em4phi = INITVALUE; - CCTK_REAL g11 = INITVALUE, g21 = INITVALUE, g22 = INITVALUE, g31 = INITVALUE, g32 = INITVALUE, g33 = INITVALUE; - CCTK_REAL gu11 = INITVALUE, gu12 = INITVALUE, gu13 = INITVALUE, gu22 = INITVALUE, gu23 = INITVALUE, gu33 = INITVALUE; - CCTK_REAL K11 = INITVALUE, K21 = INITVALUE, K22 = INITVALUE, K31 = INITVALUE, K32 = INITVALUE, K33 = INITVALUE; - CCTK_REAL Km11 = INITVALUE, Km22 = INITVALUE, Km33 = INITVALUE; + CCTK_REAL g11 = INITVALUE, g12 = INITVALUE, g13 = INITVALUE, g22 = INITVALUE, g23 = INITVALUE, g33 = INITVALUE; + CCTK_REAL gu11 = INITVALUE, gu21 = INITVALUE, gu22 = INITVALUE, gu31 = INITVALUE, gu32 = INITVALUE, gu33 = INITVALUE; + CCTK_REAL K11 = INITVALUE, K12 = INITVALUE, K13 = INITVALUE, K22 = INITVALUE, K23 = INITVALUE, K33 = INITVALUE; /* Declare local copies of grid functions */ CCTK_REAL alpL = INITVALUE; CCTK_REAL alphaL = INITVALUE; - CCTK_REAL At11L = INITVALUE, At21L = INITVALUE, At22L = INITVALUE, At31L = INITVALUE, At32L = INITVALUE, At33L = INITVALUE; + CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta2L = INITVALUE, beta3L = INITVALUE; CCTK_REAL betaxL = INITVALUE; CCTK_REAL betayL = INITVALUE; @@ -115,7 +114,7 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C CCTK_REAL dtbetaxL = INITVALUE; CCTK_REAL dtbetayL = INITVALUE; CCTK_REAL dtbetazL = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; CCTK_REAL gxxL = INITVALUE; CCTK_REAL gxyL = INITVALUE; CCTK_REAL gxzL = INITVALUE; @@ -155,6 +154,7 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C kyyL = kyy[index]; kyzL = kyz[index]; kzzL = kzz[index]; + phiL = phi[index]; trKL = trK[index]; /* Assign local copies of subblock grid functions */ @@ -168,75 +168,69 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C /* Calculate temporaries and grid functions */ g11 = gxxL; - g21 = gxyL; + g12 = gxyL; - g31 = gxzL; + g13 = gxzL; g22 = gyyL; - g32 = gyzL; + g23 = gyzL; g33 = gzzL; - detg = 2*g21*g31*g32 + g33*(g11*g22 - SQR(g21)) - g22*SQR(g31) - g11*SQR(g32); + detg = 2*g12*g13*g23 + g33*(g11*g22 - SQR(g12)) - g22*SQR(g13) - g11*SQR(g23); - gu11 = INV(detg)*(g22*g33 - SQR(g32)); + gu11 = INV(detg)*(g22*g33 - SQR(g23)); - gu12 = (g31*g32 - g21*g33)*INV(detg); + gu21 = (g13*g23 - g12*g33)*INV(detg); - gu13 = (-(g22*g31) + g21*g32)*INV(detg); + gu31 = (-(g13*g22) + g12*g23)*INV(detg); - gu22 = INV(detg)*(g11*g33 - SQR(g31)); + gu22 = INV(detg)*(g11*g33 - SQR(g13)); - gu23 = (g21*g31 - g11*g32)*INV(detg); + gu32 = (g12*g13 - g11*g23)*INV(detg); - gu33 = INV(detg)*(g11*g22 - SQR(g21)); - - em4phi = pow(detg,-3); + gu33 = INV(detg)*(g11*g22 - SQR(g12)); phiL = Log(detg)/12.; + em4phi = exp(-4*phiL); + gt11L = em4phi*g11; - gt21L = em4phi*g21; + gt12L = em4phi*g12; - gt31L = em4phi*g31; + gt13L = em4phi*g13; gt22L = em4phi*g22; - gt32L = em4phi*g32; + gt23L = em4phi*g23; gt33L = em4phi*g33; K11 = kxxL; - K21 = kxyL; + K12 = kxyL; - K31 = kxzL; + K13 = kxzL; K22 = kyyL; - K32 = kyzL; + K23 = kyzL; K33 = kzzL; - Km11 = gu11*K11 + gu12*K21 + gu13*K31; - - Km22 = gu12*K21 + gu22*K22 + gu23*K32; - - Km33 = gu13*K31 + gu23*K32 + gu33*K33; - - trKL = Km11 + Km22 + Km33; + trKL = gu11*K11 + gu22*K22 + 2*(gu21*K12 + gu31*K13 + gu32*K23) + gu33*K33; At11L = em4phi*(K11 - g11*kthird*trKL); - At21L = em4phi*(K21 - g21*kthird*trKL); + At12L = em4phi*(K12 - g12*kthird*trKL); - At31L = em4phi*(K31 - g31*kthird*trKL); + At13L = em4phi*(K13 - g13*kthird*trKL); At22L = em4phi*(K22 - g22*kthird*trKL); - At32L = em4phi*(K32 - g32*kthird*trKL); + At23L = em4phi*(K23 - g23*kthird*trKL); At33L = em4phi*(K33 - g33*kthird*trKL); @@ -260,10 +254,10 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C /* Copy local copies back to grid functions */ alpha[index] = alphaL; At11[index] = At11L; - At21[index] = At21L; + At12[index] = At12L; + At13[index] = At13L; At22[index] = At22L; - At31[index] = At31L; - At32[index] = At32L; + At23[index] = At23L; At33[index] = At33L; beta1[index] = beta1L; beta2[index] = beta2L; @@ -273,10 +267,10 @@ void ML_BSSN_convertFromADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, C dtbeta2[index] = dtbeta2L; dtbeta3[index] = dtbeta3L; gt11[index] = gt11L; - gt21[index] = gt21L; + gt12[index] = gt12L; + gt13[index] = gt13L; gt22[index] = gt22L; - gt31[index] = gt31L; - gt32[index] = gt32L; + gt23[index] = gt23L; gt33[index] = gt33L; phi[index] = phiL; trK[index] = trKL; diff --git a/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c b/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c index 32b4fc8..f71797b 100644 --- a/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c +++ b/ML_BSSN/src/ML_BSSN_convertFromADMBaseGamma.c @@ -95,13 +95,13 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa /* Declare shorthands */ CCTK_REAL detgt = INITVALUE; - CCTK_REAL Gt111 = INITVALUE, Gt121 = INITVALUE, Gt122 = INITVALUE, Gt131 = INITVALUE, Gt132 = INITVALUE, Gt133 = INITVALUE; - CCTK_REAL Gt211 = INITVALUE, Gt221 = INITVALUE, Gt222 = INITVALUE, Gt231 = INITVALUE, Gt232 = INITVALUE, Gt233 = INITVALUE; - CCTK_REAL Gt311 = INITVALUE, Gt321 = INITVALUE, Gt322 = INITVALUE, Gt331 = INITVALUE, Gt332 = INITVALUE, Gt333 = INITVALUE; - CCTK_REAL gtu11 = INITVALUE, gtu12 = INITVALUE, gtu13 = INITVALUE, gtu22 = INITVALUE, gtu23 = INITVALUE, gtu33 = INITVALUE; + CCTK_REAL Gt111 = INITVALUE, Gt112 = INITVALUE, Gt113 = INITVALUE, Gt122 = INITVALUE, Gt123 = INITVALUE, Gt133 = INITVALUE; + CCTK_REAL Gt211 = INITVALUE, Gt212 = INITVALUE, Gt213 = INITVALUE, Gt222 = INITVALUE, Gt223 = INITVALUE, Gt233 = INITVALUE; + CCTK_REAL Gt311 = INITVALUE, Gt312 = INITVALUE, Gt313 = INITVALUE, Gt322 = INITVALUE, Gt323 = INITVALUE, Gt333 = INITVALUE; + CCTK_REAL gtu11 = INITVALUE, gtu21 = INITVALUE, gtu22 = INITVALUE, gtu31 = INITVALUE, gtu32 = INITVALUE, gtu33 = INITVALUE; /* Declare local copies of grid functions */ - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; CCTK_REAL Xt1L = INITVALUE, Xt2L = INITVALUE, Xt3L = INITVALUE; /* Declare precomputed derivatives*/ @@ -109,28 +109,28 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa CCTK_REAL PDstandard4th1gt11 = INITVALUE; CCTK_REAL PDstandard4th2gt11 = INITVALUE; CCTK_REAL PDstandard4th3gt11 = INITVALUE; - CCTK_REAL PDstandard4th1gt21 = INITVALUE; - CCTK_REAL PDstandard4th2gt21 = INITVALUE; - CCTK_REAL PDstandard4th3gt21 = INITVALUE; + CCTK_REAL PDstandard4th1gt12 = INITVALUE; + CCTK_REAL PDstandard4th2gt12 = INITVALUE; + CCTK_REAL PDstandard4th3gt12 = INITVALUE; + CCTK_REAL PDstandard4th1gt13 = INITVALUE; + CCTK_REAL PDstandard4th2gt13 = INITVALUE; + CCTK_REAL PDstandard4th3gt13 = INITVALUE; CCTK_REAL PDstandard4th1gt22 = INITVALUE; CCTK_REAL PDstandard4th2gt22 = INITVALUE; CCTK_REAL PDstandard4th3gt22 = INITVALUE; - CCTK_REAL PDstandard4th1gt31 = INITVALUE; - CCTK_REAL PDstandard4th2gt31 = INITVALUE; - CCTK_REAL PDstandard4th3gt31 = INITVALUE; - CCTK_REAL PDstandard4th1gt32 = INITVALUE; - CCTK_REAL PDstandard4th2gt32 = INITVALUE; - CCTK_REAL PDstandard4th3gt32 = INITVALUE; + CCTK_REAL PDstandard4th1gt23 = INITVALUE; + CCTK_REAL PDstandard4th2gt23 = INITVALUE; + CCTK_REAL PDstandard4th3gt23 = INITVALUE; CCTK_REAL PDstandard4th1gt33 = INITVALUE; CCTK_REAL PDstandard4th2gt33 = INITVALUE; CCTK_REAL PDstandard4th3gt33 = INITVALUE; /* Assign local copies of grid functions */ gt11L = gt11[index]; - gt21L = gt21[index]; + gt12L = gt12[index]; + gt13L = gt13[index]; gt22L = gt22[index]; - gt31L = gt31[index]; - gt32L = gt32[index]; + gt23L = gt23[index]; gt33L = gt33[index]; /* Assign local copies of subblock grid functions */ @@ -141,18 +141,18 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k); PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k); - PDstandard4th1gt21 = PDstandard4th1(gt21, i, j, k); - PDstandard4th2gt21 = PDstandard4th2(gt21, i, j, k); - PDstandard4th3gt21 = PDstandard4th3(gt21, i, j, k); + PDstandard4th1gt12 = PDstandard4th1(gt12, i, j, k); + PDstandard4th2gt12 = PDstandard4th2(gt12, i, j, k); + PDstandard4th3gt12 = PDstandard4th3(gt12, i, j, k); + PDstandard4th1gt13 = PDstandard4th1(gt13, i, j, k); + PDstandard4th2gt13 = PDstandard4th2(gt13, i, j, k); + PDstandard4th3gt13 = PDstandard4th3(gt13, i, j, k); PDstandard4th1gt22 = PDstandard4th1(gt22, i, j, k); PDstandard4th2gt22 = PDstandard4th2(gt22, i, j, k); PDstandard4th3gt22 = PDstandard4th3(gt22, i, j, k); - PDstandard4th1gt31 = PDstandard4th1(gt31, i, j, k); - PDstandard4th2gt31 = PDstandard4th2(gt31, i, j, k); - PDstandard4th3gt31 = PDstandard4th3(gt31, i, j, k); - PDstandard4th1gt32 = PDstandard4th1(gt32, i, j, k); - PDstandard4th2gt32 = PDstandard4th2(gt32, i, j, k); - PDstandard4th3gt32 = PDstandard4th3(gt32, i, j, k); + PDstandard4th1gt23 = PDstandard4th1(gt23, i, j, k); + PDstandard4th2gt23 = PDstandard4th2(gt23, i, j, k); + PDstandard4th3gt23 = PDstandard4th3(gt23, i, j, k); PDstandard4th1gt33 = PDstandard4th1(gt33, i, j, k); PDstandard4th2gt33 = PDstandard4th2(gt33, i, j, k); PDstandard4th3gt33 = PDstandard4th3(gt33, i, j, k); @@ -162,77 +162,77 @@ void ML_BSSN_convertFromADMBaseGamma_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT fa /* Calculate temporaries and grid functions */ detgt = 1; - gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt32L)); + gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); - gtu12 = (gt31L*gt32L - gt21L*gt33L)*INV(detgt); + gtu21 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); - gtu13 = (-(gt22L*gt31L) + gt21L*gt32L)*INV(detgt); + gtu31 = (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt); - gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt31L)); + gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt13L)); - gtu23 = (gt21L*gt31L - gt11L*gt32L)*INV(detgt); + gtu32 = (gt12L*gt13L - gt11L*gt23L)*INV(detgt); - gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt21L)); + gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu12*PDstandard4th1gt21 + gtu13*PDstandard4th1gt31) - - gtu12*PDstandard4th2gt11 - gtu13*PDstandard4th3gt11); + Gt111 = khalf*(gtu11*PDstandard4th1gt11 + 2*(gtu21*PDstandard4th1gt12 + gtu31*PDstandard4th1gt13) - + gtu21*PDstandard4th2gt11 - gtu31*PDstandard4th3gt11); - Gt211 = khalf*(gtu12*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt21 + gtu23*PDstandard4th1gt31) - - gtu22*PDstandard4th2gt11 - gtu23*PDstandard4th3gt11); + Gt211 = khalf*(gtu21*PDstandard4th1gt11 + 2*(gtu22*PDstandard4th1gt12 + gtu32*PDstandard4th1gt13) - + gtu22*PDstandard4th2gt11 - gtu32*PDstandard4th3gt11); - Gt311 = khalf*(gtu13*PDstandard4th1gt11 + 2*(gtu23*PDstandard4th1gt21 + gtu33*PDstandard4th1gt31) - - gtu23*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); + Gt311 = khalf*(gtu31*PDstandard4th1gt11 + 2*(gtu32*PDstandard4th1gt12 + gtu33*PDstandard4th1gt13) - + gtu32*PDstandard4th2gt11 - gtu33*PDstandard4th3gt11); - Gt121 = khalf*(gtu12*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + - gtu13*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt112 = khalf*(gtu21*PDstandard4th1gt22 + gtu11*PDstandard4th2gt11 + + gtu31*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt221 = khalf*(gtu22*PDstandard4th1gt22 + gtu12*PDstandard4th2gt11 + - gtu23*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt212 = khalf*(gtu22*PDstandard4th1gt22 + gtu21*PDstandard4th2gt11 + + gtu32*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt321 = khalf*(gtu23*PDstandard4th1gt22 + gtu13*PDstandard4th2gt11 + - gtu33*(PDstandard4th1gt32 + PDstandard4th2gt31 - PDstandard4th3gt21)); + Gt312 = khalf*(gtu32*PDstandard4th1gt22 + gtu31*PDstandard4th2gt11 + + gtu33*(PDstandard4th1gt23 + PDstandard4th2gt13 - PDstandard4th3gt12)); - Gt131 = khalf*(gtu13*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + - gtu12*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt113 = khalf*(gtu31*PDstandard4th1gt33 + gtu11*PDstandard4th3gt11 + + gtu21*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt231 = khalf*(gtu23*PDstandard4th1gt33 + gtu12*PDstandard4th3gt11 + - gtu22*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt213 = khalf*(gtu32*PDstandard4th1gt33 + gtu21*PDstandard4th3gt11 + + gtu22*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt331 = khalf*(gtu33*PDstandard4th1gt33 + gtu13*PDstandard4th3gt11 + - gtu23*(PDstandard4th1gt32 - PDstandard4th2gt31 + PDstandard4th3gt21)); + Gt313 = khalf*(gtu33*PDstandard4th1gt33 + gtu31*PDstandard4th3gt11 + + gtu32*(PDstandard4th1gt23 - PDstandard4th2gt13 + PDstandard4th3gt12)); - Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu12*PDstandard4th2gt22 + - gtu13*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt122 = khalf*(gtu11*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu21*PDstandard4th2gt22 + + gtu31*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt222 = khalf*(gtu12*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu22*PDstandard4th2gt22 + - gtu23*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt222 = khalf*(gtu21*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu22*PDstandard4th2gt22 + + gtu32*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt322 = khalf*(gtu13*(-PDstandard4th1gt22 + 2*PDstandard4th2gt21) + gtu23*PDstandard4th2gt22 + - gtu33*(2*PDstandard4th2gt32 - PDstandard4th3gt22)); + Gt322 = khalf*(gtu31*(-PDstandard4th1gt22 + 2*PDstandard4th2gt12) + gtu32*PDstandard4th2gt22 + + gtu33*(2*PDstandard4th2gt23 - PDstandard4th3gt22)); - Gt132 = khalf*(gtu13*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu12*PDstandard4th3gt22); + Gt123 = khalf*(gtu31*PDstandard4th2gt33 + gtu11*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu21*PDstandard4th3gt22); - Gt232 = khalf*(gtu23*PDstandard4th2gt33 + gtu12*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + + Gt223 = khalf*(gtu32*PDstandard4th2gt33 + gtu21*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + gtu22*PDstandard4th3gt22); - Gt332 = khalf*(gtu33*PDstandard4th2gt33 + gtu13*(-PDstandard4th1gt32 + PDstandard4th2gt31 + PDstandard4th3gt21) + - gtu23*PDstandard4th3gt22); + Gt323 = khalf*(gtu33*PDstandard4th2gt33 + gtu31*(-PDstandard4th1gt23 + PDstandard4th2gt13 + PDstandard4th3gt12) + + gtu32*PDstandard4th3gt22); - Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu12*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt31 + - 2*gtu12*PDstandard4th3gt32 + gtu13*PDstandard4th3gt33); + Gt133 = khalf*(-(gtu11*PDstandard4th1gt33) - gtu21*PDstandard4th2gt33 + 2*gtu11*PDstandard4th3gt13 + + 2*gtu21*PDstandard4th3gt23 + gtu31*PDstandard4th3gt33); - Gt233 = khalf*(-(gtu12*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu12*PDstandard4th3gt31 + - 2*gtu22*PDstandard4th3gt32 + gtu23*PDstandard4th3gt33); + Gt233 = khalf*(-(gtu21*PDstandard4th1gt33) - gtu22*PDstandard4th2gt33 + 2*gtu21*PDstandard4th3gt13 + + 2*gtu22*PDstandard4th3gt23 + gtu32*PDstandard4th3gt33); - Gt333 = khalf*(-(gtu13*PDstandard4th1gt33) - gtu23*PDstandard4th2gt33 + 2*gtu13*PDstandard4th3gt31 + - 2*gtu23*PDstandard4th3gt32 + gtu33*PDstandard4th3gt33); + Gt333 = khalf*(-(gtu31*PDstandard4th1gt33) - gtu32*PDstandard4th2gt33 + 2*gtu31*PDstandard4th3gt13 + + 2*gtu32*PDstandard4th3gt23 + gtu33*PDstandard4th3gt33); - Xt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt121*gtu12 + Gt131*gtu13 + Gt132*gtu23) + Gt133*gtu33; + Xt1L = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu21 + Gt113*gtu31 + Gt123*gtu32) + Gt133*gtu33; - Xt2L = Gt211*gtu11 + Gt222*gtu22 + 2*(Gt221*gtu12 + Gt231*gtu13 + Gt232*gtu23) + Gt233*gtu33; + Xt2L = Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu21 + Gt213*gtu31 + Gt223*gtu32) + Gt233*gtu33; - Xt3L = Gt311*gtu11 + Gt322*gtu22 + 2*(Gt321*gtu12 + Gt331*gtu13 + Gt332*gtu23) + Gt333*gtu33; + Xt3L = Gt311*gtu11 + Gt322*gtu22 + 2*(Gt312*gtu21 + Gt313*gtu31 + Gt323*gtu32) + Gt333*gtu33; /* Copy local copies back to grid functions */ diff --git a/ML_BSSN/src/ML_BSSN_convertToADMBase.c b/ML_BSSN/src/ML_BSSN_convertToADMBase.c index 03e3004..f5df769 100644 --- a/ML_BSSN/src/ML_BSSN_convertToADMBase.c +++ b/ML_BSSN/src/ML_BSSN_convertToADMBase.c @@ -95,13 +95,13 @@ void ML_BSSN_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCT /* Declare shorthands */ CCTK_REAL e4phi = INITVALUE; - CCTK_REAL g11 = INITVALUE, g21 = INITVALUE, g22 = INITVALUE, g31 = INITVALUE, g32 = INITVALUE, g33 = INITVALUE; - CCTK_REAL K11 = INITVALUE, K21 = INITVALUE, K22 = INITVALUE, K31 = INITVALUE, K32 = INITVALUE, K33 = INITVALUE; + CCTK_REAL g11 = INITVALUE, g12 = INITVALUE, g13 = INITVALUE, g22 = INITVALUE, g23 = INITVALUE, g33 = INITVALUE; + CCTK_REAL K11 = INITVALUE, K12 = INITVALUE, K13 = INITVALUE, K22 = INITVALUE, K23 = INITVALUE, K33 = INITVALUE; /* Declare local copies of grid functions */ CCTK_REAL alpL = INITVALUE; CCTK_REAL alphaL = INITVALUE; - CCTK_REAL At11L = INITVALUE, At21L = INITVALUE, At22L = INITVALUE, At31L = INITVALUE, At32L = INITVALUE, At33L = INITVALUE; + CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE; CCTK_REAL beta1L = INITVALUE, beta2L = INITVALUE, beta3L = INITVALUE; CCTK_REAL betaxL = INITVALUE; CCTK_REAL betayL = INITVALUE; @@ -112,7 +112,7 @@ void ML_BSSN_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCT CCTK_REAL dtbetaxL = INITVALUE; CCTK_REAL dtbetayL = INITVALUE; CCTK_REAL dtbetazL = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; CCTK_REAL gxxL = INITVALUE; CCTK_REAL gxyL = INITVALUE; CCTK_REAL gxzL = INITVALUE; @@ -134,10 +134,10 @@ void ML_BSSN_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCT /* Assign local copies of grid functions */ alphaL = alpha[index]; At11L = At11[index]; - At21L = At21[index]; + At12L = At12[index]; + At13L = At13[index]; At22L = At22[index]; - At31L = At31[index]; - At32L = At32[index]; + At23L = At23[index]; At33L = At33[index]; beta1L = beta1[index]; beta2L = beta2[index]; @@ -147,10 +147,10 @@ void ML_BSSN_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCT dtbeta2L = dtbeta2[index]; dtbeta3L = dtbeta3[index]; gt11L = gt11[index]; - gt21L = gt21[index]; + gt12L = gt12[index]; + gt13L = gt13[index]; gt22L = gt22[index]; - gt31L = gt31[index]; - gt32L = gt32[index]; + gt23L = gt23[index]; gt33L = gt33[index]; phiL = phi[index]; trKL = trK[index]; @@ -168,49 +168,49 @@ void ML_BSSN_convertToADMBase_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCT g11 = e4phi*gt11L; - g21 = e4phi*gt21L; + g12 = e4phi*gt12L; - g31 = e4phi*gt31L; + g13 = e4phi*gt13L; g22 = e4phi*gt22L; - g32 = e4phi*gt32L; + g23 = e4phi*gt23L; g33 = e4phi*gt33L; gxxL = g11; - gxyL = g21; + gxyL = g12; - gxzL = g31; + gxzL = g13; gyyL = g22; - gyzL = g32; + gyzL = g23; gzzL = g33; K11 = At11L*e4phi + g11*kthird*trKL; - K21 = At21L*e4phi + g21*kthird*trKL; + K12 = At12L*e4phi + g12*kthird*trKL; - K31 = At31L*e4phi + g31*kthird*trKL; + K13 = At13L*e4phi + g13*kthird*trKL; K22 = At22L*e4phi + g22*kthird*trKL; - K32 = At32L*e4phi + g32*kthird*trKL; + K23 = At23L*e4phi + g23*kthird*trKL; K33 = At33L*e4phi + g33*kthird*trKL; kxxL = K11; - kxyL = K21; + kxyL = K12; - kxzL = K31; + kxzL = K13; kyyL = K22; - kyzL = K32; + kyzL = K23; kzzL = K33; diff --git a/ML_BSSN/src/ML_BSSN_enforce.c b/ML_BSSN/src/ML_BSSN_enforce.c index 5d75422..2b2f29e 100644 --- a/ML_BSSN/src/ML_BSSN_enforce.c +++ b/ML_BSSN/src/ML_BSSN_enforce.c @@ -95,28 +95,28 @@ void ML_BSSN_enforce_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL no /* Declare shorthands */ CCTK_REAL detgt = INITVALUE; - CCTK_REAL gtu11 = INITVALUE, gtu12 = INITVALUE, gtu13 = INITVALUE, gtu22 = INITVALUE, gtu23 = INITVALUE, gtu33 = INITVALUE; + CCTK_REAL gtu11 = INITVALUE, gtu21 = INITVALUE, gtu22 = INITVALUE, gtu31 = INITVALUE, gtu32 = INITVALUE, gtu33 = INITVALUE; CCTK_REAL trA = INITVALUE; /* Declare local copies of grid functions */ - CCTK_REAL At11L = INITVALUE, At21L = INITVALUE, At22L = INITVALUE, At31L = INITVALUE, At32L = INITVALUE, At33L = INITVALUE; - CCTK_REAL gt11L = INITVALUE, gt21L = INITVALUE, gt22L = INITVALUE, gt31L = INITVALUE, gt32L = INITVALUE, gt33L = INITVALUE; + CCTK_REAL At11L = INITVALUE, At12L = INITVALUE, At13L = INITVALUE, At22L = INITVALUE, At23L = INITVALUE, At33L = INITVALUE; + CCTK_REAL gt11L = INITVALUE, gt12L = INITVALUE, gt13L = INITVALUE, gt22L = INITVALUE, gt23L = INITVALUE, gt33L = INITVALUE; /* Declare precomputed derivatives*/ /* Declare derivatives */ /* Assign local copies of grid functions */ At11L = At11[index]; - At21L = At21[index]; + At12L = At12[index]; + At13L = At13[index]; At22L = At22[index]; - At31L = At31[index]; - At32L = At32[index]; + At23L = At23[index]; At33L = At33[index]; gt11L = gt11[index]; - gt21L = gt21[index]; + gt12L = gt12[index]; + gt13L = gt13[index]; gt22L = gt22[index]; - gt31L = gt31[index]; - gt32L = gt32[index]; + gt23L = gt23[index]; gt33L = gt33[index]; /* Assign local copies of subblock grid functions */ @@ -130,39 +130,39 @@ void ML_BSSN_enforce_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL no /* Calculate temporaries and grid functions */ detgt = 1; - gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt32L)); + gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); - gtu12 = (gt31L*gt32L - gt21L*gt33L)*INV(detgt); + gtu21 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); - gtu13 = (-(gt22L*gt31L) + gt21L*gt32L)*INV(detgt); + gtu31 = (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt); - gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt31L)); + gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt13L)); - gtu23 = (gt21L*gt31L - gt11L*gt32L)*INV(detgt); + gtu32 = (gt12L*gt13L - gt11L*gt23L)*INV(detgt); - gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt21L)); + gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); - trA = At11L*gtu11 + At22L*gtu22 + 2*(At21L*gtu12 + At31L*gtu13 + At32L*gtu23) + At33L*gtu33; + trA = At11L*gtu11 + At22L*gtu22 + 2*(At12L*gtu21 + At13L*gtu31 + At23L*gtu32) + At33L*gtu33; At11L = At11L - gt11L*kthird*trA; - At21L = At21L - gt21L*kthird*trA; + At12L = At12L - gt12L*kthird*trA; - At31L = At31L - gt31L*kthird*trA; + At13L = At13L - gt13L*kthird*trA; At22L = At22L - gt22L*kthird*trA; - At32L = At32L - gt32L*kthird*trA; + At23L = At23L - gt23L*kthird*trA; At33L = At33L - gt33L*kthird*trA; /* Copy local copies back to grid functions */ At11[index] = At11L; - At21[index] = At21L; + At12[index] = At12L; + At13[index] = At13L; At22[index] = At22L; - At31[index] = At31L; - At32[index] = At32L; + At23[index] = At23L; At33[index] = At33L; /* Copy local copies back to subblock grid functions */ diff --git a/ML_BSSN/src/RegisterMoL.c b/ML_BSSN/src/RegisterMoL.c index b0051a5..aaea9c7 100644 --- a/ML_BSSN/src/RegisterMoL.c +++ b/ML_BSSN/src/RegisterMoL.c @@ -16,10 +16,10 @@ void ML_BSSN_RegisterVars(CCTK_ARGUMENTS) /* Register all the evolved grid functions with MoL */ ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At11"), CCTK_VarIndex("ML_BSSN::At11rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At21"), CCTK_VarIndex("ML_BSSN::At21rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At31"), CCTK_VarIndex("ML_BSSN::At31rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At12"), CCTK_VarIndex("ML_BSSN::At12rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At13"), CCTK_VarIndex("ML_BSSN::At13rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At22"), CCTK_VarIndex("ML_BSSN::At22rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At32"), CCTK_VarIndex("ML_BSSN::At32rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At23"), CCTK_VarIndex("ML_BSSN::At23rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::At33"), CCTK_VarIndex("ML_BSSN::At33rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::dtalpha"), CCTK_VarIndex("ML_BSSN::dtalpharhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::dtbeta1"), CCTK_VarIndex("ML_BSSN::dtbeta1rhs")); @@ -31,10 +31,10 @@ void ML_BSSN_RegisterVars(CCTK_ARGUMENTS) ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::alpha"), CCTK_VarIndex("ML_BSSN::alpharhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::phi"), CCTK_VarIndex("ML_BSSN::phirhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt11"), CCTK_VarIndex("ML_BSSN::gt11rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt21"), CCTK_VarIndex("ML_BSSN::gt21rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt31"), CCTK_VarIndex("ML_BSSN::gt31rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt12"), CCTK_VarIndex("ML_BSSN::gt12rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt13"), CCTK_VarIndex("ML_BSSN::gt13rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt22"), CCTK_VarIndex("ML_BSSN::gt22rhs")); - ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt32"), CCTK_VarIndex("ML_BSSN::gt32rhs")); + ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt23"), CCTK_VarIndex("ML_BSSN::gt23rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::gt33"), CCTK_VarIndex("ML_BSSN::gt33rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::beta1"), CCTK_VarIndex("ML_BSSN::beta1rhs")); ierr += MoLRegisterEvolved(CCTK_VarIndex("ML_BSSN::beta2"), CCTK_VarIndex("ML_BSSN::beta2rhs")); diff --git a/ML_BSSN/src/RegisterSymmetries.c b/ML_BSSN/src/RegisterSymmetries.c index 2db5dee..2cf86ef 100644 --- a/ML_BSSN/src/RegisterSymmetries.c +++ b/ML_BSSN/src/RegisterSymmetries.c @@ -27,12 +27,12 @@ void ML_BSSN_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = -1; sym[1] = -1; sym[2] = 1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::At21"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::At12"); sym[0] = -1; sym[1] = 1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::At31"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::At13"); sym[0] = 1; sym[1] = 1; @@ -42,7 +42,7 @@ void ML_BSSN_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = 1; sym[1] = -1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::At32"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::At23"); sym[0] = 1; sym[1] = 1; @@ -102,12 +102,12 @@ void ML_BSSN_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = -1; sym[1] = -1; sym[2] = 1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::gt21"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::gt12"); sym[0] = -1; sym[1] = 1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::gt31"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::gt13"); sym[0] = 1; sym[1] = 1; @@ -117,7 +117,7 @@ void ML_BSSN_RegisterSymmetries(CCTK_ARGUMENTS) sym[0] = 1; sym[1] = -1; sym[2] = -1; - SetCartSymVN(cctkGH, sym, "ML_BSSN::gt32"); + SetCartSymVN(cctkGH, sym, "ML_BSSN::gt23"); sym[0] = 1; sym[1] = 1; @@ -1,9 +1,32 @@ McLachlan +Copyright (C) 2007 Erik Schnetter <schnetter@cct.lsu.edu> + + + A suite of spacetime codes. The name "McLachlan" is in honour of Sarah McLachlan, the Canadian singer. -The code requires Cactus <http://www.cactuscode.org/> and Carpet -<http://www.carpetcode.org/>. The code is generated with Kranc -<http://numrel.aei.mpg.de/Research/Kranc/>, which requires Mathematica -to run. +The code is generated with Kranc +<http://numrel.aei.mpg.de/Research/Kranc/>, which requires +Mathematica. The code also requires Cactus +<http://www.cactuscode.org/> and Carpet <http://www.carpetcode.org/>. + +We thank all authors of Cactus and Kranc for these fine tools. + + + +This program is free software; you can redistribute it and/or modify +it under the terms of the GNU General Public License as published by +the Free Software Foundation; either version 2 of the License, or (at +your option) any later version. + +This program is distributed in the hope that it will be useful, but +WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +General Public License for more details. + +You should have received a copy of the GNU General Public License +along with this program; if not, write to the Free Software +Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 +USA diff --git a/m/McLachlan.m b/m/McLachlan.m index cc2889a..308f1cc 100644 --- a/m/McLachlan.m +++ b/m/McLachlan.m @@ -55,16 +55,16 @@ SetTensorAttribute[At, TensorWeight, -2/3]; SetTensorAttribute[cXt, TensorWeight, +2/3]; SetTensorAttribute[cS, TensorWeight, +2 ]; -Map [AssertSymmetricDecreasing, +Map [AssertSymmetricIncreasing, {g[la,lb], K[la,lb], R[la,lb], gt[la,lb], At[la,lb], Rt[la,lb], Rphi[la,lb]}]; -AssertSymmetricDecreasing [G[ua,lb,lc], lb, lc]; -AssertSymmetricDecreasing [Gt[ua,lb,lc], lb, lc]; -AssertSymmetricDecreasing [gK[la,lb,lc], la, lb]; -Map [AssertSymmetricIncreasing, {gu[ua,ub], gtu[ua,ub], Atu[ua,ub]}]; -AssertSymmetricIncreasing [dgtu[ua,ub,lc], ua, ub]; -AssertSymmetricIncreasing [ddgtu[ua,ub,lc,ld], ua, ub]; -AssertSymmetricDecreasing [ddgtu[ua,ub,lc,ld], lc, ld]; +AssertSymmetricIncreasing [G[ua,lb,lc], lb, lc]; +AssertSymmetricIncreasing [Gt[ua,lb,lc], lb, lc]; +AssertSymmetricIncreasing [gK[la,lb,lc], la, lb]; +Map [AssertSymmetricDecreasing, {gu[ua,ub], gtu[ua,ub], Atu[ua,ub]}]; +AssertSymmetricDecreasing [dgtu[ua,ub,lc], ua, ub]; +AssertSymmetricDecreasing [ddgtu[ua,ub,lc,ld], ua, ub]; +AssertSymmetricIncreasing [ddgtu[ua,ub,lc,ld], lc, ld]; DefineConnection [CD, PD, G]; DefineConnection [CDt, PD, Gt]; @@ -195,16 +195,16 @@ convertFromADMBaseCalc = Equations -> { g11 -> gxx, - g21 -> gxy, - g31 -> gxz, + g12 -> gxy, + g13 -> gxz, g22 -> gyy, - g32 -> gyz, + g23 -> gyz, g33 -> gzz, K11 -> kxx, - K21 -> kxy, - K31 -> kxz, + K12 -> kxy, + K13 -> kxz, K22 -> kyy, - K32 -> kyz, + K23 -> kyz, K33 -> kzz, (* TODO: this is incomplete; it ignores dtalp and dtbeta^i *) alpha -> alp, @@ -219,36 +219,35 @@ convertFromADMBaseCalcBSSN = Name -> "ML_BSSN_convertFromADMBase", Schedule -> {"AT initial AFTER ADMBase_PostInitial"}, ConditionalOnKeyword -> {"my_initial_data", "ADMBase"}, - Shorthands -> {g[la,lb], detg, gu[ua,ub], em4phi, K[la,lb], Km[ua,lb]}, + Shorthands -> {g[la,lb], detg, gu[ua,ub], em4phi, K[la,lb]}, Equations -> { g11 -> gxx, - g21 -> gxy, - g31 -> gxz, + g12 -> gxy, + g13 -> gxz, g22 -> gyy, - g32 -> gyz, + g23 -> gyz, g33 -> gzz, detg -> detgExpr, gu[ua,ub] -> 1/detg detgExpr MatrixInverse [g[ua,ub]], - (* em4phi -> Exp [-4 phi], *) - em4phi -> 1 / detg^3, - phi -> Log [detg] / 12, - gt[la,lb] -> em4phi g[la,lb], + phi -> Log [detg] / 12, + em4phi -> Exp [-4 phi], + gt[la,lb] -> em4phi g[la,lb], K11 -> kxx, - K21 -> kxy, - K31 -> kxz, + K12 -> kxy, + K13 -> kxz, K22 -> kyy, - K32 -> kyz, + K23 -> kyz, K33 -> kzz, - Km[ua,lb] -> gu[ua,uc] K[lc,lb], - trK -> Km[ua,la], + trK -> gu[ua,ub] K[la,lb], At[la,lb] -> em4phi (K[la,lb] - (1/3) g[la,lb] trK), alpha -> alp, + (* TODO: this is wrong *) dtalpha -> dtalp, beta1 -> betax, @@ -289,16 +288,16 @@ convertToADMBaseCalc = Equations -> { gxx -> g11, - gxy -> g21, - gxz -> g31, + gxy -> g12, + gxz -> g13, gyy -> g22, - gyz -> g32, + gyz -> g23, gzz -> g33, kxx -> K11, - kxy -> K21, - kxz -> K31, + kxy -> K12, + kxz -> K13, kyy -> K22, - kyz -> K32, + kyz -> K23, kzz -> K33, (* TODO: this is wrong; it sets dtalp and dtbeta^i incorrectly *) alp -> alpha, @@ -322,23 +321,25 @@ convertToADMBaseCalcBSSN = e4phi -> Exp [4 phi], g[la,lb] -> e4phi gt[la,lb], gxx -> g11, - gxy -> g21, - gxz -> g31, + gxy -> g12, + gxz -> g13, gyy -> g22, - gyz -> g32, + gyz -> g23, gzz -> g33, K[la,lb] -> e4phi At[la,lb] + (1/3) g[la,lb] trK, kxx -> K11, - kxy -> K21, - kxz -> K31, + kxy -> K12, + kxz -> K13, kyy -> K22, - kyz -> K32, + kyz -> K23, kzz -> K33, alp -> alpha, + (* TODO: this is wrong *) dtalp -> dtalpha, betax -> beta1, betay -> beta2, betaz -> beta3, + (* TODO: this is wrong *) dtbetax -> dtbeta1, dtbetay -> dtbeta2, dtbetaz -> dtbeta3 @@ -414,8 +415,6 @@ evolCalcBSSN = + 4 CDt[phi,li] CDt[phi,lj] - 4 gt[li,lj] gtu[ul,un] CDt[phi,ln] CDt[phi,ll], - R[la,lb] -> Rt[la,lb] + Rphi[la,lb], - Atm[ua,lb] -> gtu[ua,uc] At[lc,lb], Atu[ua,ub] -> Atm[ua,lc] gtu[ub,uc], @@ -431,6 +430,8 @@ evolCalcBSSN = + 1/(2 detg) (+ KD[ua,lb] ddetg[lc] + KD[ua,lc] ddetg[lb] - (1/3) g[lb,lc] gu[ua,ud] ddetg[ld]), + R[la,lb] -> Rt[la,lb] + Rphi[la,lb], + (* PRD 62, 044034 (2000), eqn. (10) *) dot[phi] -> - (1/6) alpha trK + Lie[phi, beta] + (1/6) phi PD[beta[ua],la], @@ -456,6 +457,7 @@ evolCalcBSSN = + alpha (Atm[ua,lb] Atm[ub,la] + (1/3) trK^2) + Lie[trK, beta], (* PRD 62, 044034 (2000), eqn. (12) *) + (* TODO: use Hamiltonian constraint to make tracefree *) dot[At[la,lb]] -> + em4phi (+ (- CD[alpha,la,lb] + alpha R[la,lb]) - (1/3) g[la,lb] gu[uc,ud] (- CD[alpha,lc,ld] + alpha R[lc,ld])) @@ -521,10 +523,10 @@ constraintsCalcBSSN = Name -> "ML_BSSN_constraints", Schedule -> {"AT analysis"}, Where -> Interior, - Shorthands -> {detgt, ddetgt[la], gtu[ua,ub], Gt[ua,lb,lc], e4phi, + Shorthands -> {detgt, ddetgt[la], gtu[ua,ub], Gt[ua,lb,lc], e4phi, em4phi, g[la,lb], detg, gu[ua,ub], ddetg[la], G[ua,lb,lc], - Rt[la,lb], Rphi[la,lb], R[la,lb], trR, - K[la,lb], Km[la,lb], gK[la,lb,lc]}, + Rt[la,lb], Rphi[la,lb], R[la,lb], trR, Atm[la,lb], + gK[la,lb,lc]}, Equations -> { detgt -> 1 (* detgtExpr *), @@ -533,16 +535,6 @@ constraintsCalcBSSN = Gt[ua,lb,lc] -> 1/2 gtu[ua,ud] (PD[gt[lb,ld],lc] + PD[gt[lc,ld],lb] - PD[gt[lb,lc],ld]), - e4phi -> Exp [4 phi], - g[la,lb] -> e4phi gt[la,lb], - detg -> detgExpr, - gu[ua,ub] -> 1/detg detgExpr MatrixInverse [g[ua,ub]], - (* ddetg[la] -> PD[e4phi detg,la], *) - ddetg[la] -> e4phi ddetgt[la] + 4 detgt e4phi PD[phi,la], - G[ua,lb,lc] -> Gt[ua,lb,lc] - + 1/(2 detg) (+ KD[ua,lb] ddetg[lc] + KD[ua,lc] ddetg[lb] - - (1/3) g[lb,lc] gu[ua,ud] ddetg[ld]), - (* PRD 62, 044034 (2000), eqn. (18) *) Rt[li,lj] -> - (1/2) gtu[ul,um] PD[gt[li,lj],ll,lm] + gt[lk,li] PD[Xt[uk],lj] + gt[lk,lj] PD[Xt[uk],li] @@ -551,19 +543,35 @@ constraintsCalcBSSN = + 2 Gt[uk,ll,lj] gt[li,ln] Gt[un,lk,lm] + Gt[uk,li,lm] gt[lk,ln] Gt[un,ll,lj]), (* PRD 62, 044034 (2000), eqn. (15) *) - (* TODO: Check that CDt takes the tensor weight of phi into account *) + (* TODO: this term seems to be wrong; + the Ricci scalar is not zero for BL data *) Rphi[li,lj] -> - 2 CDt[phi,lj,li] - 2 gt[li,lj] gtu[ul,un] CDt[phi,ll,ln] + 4 CDt[phi,li] CDt[phi,lj] - 4 gt[li,lj] gtu[ul,un] CDt[phi,ln] CDt[phi,ll], + e4phi -> Exp [4 phi], + em4phi -> 1 / e4phi, + g[la,lb] -> e4phi gt[la,lb], + (* detg -> detgExpr, *) + (* gu[ua,ub] -> 1/detg detgExpr MatrixInverse [g[ua,ub]], *) + detg -> e4phi^3, + gu[ua,ub] -> em4phi gtu[ua,ub], + (* ddetg[la] -> PD[e4phi detg,la], *) + ddetg[la] -> e4phi ddetgt[la] + 4 detgt e4phi PD[phi,la], + G[ua,lb,lc] -> Gt[ua,lb,lc] + + 1/(2 detg) (+ KD[ua,lb] ddetg[lc] + KD[ua,lc] ddetg[lb] + - (1/3) g[lb,lc] gu[ua,ud] ddetg[ld]), + R[la,lb] -> Rt[la,lb] + Rphi[la,lb], trR -> gu[ua,ub] R[la,lb], - K[la,lb] -> e4phi At[la,lb] + (1/3) g[la,lb] trK, - Km[ua,lb] -> gu[ua,uc] K[lc,lb], + (* K[la,lb] -> e4phi At[la,lb] + (1/3) g[la,lb] trK, *) + (* Km[ua,lb] -> gu[ua,uc] K[lc,lb], *) + Atm[ua,lb] -> gtu[ua,uc] At[lc,lb], - H -> trR - Km[ua,lb] Km[ub,la] + trK^2, + (* H -> trR - Km[ua,lb] Km[ub,la] + trK^2, *) + H -> trR - Atm[ua,lb] Atm[ub,la] + (2/3) trK^2, (* gK[la,lb,lc] -> CD[K[la,lb],lc], *) gK[la,lb,lc] -> + 4 e4phi PD[phi,lc] At[la,lb] + e4phi CD[At[la,lb],lc] @@ -571,7 +579,9 @@ constraintsCalcBSSN = M[la] -> gu[ub,uc] (gK[lc,la,lb] - gK[lc,lb,la]), (* det gamma-tilde *) - cS -> Log [detgt], + (* TODO cS -> Log [detgt], *) + (* TODO: output the Ricci scalar for debugging *) + cS -> trR, (* Gamma constraint *) cXt[ua] -> gtu[ub,uc] Gt[ua,lb,lc] - Xt[ua], diff --git a/par/ks_bssn_1.par b/par/ks_bssn_1.par index 38c2850..8a13b48 100644 --- a/par/ks_bssn_1.par +++ b/par/ks_bssn_1.par @@ -1,12 +1,41 @@ ActiveThorns = " - Boundary CartGrid3D CoordBase IOUtil InitBase MoL SymBase - ADMBase ADMCoupling CoordGauge StaticConformal + Boundary + CartGrid3D + CoordBase + IOUtil + InitBase + MoL + SymBase + + ADMAnalysis + ADMBase + ADMConstraints + ADMCoupling + ADMMacros + CoordGauge + SpaceMask + StaticConformal + NaNChecker - Carpet CarpetIOASCII CarpetIOBasic CarpetIOScalar CarpetLib CarpetReduce LoopControl + + Carpet + CarpetIOASCII + CarpetIOBasic + CarpetIOScalar + CarpetLib + CarpetReduce + LoopControl + ReflectionSymmetry - Exact Formaline GSL + + Exact + Formaline + GSL + Slab + GenericFD + ML_BSSN " @@ -25,9 +54,12 @@ CoordBase::dx = 0.2 CoordBase::dy = 0.2 CoordBase::dz = 0.2 -ReflectionSymmetry::reflection_x = yes -ReflectionSymmetry::reflection_y = yes -ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::reflection_x = yes +ReflectionSymmetry::reflection_y = yes +ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::avoid_origin_x = no +ReflectionSymmetry::avoid_origin_y = no +ReflectionSymmetry::avoid_origin_z = no CoordBase::boundary_shiftout_x_lower = 1 CoordBase::boundary_shiftout_y_lower = 1 @@ -52,15 +84,20 @@ ADMBase::initial_shift = "exact" ADMBase::initial_dtlapse = "zero" ADMBase::initial_dtshift = "zero" -Exact::exact_model = "Kerr/Kerr-Schild" -Exact::Kerr_KerrSchild__mass = 1.0 -Exact::Kerr_KerrSchild__spin = 0.0 +#Exact::exact_model = "Kerr/Kerr-Schild" +#Exact::Kerr_KerrSchild__mass = 1.0 +#Exact::Kerr_KerrSchild__spin = 0.0 + +Exact::exact_model = "Schwarzschild/BL" +Exact::Schwarzschild_BL__mass = 1.0 ML_BSSN::harmonicN = 0 # 1+log ML_BSSN::harmonicF = 2.0 # 1+log ML_BSSN::ShiftGammaCoeff = 0.75 ML_BSSN::BetaDriver = 0.5 +ADMMacros::spatial_order = 4 + IO::out_dir = $parfile @@ -78,6 +115,15 @@ IOScalar::outScalar_vars = " ADMBase::curv ADMBase::lapse ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma ML_BSSN::Ham ML_BSSN::mom ML_BSSN::cons_detg @@ -97,6 +143,15 @@ IOASCII::out1D_vars = " ADMBase::curv ADMBase::lapse ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma ML_BSSN::Ham ML_BSSN::mom ML_BSSN::cons_detg diff --git a/par/ks_bssn_2.par b/par/ks_bssn_2.par index 957c1bd..ac12b53 100644 --- a/par/ks_bssn_2.par +++ b/par/ks_bssn_2.par @@ -1,12 +1,40 @@ ActiveThorns = " - Boundary CartGrid3D CoordBase IOUtil InitBase MoL SymBase - ADMBase ADMCoupling CoordGauge StaticConformal + Boundary + CartGrid3D + CoordBase + IOUtil + InitBase + MoL + SymBase + + ADMBase + ADMConstraints + ADMCoupling + ADMMacros + CoordGauge + SpaceMask + StaticConformal + NaNChecker - Carpet CarpetIOASCII CarpetIOBasic CarpetIOScalar CarpetLib CarpetReduce LoopControl + + Carpet + CarpetIOASCII + CarpetIOBasic + CarpetIOScalar + CarpetLib + CarpetReduce + LoopControl + ReflectionSymmetry - Exact Formaline GSL + + Exact + Formaline + GSL + Slab + GenericFD + ML_BSSN " @@ -25,9 +53,12 @@ CoordBase::dx = 0.1 CoordBase::dy = 0.1 CoordBase::dz = 0.1 -ReflectionSymmetry::reflection_x = yes -ReflectionSymmetry::reflection_y = yes -ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::reflection_x = yes +ReflectionSymmetry::reflection_y = yes +ReflectionSymmetry::reflection_z = yes +ReflectionSymmetry::avoid_origin_x = no +ReflectionSymmetry::avoid_origin_y = no +ReflectionSymmetry::avoid_origin_z = no CoordBase::boundary_shiftout_x_lower = 1 CoordBase::boundary_shiftout_y_lower = 1 @@ -61,6 +92,8 @@ ML_BSSN::harmonicF = 2.0 # 1+log ML_BSSN::ShiftGammaCoeff = 0.75 ML_BSSN::BetaDriver = 0.5 +ADMMacros::spatial_order = 4 + IO::out_dir = $parfile @@ -78,6 +111,15 @@ IOScalar::outScalar_vars = " ADMBase::curv ADMBase::lapse ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma ML_BSSN::Ham ML_BSSN::mom ML_BSSN::cons_detg @@ -97,6 +139,15 @@ IOASCII::out1D_vars = " ADMBase::curv ADMBase::lapse ADMBase::shift + ADMAnalysis::trace_of_K + ADMAnalysis::ricci_scalar + ADMConstraints::Hamiltonian + ADMConstraints::momentum + ML_BSSN::log_confac + ML_BSSN::metric + ML_BSSN::trace_curv + ML_BSSN::curv + ML_BSSN::Gamma ML_BSSN::Ham ML_BSSN::mom ML_BSSN::cons_detg |