diff options
| author | Peter Diener <diener@10-4-34-85.lsu.edu> | 2007-11-12 09:22:44 -0600 |
|---|---|---|
| committer | Peter Diener <diener@10-4-34-85.lsu.edu> | 2007-11-12 09:22:44 -0600 |
| commit | c2dcf6cfdd5a7096dd3f695e73b3f4b59f58516e (patch) | |
| tree | 4a8725ce70b8eb7f9a46a549f2f80be5fae4eda4 | |
| parent | 865a8b88bea3c3676f0238355339b84ecae8c8a6 (diff) | |
Fix RHS for gamma
Implementing the gamma RHS equation (PRD 67 084023 (2003), eqn (26)).
The gamma RHS now converges.
Signed-off-by: Peter Diener <diener@10-4-34-85.lsu.edu>
| -rw-r--r-- | ML_BSSN/src/ML_BSSN_RHS.c | 335 | ||||
| -rw-r--r-- | m/McLachlan.m | 12 |
2 files changed, 51 insertions, 296 deletions
diff --git a/ML_BSSN/src/ML_BSSN_RHS.c b/ML_BSSN/src/ML_BSSN_RHS.c index 9a59a49..65ff8c8 100644 --- a/ML_BSSN/src/ML_BSSN_RHS.c +++ b/ML_BSSN/src/ML_BSSN_RHS.c @@ -98,15 +98,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal CCTK_REAL Atm31 = INITVALUE, Atm32 = INITVALUE, Atm33 = 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 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, 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 dgtu111 = INITVALUE, dgtu211 = INITVALUE, dgtu212 = INITVALUE, dgtu222 = INITVALUE, dgtu311 = INITVALUE, dgtu313 = INITVALUE; + CCTK_REAL dgtu322 = INITVALUE, dgtu323 = INITVALUE, dgtu333 = INITVALUE; CCTK_REAL e4phi = INITVALUE; CCTK_REAL em4phi = INITVALUE; CCTK_REAL g11 = INITVALUE; @@ -503,27 +498,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gtu11*gtu33*PDstandardNth1gt13 - gtu21*gtu32*PDstandardNth1gt22 - gtu31*gtu32*PDstandardNth1gt23 - gtu21*gtu33*PDstandardNth1gt23 - gtu31*gtu33*PDstandardNth1gt33 - PDstandardNth1gt13*SQR(gtu31); - dgtu221 = -2*(gtu21*gtu22*PDstandardNth1gt12 + gtu21*gtu32*PDstandardNth1gt13 + gtu22*gtu32*PDstandardNth1gt23) - - PDstandardNth1gt11*SQR(gtu21) - PDstandardNth1gt22*SQR(gtu22) - PDstandardNth1gt33*SQR(gtu32); - - dgtu321 = -(gtu21*gtu31*PDstandardNth1gt11) - gtu22*gtu31*PDstandardNth1gt12 - gtu21*gtu32*PDstandardNth1gt12 - - gtu31*gtu32*PDstandardNth1gt13 - gtu21*gtu33*PDstandardNth1gt13 - gtu22*gtu32*PDstandardNth1gt22 - - gtu22*gtu33*PDstandardNth1gt23 - gtu32*gtu33*PDstandardNth1gt33 - PDstandardNth1gt23*SQR(gtu32); - - dgtu331 = -2*(gtu31*gtu32*PDstandardNth1gt12 + gtu31*gtu33*PDstandardNth1gt13 + gtu32*gtu33*PDstandardNth1gt23) - - PDstandardNth1gt11*SQR(gtu31) - PDstandardNth1gt22*SQR(gtu32) - PDstandardNth1gt33*SQR(gtu33); - - dgtu112 = -2*(gtu11*gtu21*PDstandardNth2gt12 + gtu11*gtu31*PDstandardNth2gt13 + gtu21*gtu31*PDstandardNth2gt23) - - PDstandardNth2gt11*SQR(gtu11) - PDstandardNth2gt22*SQR(gtu21) - PDstandardNth2gt33*SQR(gtu31); - dgtu212 = -(gtu11*gtu21*PDstandardNth2gt11) - gtu11*gtu22*PDstandardNth2gt12 - gtu21*gtu31*PDstandardNth2gt13 - gtu11*gtu32*PDstandardNth2gt13 - gtu21*gtu22*PDstandardNth2gt22 - gtu22*gtu31*PDstandardNth2gt23 - gtu21*gtu32*PDstandardNth2gt23 - gtu31*gtu32*PDstandardNth2gt33 - PDstandardNth2gt12*SQR(gtu21); - dgtu312 = -(gtu11*gtu31*PDstandardNth2gt11) - gtu21*gtu31*PDstandardNth2gt12 - gtu11*gtu32*PDstandardNth2gt12 - - gtu11*gtu33*PDstandardNth2gt13 - gtu21*gtu32*PDstandardNth2gt22 - gtu31*gtu32*PDstandardNth2gt23 - - gtu21*gtu33*PDstandardNth2gt23 - gtu31*gtu33*PDstandardNth2gt33 - PDstandardNth2gt13*SQR(gtu31); - dgtu222 = -2*(gtu21*gtu22*PDstandardNth2gt12 + gtu21*gtu32*PDstandardNth2gt13 + gtu22*gtu32*PDstandardNth2gt23) - PDstandardNth2gt11*SQR(gtu21) - PDstandardNth2gt22*SQR(gtu22) - PDstandardNth2gt33*SQR(gtu32); @@ -531,23 +509,10 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gtu31*gtu32*PDstandardNth2gt13 - gtu21*gtu33*PDstandardNth2gt13 - gtu22*gtu32*PDstandardNth2gt22 - gtu22*gtu33*PDstandardNth2gt23 - gtu32*gtu33*PDstandardNth2gt33 - PDstandardNth2gt23*SQR(gtu32); - dgtu332 = -2*(gtu31*gtu32*PDstandardNth2gt12 + gtu31*gtu33*PDstandardNth2gt13 + gtu32*gtu33*PDstandardNth2gt23) - - PDstandardNth2gt11*SQR(gtu31) - PDstandardNth2gt22*SQR(gtu32) - PDstandardNth2gt33*SQR(gtu33); - - dgtu113 = -2*(gtu11*gtu21*PDstandardNth3gt12 + gtu11*gtu31*PDstandardNth3gt13 + gtu21*gtu31*PDstandardNth3gt23) - - PDstandardNth3gt11*SQR(gtu11) - PDstandardNth3gt22*SQR(gtu21) - PDstandardNth3gt33*SQR(gtu31); - - dgtu213 = -(gtu11*gtu21*PDstandardNth3gt11) - gtu11*gtu22*PDstandardNth3gt12 - gtu21*gtu31*PDstandardNth3gt13 - - gtu11*gtu32*PDstandardNth3gt13 - gtu21*gtu22*PDstandardNth3gt22 - gtu22*gtu31*PDstandardNth3gt23 - - gtu21*gtu32*PDstandardNth3gt23 - gtu31*gtu32*PDstandardNth3gt33 - PDstandardNth3gt12*SQR(gtu21); - dgtu313 = -(gtu11*gtu31*PDstandardNth3gt11) - gtu21*gtu31*PDstandardNth3gt12 - gtu11*gtu32*PDstandardNth3gt12 - gtu11*gtu33*PDstandardNth3gt13 - gtu21*gtu32*PDstandardNth3gt22 - gtu31*gtu32*PDstandardNth3gt23 - gtu21*gtu33*PDstandardNth3gt23 - gtu31*gtu33*PDstandardNth3gt33 - PDstandardNth3gt13*SQR(gtu31); - dgtu223 = -2*(gtu21*gtu22*PDstandardNth3gt12 + gtu21*gtu32*PDstandardNth3gt13 + gtu22*gtu32*PDstandardNth3gt23) - - PDstandardNth3gt11*SQR(gtu21) - PDstandardNth3gt22*SQR(gtu22) - PDstandardNth3gt33*SQR(gtu32); - dgtu323 = -(gtu21*gtu31*PDstandardNth3gt11) - gtu22*gtu31*PDstandardNth3gt12 - gtu21*gtu32*PDstandardNth3gt12 - gtu31*gtu32*PDstandardNth3gt13 - gtu21*gtu33*PDstandardNth3gt13 - gtu22*gtu32*PDstandardNth3gt22 - gtu22*gtu33*PDstandardNth3gt23 - gtu32*gtu33*PDstandardNth3gt33 - PDstandardNth3gt23*SQR(gtu32); @@ -555,210 +520,6 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal dgtu333 = -2*(gtu31*gtu32*PDstandardNth3gt12 + gtu31*gtu33*PDstandardNth3gt13 + gtu32*gtu33*PDstandardNth3gt23) - PDstandardNth3gt11*SQR(gtu31) - PDstandardNth3gt22*SQR(gtu32) - PDstandardNth3gt33*SQR(gtu33); - ddgtu1111 = -2*(gtu11*gtu21*PDstandardNth11gt12 + gtu11*gtu31*PDstandardNth11gt13 + gtu21*gtu31*PDstandardNth11gt23 + - dgtu111*gtu11*PDstandardNth1gt11 + dgtu211*gtu11*PDstandardNth1gt12 + dgtu111*gtu21*PDstandardNth1gt12 + - dgtu311*gtu11*PDstandardNth1gt13 + dgtu111*gtu31*PDstandardNth1gt13 + dgtu211*gtu21*PDstandardNth1gt22 + - dgtu311*gtu21*PDstandardNth1gt23 + dgtu211*gtu31*PDstandardNth1gt23 + dgtu311*gtu31*PDstandardNth1gt33) - - PDstandardNth11gt11*SQR(gtu11) - PDstandardNth11gt22*SQR(gtu21) - PDstandardNth11gt33*SQR(gtu31); - - ddgtu2111 = -(gtu11*gtu21*PDstandardNth11gt11) - gtu11*gtu22*PDstandardNth11gt12 - gtu21*gtu31*PDstandardNth11gt13 - - gtu11*gtu32*PDstandardNth11gt13 - gtu21*gtu22*PDstandardNth11gt22 - gtu22*gtu31*PDstandardNth11gt23 - - gtu21*gtu32*PDstandardNth11gt23 - gtu31*gtu32*PDstandardNth11gt33 - dgtu211*gtu11*PDstandardNth1gt11 - - dgtu111*gtu21*PDstandardNth1gt11 - dgtu221*gtu11*PDstandardNth1gt12 - 2*dgtu211*gtu21*PDstandardNth1gt12 - - dgtu111*gtu22*PDstandardNth1gt12 - dgtu321*gtu11*PDstandardNth1gt13 - dgtu311*gtu21*PDstandardNth1gt13 - - dgtu211*gtu31*PDstandardNth1gt13 - dgtu111*gtu32*PDstandardNth1gt13 - dgtu221*gtu21*PDstandardNth1gt22 - - dgtu211*gtu22*PDstandardNth1gt22 - dgtu321*gtu21*PDstandardNth1gt23 - dgtu311*gtu22*PDstandardNth1gt23 - - dgtu221*gtu31*PDstandardNth1gt23 - dgtu211*gtu32*PDstandardNth1gt23 - dgtu321*gtu31*PDstandardNth1gt33 - - dgtu311*gtu32*PDstandardNth1gt33 - PDstandardNth11gt12*SQR(gtu21); - - ddgtu3111 = -(gtu11*gtu31*PDstandardNth11gt11) - gtu21*gtu31*PDstandardNth11gt12 - gtu11*gtu32*PDstandardNth11gt12 - - gtu11*gtu33*PDstandardNth11gt13 - gtu21*gtu32*PDstandardNth11gt22 - gtu31*gtu32*PDstandardNth11gt23 - - gtu21*gtu33*PDstandardNth11gt23 - gtu31*gtu33*PDstandardNth11gt33 - dgtu311*gtu11*PDstandardNth1gt11 - - dgtu111*gtu31*PDstandardNth1gt11 - dgtu321*gtu11*PDstandardNth1gt12 - dgtu311*gtu21*PDstandardNth1gt12 - - dgtu211*gtu31*PDstandardNth1gt12 - dgtu111*gtu32*PDstandardNth1gt12 - dgtu331*gtu11*PDstandardNth1gt13 - - 2*dgtu311*gtu31*PDstandardNth1gt13 - dgtu111*gtu33*PDstandardNth1gt13 - dgtu321*gtu21*PDstandardNth1gt22 - - dgtu211*gtu32*PDstandardNth1gt22 - dgtu331*gtu21*PDstandardNth1gt23 - dgtu321*gtu31*PDstandardNth1gt23 - - dgtu311*gtu32*PDstandardNth1gt23 - dgtu211*gtu33*PDstandardNth1gt23 - dgtu331*gtu31*PDstandardNth1gt33 - - dgtu311*gtu33*PDstandardNth1gt33 - PDstandardNth11gt13*SQR(gtu31); - - ddgtu1112 = -2*(gtu11*gtu21*PDstandardNth12gt12 + gtu11*gtu31*PDstandardNth12gt13 + gtu21*gtu31*PDstandardNth12gt23 + - dgtu112*gtu11*PDstandardNth1gt11 + dgtu212*gtu11*PDstandardNth1gt12 + dgtu112*gtu21*PDstandardNth1gt12 + - dgtu312*gtu11*PDstandardNth1gt13 + dgtu112*gtu31*PDstandardNth1gt13 + dgtu212*gtu21*PDstandardNth1gt22 + - dgtu312*gtu21*PDstandardNth1gt23 + dgtu212*gtu31*PDstandardNth1gt23 + dgtu312*gtu31*PDstandardNth1gt33) - - PDstandardNth12gt11*SQR(gtu11) - PDstandardNth12gt22*SQR(gtu21) - PDstandardNth12gt33*SQR(gtu31); - - ddgtu2112 = -(gtu11*gtu21*PDstandardNth12gt11) - gtu11*gtu22*PDstandardNth12gt12 - gtu21*gtu31*PDstandardNth12gt13 - - gtu11*gtu32*PDstandardNth12gt13 - gtu21*gtu22*PDstandardNth12gt22 - gtu22*gtu31*PDstandardNth12gt23 - - gtu21*gtu32*PDstandardNth12gt23 - gtu31*gtu32*PDstandardNth12gt33 - dgtu212*gtu11*PDstandardNth1gt11 - - dgtu112*gtu21*PDstandardNth1gt11 - dgtu222*gtu11*PDstandardNth1gt12 - 2*dgtu212*gtu21*PDstandardNth1gt12 - - dgtu112*gtu22*PDstandardNth1gt12 - dgtu322*gtu11*PDstandardNth1gt13 - dgtu312*gtu21*PDstandardNth1gt13 - - dgtu212*gtu31*PDstandardNth1gt13 - dgtu112*gtu32*PDstandardNth1gt13 - dgtu222*gtu21*PDstandardNth1gt22 - - dgtu212*gtu22*PDstandardNth1gt22 - dgtu322*gtu21*PDstandardNth1gt23 - dgtu312*gtu22*PDstandardNth1gt23 - - dgtu222*gtu31*PDstandardNth1gt23 - dgtu212*gtu32*PDstandardNth1gt23 - dgtu322*gtu31*PDstandardNth1gt33 - - dgtu312*gtu32*PDstandardNth1gt33 - PDstandardNth12gt12*SQR(gtu21); - - ddgtu3112 = -(gtu11*gtu31*PDstandardNth12gt11) - gtu21*gtu31*PDstandardNth12gt12 - gtu11*gtu32*PDstandardNth12gt12 - - gtu11*gtu33*PDstandardNth12gt13 - gtu21*gtu32*PDstandardNth12gt22 - gtu31*gtu32*PDstandardNth12gt23 - - gtu21*gtu33*PDstandardNth12gt23 - gtu31*gtu33*PDstandardNth12gt33 - dgtu312*gtu11*PDstandardNth1gt11 - - dgtu112*gtu31*PDstandardNth1gt11 - dgtu322*gtu11*PDstandardNth1gt12 - dgtu312*gtu21*PDstandardNth1gt12 - - dgtu212*gtu31*PDstandardNth1gt12 - dgtu112*gtu32*PDstandardNth1gt12 - dgtu332*gtu11*PDstandardNth1gt13 - - 2*dgtu312*gtu31*PDstandardNth1gt13 - dgtu112*gtu33*PDstandardNth1gt13 - dgtu322*gtu21*PDstandardNth1gt22 - - dgtu212*gtu32*PDstandardNth1gt22 - dgtu332*gtu21*PDstandardNth1gt23 - dgtu322*gtu31*PDstandardNth1gt23 - - dgtu312*gtu32*PDstandardNth1gt23 - dgtu212*gtu33*PDstandardNth1gt23 - dgtu332*gtu31*PDstandardNth1gt33 - - dgtu312*gtu33*PDstandardNth1gt33 - PDstandardNth12gt13*SQR(gtu31); - - ddgtu2212 = -2*(gtu21*gtu22*PDstandardNth12gt12 + gtu21*gtu32*PDstandardNth12gt13 + gtu22*gtu32*PDstandardNth12gt23 + - dgtu212*gtu21*PDstandardNth1gt11 + dgtu222*gtu21*PDstandardNth1gt12 + dgtu212*gtu22*PDstandardNth1gt12 + - dgtu322*gtu21*PDstandardNth1gt13 + dgtu212*gtu32*PDstandardNth1gt13 + dgtu222*gtu22*PDstandardNth1gt22 + - dgtu322*gtu22*PDstandardNth1gt23 + dgtu222*gtu32*PDstandardNth1gt23 + dgtu322*gtu32*PDstandardNth1gt33) - - PDstandardNth12gt11*SQR(gtu21) - PDstandardNth12gt22*SQR(gtu22) - PDstandardNth12gt33*SQR(gtu32); - - ddgtu3212 = -(gtu21*gtu31*PDstandardNth12gt11) - gtu22*gtu31*PDstandardNth12gt12 - gtu21*gtu32*PDstandardNth12gt12 - - gtu31*gtu32*PDstandardNth12gt13 - gtu21*gtu33*PDstandardNth12gt13 - gtu22*gtu32*PDstandardNth12gt22 - - gtu22*gtu33*PDstandardNth12gt23 - gtu32*gtu33*PDstandardNth12gt33 - dgtu312*gtu21*PDstandardNth1gt11 - - dgtu212*gtu31*PDstandardNth1gt11 - dgtu322*gtu21*PDstandardNth1gt12 - dgtu312*gtu22*PDstandardNth1gt12 - - dgtu222*gtu31*PDstandardNth1gt12 - dgtu212*gtu32*PDstandardNth1gt12 - dgtu332*gtu21*PDstandardNth1gt13 - - dgtu322*gtu31*PDstandardNth1gt13 - dgtu312*gtu32*PDstandardNth1gt13 - dgtu212*gtu33*PDstandardNth1gt13 - - dgtu322*gtu22*PDstandardNth1gt22 - dgtu222*gtu32*PDstandardNth1gt22 - dgtu332*gtu22*PDstandardNth1gt23 - - 2*dgtu322*gtu32*PDstandardNth1gt23 - dgtu222*gtu33*PDstandardNth1gt23 - dgtu332*gtu32*PDstandardNth1gt33 - - dgtu322*gtu33*PDstandardNth1gt33 - PDstandardNth12gt23*SQR(gtu32); - - ddgtu1113 = -2*(gtu11*gtu21*PDstandardNth13gt12 + gtu11*gtu31*PDstandardNth13gt13 + gtu21*gtu31*PDstandardNth13gt23 + - dgtu113*gtu11*PDstandardNth1gt11 + dgtu213*gtu11*PDstandardNth1gt12 + dgtu113*gtu21*PDstandardNth1gt12 + - dgtu313*gtu11*PDstandardNth1gt13 + dgtu113*gtu31*PDstandardNth1gt13 + dgtu213*gtu21*PDstandardNth1gt22 + - dgtu313*gtu21*PDstandardNth1gt23 + dgtu213*gtu31*PDstandardNth1gt23 + dgtu313*gtu31*PDstandardNth1gt33) - - PDstandardNth13gt11*SQR(gtu11) - PDstandardNth13gt22*SQR(gtu21) - PDstandardNth13gt33*SQR(gtu31); - - ddgtu2113 = -(gtu11*gtu21*PDstandardNth13gt11) - gtu11*gtu22*PDstandardNth13gt12 - gtu21*gtu31*PDstandardNth13gt13 - - gtu11*gtu32*PDstandardNth13gt13 - gtu21*gtu22*PDstandardNth13gt22 - gtu22*gtu31*PDstandardNth13gt23 - - gtu21*gtu32*PDstandardNth13gt23 - gtu31*gtu32*PDstandardNth13gt33 - dgtu213*gtu11*PDstandardNth1gt11 - - dgtu113*gtu21*PDstandardNth1gt11 - dgtu223*gtu11*PDstandardNth1gt12 - 2*dgtu213*gtu21*PDstandardNth1gt12 - - dgtu113*gtu22*PDstandardNth1gt12 - dgtu323*gtu11*PDstandardNth1gt13 - dgtu313*gtu21*PDstandardNth1gt13 - - dgtu213*gtu31*PDstandardNth1gt13 - dgtu113*gtu32*PDstandardNth1gt13 - dgtu223*gtu21*PDstandardNth1gt22 - - dgtu213*gtu22*PDstandardNth1gt22 - dgtu323*gtu21*PDstandardNth1gt23 - dgtu313*gtu22*PDstandardNth1gt23 - - dgtu223*gtu31*PDstandardNth1gt23 - dgtu213*gtu32*PDstandardNth1gt23 - dgtu323*gtu31*PDstandardNth1gt33 - - dgtu313*gtu32*PDstandardNth1gt33 - PDstandardNth13gt12*SQR(gtu21); - - ddgtu3113 = -(gtu11*gtu31*PDstandardNth13gt11) - gtu21*gtu31*PDstandardNth13gt12 - gtu11*gtu32*PDstandardNth13gt12 - - gtu11*gtu33*PDstandardNth13gt13 - gtu21*gtu32*PDstandardNth13gt22 - gtu31*gtu32*PDstandardNth13gt23 - - gtu21*gtu33*PDstandardNth13gt23 - gtu31*gtu33*PDstandardNth13gt33 - dgtu313*gtu11*PDstandardNth1gt11 - - dgtu113*gtu31*PDstandardNth1gt11 - dgtu323*gtu11*PDstandardNth1gt12 - dgtu313*gtu21*PDstandardNth1gt12 - - dgtu213*gtu31*PDstandardNth1gt12 - dgtu113*gtu32*PDstandardNth1gt12 - dgtu333*gtu11*PDstandardNth1gt13 - - 2*dgtu313*gtu31*PDstandardNth1gt13 - dgtu113*gtu33*PDstandardNth1gt13 - dgtu323*gtu21*PDstandardNth1gt22 - - dgtu213*gtu32*PDstandardNth1gt22 - dgtu333*gtu21*PDstandardNth1gt23 - dgtu323*gtu31*PDstandardNth1gt23 - - dgtu313*gtu32*PDstandardNth1gt23 - dgtu213*gtu33*PDstandardNth1gt23 - dgtu333*gtu31*PDstandardNth1gt33 - - dgtu313*gtu33*PDstandardNth1gt33 - PDstandardNth13gt13*SQR(gtu31); - - ddgtu3213 = -(gtu21*gtu31*PDstandardNth13gt11) - gtu22*gtu31*PDstandardNth13gt12 - gtu21*gtu32*PDstandardNth13gt12 - - gtu31*gtu32*PDstandardNth13gt13 - gtu21*gtu33*PDstandardNth13gt13 - gtu22*gtu32*PDstandardNth13gt22 - - gtu22*gtu33*PDstandardNth13gt23 - gtu32*gtu33*PDstandardNth13gt33 - dgtu313*gtu21*PDstandardNth1gt11 - - dgtu213*gtu31*PDstandardNth1gt11 - dgtu323*gtu21*PDstandardNth1gt12 - dgtu313*gtu22*PDstandardNth1gt12 - - dgtu223*gtu31*PDstandardNth1gt12 - dgtu213*gtu32*PDstandardNth1gt12 - dgtu333*gtu21*PDstandardNth1gt13 - - dgtu323*gtu31*PDstandardNth1gt13 - dgtu313*gtu32*PDstandardNth1gt13 - dgtu213*gtu33*PDstandardNth1gt13 - - dgtu323*gtu22*PDstandardNth1gt22 - dgtu223*gtu32*PDstandardNth1gt22 - dgtu333*gtu22*PDstandardNth1gt23 - - 2*dgtu323*gtu32*PDstandardNth1gt23 - dgtu223*gtu33*PDstandardNth1gt23 - dgtu333*gtu32*PDstandardNth1gt33 - - dgtu323*gtu33*PDstandardNth1gt33 - PDstandardNth13gt23*SQR(gtu32); - - ddgtu3313 = -2*(gtu31*gtu32*PDstandardNth13gt12 + gtu31*gtu33*PDstandardNth13gt13 + gtu32*gtu33*PDstandardNth13gt23 + - dgtu313*gtu31*PDstandardNth1gt11 + dgtu323*gtu31*PDstandardNth1gt12 + dgtu313*gtu32*PDstandardNth1gt12 + - dgtu333*gtu31*PDstandardNth1gt13 + dgtu313*gtu33*PDstandardNth1gt13 + dgtu323*gtu32*PDstandardNth1gt22 + - dgtu333*gtu32*PDstandardNth1gt23 + dgtu323*gtu33*PDstandardNth1gt23 + dgtu333*gtu33*PDstandardNth1gt33) - - PDstandardNth13gt11*SQR(gtu31) - PDstandardNth13gt22*SQR(gtu32) - PDstandardNth13gt33*SQR(gtu33); - - ddgtu2122 = -(gtu11*gtu21*PDstandardNth22gt11) - gtu11*gtu22*PDstandardNth22gt12 - gtu21*gtu31*PDstandardNth22gt13 - - gtu11*gtu32*PDstandardNth22gt13 - gtu21*gtu22*PDstandardNth22gt22 - gtu22*gtu31*PDstandardNth22gt23 - - gtu21*gtu32*PDstandardNth22gt23 - gtu31*gtu32*PDstandardNth22gt33 - dgtu212*gtu11*PDstandardNth2gt11 - - dgtu112*gtu21*PDstandardNth2gt11 - dgtu222*gtu11*PDstandardNth2gt12 - 2*dgtu212*gtu21*PDstandardNth2gt12 - - dgtu112*gtu22*PDstandardNth2gt12 - dgtu322*gtu11*PDstandardNth2gt13 - dgtu312*gtu21*PDstandardNth2gt13 - - dgtu212*gtu31*PDstandardNth2gt13 - dgtu112*gtu32*PDstandardNth2gt13 - dgtu222*gtu21*PDstandardNth2gt22 - - dgtu212*gtu22*PDstandardNth2gt22 - dgtu322*gtu21*PDstandardNth2gt23 - dgtu312*gtu22*PDstandardNth2gt23 - - dgtu222*gtu31*PDstandardNth2gt23 - dgtu212*gtu32*PDstandardNth2gt23 - dgtu322*gtu31*PDstandardNth2gt33 - - dgtu312*gtu32*PDstandardNth2gt33 - PDstandardNth22gt12*SQR(gtu21); - - ddgtu2222 = -2*(gtu21*gtu22*PDstandardNth22gt12 + gtu21*gtu32*PDstandardNth22gt13 + gtu22*gtu32*PDstandardNth22gt23 + - dgtu212*gtu21*PDstandardNth2gt11 + dgtu222*gtu21*PDstandardNth2gt12 + dgtu212*gtu22*PDstandardNth2gt12 + - dgtu322*gtu21*PDstandardNth2gt13 + dgtu212*gtu32*PDstandardNth2gt13 + dgtu222*gtu22*PDstandardNth2gt22 + - dgtu322*gtu22*PDstandardNth2gt23 + dgtu222*gtu32*PDstandardNth2gt23 + dgtu322*gtu32*PDstandardNth2gt33) - - PDstandardNth22gt11*SQR(gtu21) - PDstandardNth22gt22*SQR(gtu22) - PDstandardNth22gt33*SQR(gtu32); - - ddgtu3222 = -(gtu21*gtu31*PDstandardNth22gt11) - gtu22*gtu31*PDstandardNth22gt12 - gtu21*gtu32*PDstandardNth22gt12 - - gtu31*gtu32*PDstandardNth22gt13 - gtu21*gtu33*PDstandardNth22gt13 - gtu22*gtu32*PDstandardNth22gt22 - - gtu22*gtu33*PDstandardNth22gt23 - gtu32*gtu33*PDstandardNth22gt33 - dgtu312*gtu21*PDstandardNth2gt11 - - dgtu212*gtu31*PDstandardNth2gt11 - dgtu322*gtu21*PDstandardNth2gt12 - dgtu312*gtu22*PDstandardNth2gt12 - - dgtu222*gtu31*PDstandardNth2gt12 - dgtu212*gtu32*PDstandardNth2gt12 - dgtu332*gtu21*PDstandardNth2gt13 - - dgtu322*gtu31*PDstandardNth2gt13 - dgtu312*gtu32*PDstandardNth2gt13 - dgtu212*gtu33*PDstandardNth2gt13 - - dgtu322*gtu22*PDstandardNth2gt22 - dgtu222*gtu32*PDstandardNth2gt22 - dgtu332*gtu22*PDstandardNth2gt23 - - 2*dgtu322*gtu32*PDstandardNth2gt23 - dgtu222*gtu33*PDstandardNth2gt23 - dgtu332*gtu32*PDstandardNth2gt33 - - dgtu322*gtu33*PDstandardNth2gt33 - PDstandardNth22gt23*SQR(gtu32); - - ddgtu2123 = -(gtu11*gtu21*PDstandardNth23gt11) - gtu11*gtu22*PDstandardNth23gt12 - gtu21*gtu31*PDstandardNth23gt13 - - gtu11*gtu32*PDstandardNth23gt13 - gtu21*gtu22*PDstandardNth23gt22 - gtu22*gtu31*PDstandardNth23gt23 - - gtu21*gtu32*PDstandardNth23gt23 - gtu31*gtu32*PDstandardNth23gt33 - dgtu213*gtu11*PDstandardNth2gt11 - - dgtu113*gtu21*PDstandardNth2gt11 - dgtu223*gtu11*PDstandardNth2gt12 - 2*dgtu213*gtu21*PDstandardNth2gt12 - - dgtu113*gtu22*PDstandardNth2gt12 - dgtu323*gtu11*PDstandardNth2gt13 - dgtu313*gtu21*PDstandardNth2gt13 - - dgtu213*gtu31*PDstandardNth2gt13 - dgtu113*gtu32*PDstandardNth2gt13 - dgtu223*gtu21*PDstandardNth2gt22 - - dgtu213*gtu22*PDstandardNth2gt22 - dgtu323*gtu21*PDstandardNth2gt23 - dgtu313*gtu22*PDstandardNth2gt23 - - dgtu223*gtu31*PDstandardNth2gt23 - dgtu213*gtu32*PDstandardNth2gt23 - dgtu323*gtu31*PDstandardNth2gt33 - - dgtu313*gtu32*PDstandardNth2gt33 - PDstandardNth23gt12*SQR(gtu21); - - ddgtu3123 = -(gtu11*gtu31*PDstandardNth23gt11) - gtu21*gtu31*PDstandardNth23gt12 - gtu11*gtu32*PDstandardNth23gt12 - - gtu11*gtu33*PDstandardNth23gt13 - gtu21*gtu32*PDstandardNth23gt22 - gtu31*gtu32*PDstandardNth23gt23 - - gtu21*gtu33*PDstandardNth23gt23 - gtu31*gtu33*PDstandardNth23gt33 - dgtu313*gtu11*PDstandardNth2gt11 - - dgtu113*gtu31*PDstandardNth2gt11 - dgtu323*gtu11*PDstandardNth2gt12 - dgtu313*gtu21*PDstandardNth2gt12 - - dgtu213*gtu31*PDstandardNth2gt12 - dgtu113*gtu32*PDstandardNth2gt12 - dgtu333*gtu11*PDstandardNth2gt13 - - 2*dgtu313*gtu31*PDstandardNth2gt13 - dgtu113*gtu33*PDstandardNth2gt13 - dgtu323*gtu21*PDstandardNth2gt22 - - dgtu213*gtu32*PDstandardNth2gt22 - dgtu333*gtu21*PDstandardNth2gt23 - dgtu323*gtu31*PDstandardNth2gt23 - - dgtu313*gtu32*PDstandardNth2gt23 - dgtu213*gtu33*PDstandardNth2gt23 - dgtu333*gtu31*PDstandardNth2gt33 - - dgtu313*gtu33*PDstandardNth2gt33 - PDstandardNth23gt13*SQR(gtu31); - - ddgtu2223 = -2*(gtu21*gtu22*PDstandardNth23gt12 + gtu21*gtu32*PDstandardNth23gt13 + gtu22*gtu32*PDstandardNth23gt23 + - dgtu213*gtu21*PDstandardNth2gt11 + dgtu223*gtu21*PDstandardNth2gt12 + dgtu213*gtu22*PDstandardNth2gt12 + - dgtu323*gtu21*PDstandardNth2gt13 + dgtu213*gtu32*PDstandardNth2gt13 + dgtu223*gtu22*PDstandardNth2gt22 + - dgtu323*gtu22*PDstandardNth2gt23 + dgtu223*gtu32*PDstandardNth2gt23 + dgtu323*gtu32*PDstandardNth2gt33) - - PDstandardNth23gt11*SQR(gtu21) - PDstandardNth23gt22*SQR(gtu22) - PDstandardNth23gt33*SQR(gtu32); - - ddgtu3223 = -(gtu21*gtu31*PDstandardNth23gt11) - gtu22*gtu31*PDstandardNth23gt12 - gtu21*gtu32*PDstandardNth23gt12 - - gtu31*gtu32*PDstandardNth23gt13 - gtu21*gtu33*PDstandardNth23gt13 - gtu22*gtu32*PDstandardNth23gt22 - - gtu22*gtu33*PDstandardNth23gt23 - gtu32*gtu33*PDstandardNth23gt33 - dgtu313*gtu21*PDstandardNth2gt11 - - dgtu213*gtu31*PDstandardNth2gt11 - dgtu323*gtu21*PDstandardNth2gt12 - dgtu313*gtu22*PDstandardNth2gt12 - - dgtu223*gtu31*PDstandardNth2gt12 - dgtu213*gtu32*PDstandardNth2gt12 - dgtu333*gtu21*PDstandardNth2gt13 - - dgtu323*gtu31*PDstandardNth2gt13 - dgtu313*gtu32*PDstandardNth2gt13 - dgtu213*gtu33*PDstandardNth2gt13 - - dgtu323*gtu22*PDstandardNth2gt22 - dgtu223*gtu32*PDstandardNth2gt22 - dgtu333*gtu22*PDstandardNth2gt23 - - 2*dgtu323*gtu32*PDstandardNth2gt23 - dgtu223*gtu33*PDstandardNth2gt23 - dgtu333*gtu32*PDstandardNth2gt33 - - dgtu323*gtu33*PDstandardNth2gt33 - PDstandardNth23gt23*SQR(gtu32); - - ddgtu3323 = -2*(gtu31*gtu32*PDstandardNth23gt12 + gtu31*gtu33*PDstandardNth23gt13 + gtu32*gtu33*PDstandardNth23gt23 + - dgtu313*gtu31*PDstandardNth2gt11 + dgtu323*gtu31*PDstandardNth2gt12 + dgtu313*gtu32*PDstandardNth2gt12 + - dgtu333*gtu31*PDstandardNth2gt13 + dgtu313*gtu33*PDstandardNth2gt13 + dgtu323*gtu32*PDstandardNth2gt22 + - dgtu333*gtu32*PDstandardNth2gt23 + dgtu323*gtu33*PDstandardNth2gt23 + dgtu333*gtu33*PDstandardNth2gt33) - - PDstandardNth23gt11*SQR(gtu31) - PDstandardNth23gt22*SQR(gtu32) - PDstandardNth23gt33*SQR(gtu33); - - ddgtu3133 = -(gtu11*gtu31*PDstandardNth33gt11) - gtu21*gtu31*PDstandardNth33gt12 - gtu11*gtu32*PDstandardNth33gt12 - - gtu11*gtu33*PDstandardNth33gt13 - gtu21*gtu32*PDstandardNth33gt22 - gtu31*gtu32*PDstandardNth33gt23 - - gtu21*gtu33*PDstandardNth33gt23 - gtu31*gtu33*PDstandardNth33gt33 - dgtu313*gtu11*PDstandardNth3gt11 - - dgtu113*gtu31*PDstandardNth3gt11 - dgtu323*gtu11*PDstandardNth3gt12 - dgtu313*gtu21*PDstandardNth3gt12 - - dgtu213*gtu31*PDstandardNth3gt12 - dgtu113*gtu32*PDstandardNth3gt12 - dgtu333*gtu11*PDstandardNth3gt13 - - 2*dgtu313*gtu31*PDstandardNth3gt13 - dgtu113*gtu33*PDstandardNth3gt13 - dgtu323*gtu21*PDstandardNth3gt22 - - dgtu213*gtu32*PDstandardNth3gt22 - dgtu333*gtu21*PDstandardNth3gt23 - dgtu323*gtu31*PDstandardNth3gt23 - - dgtu313*gtu32*PDstandardNth3gt23 - dgtu213*gtu33*PDstandardNth3gt23 - dgtu333*gtu31*PDstandardNth3gt33 - - dgtu313*gtu33*PDstandardNth3gt33 - PDstandardNth33gt13*SQR(gtu31); - - ddgtu3233 = -(gtu21*gtu31*PDstandardNth33gt11) - gtu22*gtu31*PDstandardNth33gt12 - gtu21*gtu32*PDstandardNth33gt12 - - gtu31*gtu32*PDstandardNth33gt13 - gtu21*gtu33*PDstandardNth33gt13 - gtu22*gtu32*PDstandardNth33gt22 - - gtu22*gtu33*PDstandardNth33gt23 - gtu32*gtu33*PDstandardNth33gt33 - dgtu313*gtu21*PDstandardNth3gt11 - - dgtu213*gtu31*PDstandardNth3gt11 - dgtu323*gtu21*PDstandardNth3gt12 - dgtu313*gtu22*PDstandardNth3gt12 - - dgtu223*gtu31*PDstandardNth3gt12 - dgtu213*gtu32*PDstandardNth3gt12 - dgtu333*gtu21*PDstandardNth3gt13 - - dgtu323*gtu31*PDstandardNth3gt13 - dgtu313*gtu32*PDstandardNth3gt13 - dgtu213*gtu33*PDstandardNth3gt13 - - dgtu323*gtu22*PDstandardNth3gt22 - dgtu223*gtu32*PDstandardNth3gt22 - dgtu333*gtu22*PDstandardNth3gt23 - - 2*dgtu323*gtu32*PDstandardNth3gt23 - dgtu223*gtu33*PDstandardNth3gt23 - dgtu333*gtu32*PDstandardNth3gt33 - - dgtu323*gtu33*PDstandardNth3gt33 - PDstandardNth33gt23*SQR(gtu32); - - ddgtu3333 = -2*(gtu31*gtu32*PDstandardNth33gt12 + gtu31*gtu33*PDstandardNth33gt13 + gtu32*gtu33*PDstandardNth33gt23 + - dgtu313*gtu31*PDstandardNth3gt11 + dgtu323*gtu31*PDstandardNth3gt12 + dgtu313*gtu32*PDstandardNth3gt12 + - dgtu333*gtu31*PDstandardNth3gt13 + dgtu313*gtu33*PDstandardNth3gt13 + dgtu323*gtu32*PDstandardNth3gt22 + - dgtu333*gtu32*PDstandardNth3gt23 + dgtu323*gtu33*PDstandardNth3gt23 + dgtu333*gtu33*PDstandardNth3gt33) - - PDstandardNth33gt11*SQR(gtu31) - PDstandardNth33gt22*SQR(gtu32) - PDstandardNth33gt33*SQR(gtu33); - Gt111 = khalf*(gtu11*PDstandardNth1gt11 + 2*(gtu21*PDstandardNth1gt12 + gtu31*PDstandardNth1gt13) - gtu21*PDstandardNth2gt11 - gtu31*PDstandardNth3gt11); @@ -1281,55 +1042,49 @@ void ML_BSSN_RHS_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REAL normal gt33L*ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3) + 2*(gt13L*PDstandardNth3beta1 + gt23L*PDstandardNth3beta2 + gt33L*PDstandardNth3beta3) + beta3L*PDstandardNth3gt33; - Xt1rhsL = kthird*(-3*(beta1L*(ddgtu1111 + ddgtu2112 + ddgtu3113) + beta2L*(ddgtu1112 + ddgtu2122 + ddgtu3123) + - beta3L*(ddgtu1113 + ddgtu2123 + ddgtu3133)) + 16*(gtu21*PDstandardNth12beta1 + gtu31*PDstandardNth13beta1) + - (7*dgtu111 + 4*(dgtu212 + dgtu313))*PDstandardNth1beta1 + - gtu11*(10*PDstandardNth11beta1 + 4*(PDstandardNth12beta2 + PDstandardNth13beta3) - 4*alphaL*PDstandardNth1trK) + - 12*gtu32*PDstandardNth23beta1 + (9*dgtu211 + 6*dgtu323)*PDstandardNth2beta1 + - (dgtu212 - 2*(dgtu111 + dgtu313))*PDstandardNth2beta2 + - 4*(gtu21*(PDstandardNth22beta2 + PDstandardNth23beta3) + gtu31*(PDstandardNth23beta2 + PDstandardNth33beta3)) - - 6*(Atu11*PDstandardNth1alpha + Atu21*PDstandardNth2alpha + Atu31*PDstandardNth3alpha) + - (9*dgtu311 + 6*dgtu333)*PDstandardNth3beta1 + - 6*(gtu22*PDstandardNth22beta1 + dgtu222*PDstandardNth2beta1 + gtu33*PDstandardNth33beta1 + - dgtu322*PDstandardNth3beta1) + 3*(dgtu112*PDstandardNth1beta2 + dgtu113*PDstandardNth1beta3 + - dgtu213*PDstandardNth2beta3 + dgtu312*PDstandardNth3beta2) + - (-2*(dgtu111 + dgtu212) + dgtu313)*PDstandardNth3beta3 + - alphaL*(12*(Atu21*Gt112 + Atu31*Gt113 + Atu32*Gt123) + 6*(Atu11*Gt111 + Atu22*Gt122 + Atu33*Gt133) + - 36*(Atu11*PDstandardNth1phi + Atu21*PDstandardNth2phi + Atu31*PDstandardNth3phi) - - 4*(gtu21*PDstandardNth2trK + gtu31*PDstandardNth3trK))); - - Xt2rhsL = kthird*(-3*(beta1L*(ddgtu2111 + ddgtu2212 + ddgtu3213) + beta2L*(ddgtu2112 + ddgtu2222 + ddgtu3223) + - beta3L*(ddgtu2113 + ddgtu2223 + ddgtu3233)) + 12*gtu31*PDstandardNth13beta2 + - (dgtu211 - 2*(dgtu222 + dgtu323))*PDstandardNth1beta1 + (9*dgtu212 + 6*dgtu313)*PDstandardNth1beta2 + - gtu21*(16*PDstandardNth12beta2 + 4*PDstandardNth13beta3 - 4*alphaL*PDstandardNth1trK) + - (7*dgtu222 + 4*dgtu323)*PDstandardNth2beta2 + - 4*(gtu21*PDstandardNth11beta1 + gtu32*PDstandardNth13beta1 + - gtu22*(PDstandardNth12beta1 + PDstandardNth23beta3) + dgtu211*PDstandardNth2beta2) + - gtu22*(10*PDstandardNth22beta2 - 4*alphaL*PDstandardNth2trK) - - 6*(Atu21*PDstandardNth1alpha + Atu22*PDstandardNth2alpha + Atu32*PDstandardNth3alpha) + - 3*(dgtu213*PDstandardNth1beta3 + dgtu221*PDstandardNth2beta1 + dgtu223*PDstandardNth2beta3 + - dgtu321*PDstandardNth3beta1) + (9*dgtu322 + 6*dgtu333)*PDstandardNth3beta2 + - 6*(gtu11*PDstandardNth11beta2 + dgtu111*PDstandardNth1beta2 + gtu33*PDstandardNth33beta2 + - dgtu311*PDstandardNth3beta2) + (-2*(dgtu211 + dgtu222) + dgtu323)*PDstandardNth3beta3 + - alphaL*(12*(Atu21*Gt212 + Atu31*Gt213 + Atu32*Gt223) + 6*(Atu11*Gt211 + Atu22*Gt222 + Atu33*Gt233) + - 36*(Atu21*PDstandardNth1phi + Atu22*PDstandardNth2phi + Atu32*PDstandardNth3phi)) + - gtu32*(16*PDstandardNth23beta2 + 4*PDstandardNth33beta3 - 4*alphaL*PDstandardNth3trK)); - - Xt3rhsL = kthird*(-3*(beta1L*(ddgtu3111 + ddgtu3212 + ddgtu3313) + beta2L*(ddgtu3112 + ddgtu3222 + ddgtu3323) + - beta3L*(ddgtu3113 + ddgtu3223 + ddgtu3333)) + 12*gtu21*PDstandardNth12beta3 + - (dgtu311 - 2*(dgtu322 + dgtu333))*PDstandardNth1beta1 + (6*dgtu212 + 9*dgtu313)*PDstandardNth1beta3 + - gtu31*(16*PDstandardNth13beta3 - 4*alphaL*PDstandardNth1trK) + - (dgtu322 - 2*(dgtu311 + dgtu333))*PDstandardNth2beta2 + (6*dgtu222 + 9*dgtu323)*PDstandardNth2beta3 + - 6*(gtu11*PDstandardNth11beta3 + dgtu111*PDstandardNth1beta3 + gtu22*PDstandardNth22beta3 + - dgtu211*PDstandardNth2beta3) + gtu32*(16*PDstandardNth23beta3 - 4*alphaL*PDstandardNth2trK) - - 6*(Atu31*PDstandardNth1alpha + Atu32*PDstandardNth2alpha + Atu33*PDstandardNth3alpha) + - 3*(dgtu312*PDstandardNth1beta2 + dgtu321*PDstandardNth2beta1 + dgtu331*PDstandardNth3beta1 + - dgtu332*PDstandardNth3beta2) + (4*dgtu322 + 7*dgtu333)*PDstandardNth3beta3 + - 4*(gtu31*(PDstandardNth11beta1 + PDstandardNth12beta2) + gtu32*(PDstandardNth12beta1 + PDstandardNth22beta2) + - gtu33*(PDstandardNth13beta1 + PDstandardNth23beta2) + dgtu311*PDstandardNth3beta3) + - alphaL*(12*(Atu21*Gt312 + Atu31*Gt313 + Atu32*Gt323) + 6*(Atu11*Gt311 + Atu22*Gt322 + Atu33*Gt333) + - 36*(Atu31*PDstandardNth1phi + Atu32*PDstandardNth2phi + Atu33*PDstandardNth3phi)) + - gtu33*(10*PDstandardNth33beta3 - 4*alphaL*PDstandardNth3trK)); + Xt1rhsL = gtu11*PDstandardNth11beta1 + beta1L*PDstandardNth1Xt1 + gtu22*PDstandardNth22beta1 + + (dgtu211 + dgtu222 + dgtu323)*PDstandardNth2beta1 + beta2L*PDstandardNth2Xt1 + gtu33*PDstandardNth33beta1 + + kthird*(gtu11*(PDstandardNth11beta1 + PDstandardNth12beta2 + PDstandardNth13beta3) + + gtu21*(PDstandardNth12beta1 + PDstandardNth22beta2 + PDstandardNth23beta3) + + gtu31*(PDstandardNth13beta1 + PDstandardNth23beta2 + PDstandardNth33beta3)) - + 2*(Atu11*PDstandardNth1alpha + Atu21*PDstandardNth2alpha + Atu31*PDstandardNth3alpha) + + (dgtu311 + dgtu322 + dgtu333)*PDstandardNth3beta1 + + (dgtu111 + dgtu212 + dgtu313)*(PDstandardNth1beta1 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) + + 2*(gtu21*PDstandardNth12beta1 + gtu31*PDstandardNth13beta1 + gtu32*PDstandardNth23beta1 + + alphaL*(Atu11*Gt111 + Atu22*Gt122 + 2*(Atu21*Gt112 + Atu31*Gt113 + Atu32*Gt123) + Atu33*Gt133 + + 6*(Atu11*PDstandardNth1phi + Atu21*PDstandardNth2phi + Atu31*PDstandardNth3phi) - + ktwothird*(gtu11*PDstandardNth1trK + gtu21*PDstandardNth2trK + gtu31*PDstandardNth3trK))) + + beta3L*PDstandardNth3Xt1; + + Xt2rhsL = gtu11*PDstandardNth11beta2 + (dgtu111 + dgtu212 + dgtu313)*PDstandardNth1beta2 + beta1L*PDstandardNth1Xt2 + + gtu22*PDstandardNth22beta2 + beta2L*PDstandardNth2Xt2 + gtu33*PDstandardNth33beta2 + + kthird*(gtu21*(PDstandardNth11beta1 + PDstandardNth12beta2 + PDstandardNth13beta3) + + gtu22*(PDstandardNth12beta1 + PDstandardNth22beta2 + PDstandardNth23beta3) + + gtu32*(PDstandardNth13beta1 + PDstandardNth23beta2 + PDstandardNth33beta3)) - + 2*(Atu21*PDstandardNth1alpha + Atu22*PDstandardNth2alpha + Atu32*PDstandardNth3alpha) + + (dgtu311 + dgtu322 + dgtu333)*PDstandardNth3beta2 + + (dgtu211 + dgtu222 + dgtu323)*(PDstandardNth2beta2 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) + + 2*(gtu21*PDstandardNth12beta2 + gtu31*PDstandardNth13beta2 + gtu32*PDstandardNth23beta2 + + alphaL*(Atu11*Gt211 + Atu22*Gt222 + 2*(Atu21*Gt212 + Atu31*Gt213 + Atu32*Gt223) + Atu33*Gt233 + + 6*(Atu21*PDstandardNth1phi + Atu22*PDstandardNth2phi + Atu32*PDstandardNth3phi) - + ktwothird*(gtu21*PDstandardNth1trK + gtu22*PDstandardNth2trK + gtu32*PDstandardNth3trK))) + + beta3L*PDstandardNth3Xt2; + + Xt3rhsL = gtu11*PDstandardNth11beta3 + (dgtu111 + dgtu212 + dgtu313)*PDstandardNth1beta3 + beta1L*PDstandardNth1Xt3 + + gtu22*PDstandardNth22beta3 + (dgtu211 + dgtu222 + dgtu323)*PDstandardNth2beta3 + beta2L*PDstandardNth2Xt3 + + gtu33*PDstandardNth33beta3 + kthird*(gtu31*(PDstandardNth11beta1 + PDstandardNth12beta2 + PDstandardNth13beta3) + + gtu32*(PDstandardNth12beta1 + PDstandardNth22beta2 + PDstandardNth23beta3) + + gtu33*(PDstandardNth13beta1 + PDstandardNth23beta2 + PDstandardNth33beta3)) - + 2*(Atu31*PDstandardNth1alpha + Atu32*PDstandardNth2alpha + Atu33*PDstandardNth3alpha) + + (dgtu311 + dgtu322 + dgtu333)*(PDstandardNth3beta3 - + ktwothird*(PDstandardNth1beta1 + PDstandardNth2beta2 + PDstandardNth3beta3)) + + 2*(gtu21*PDstandardNth12beta3 + gtu31*PDstandardNth13beta3 + gtu32*PDstandardNth23beta3 + + alphaL*(Atu11*Gt311 + Atu22*Gt322 + 2*(Atu21*Gt312 + Atu31*Gt313 + Atu32*Gt323) + Atu33*Gt333 + + 6*(Atu31*PDstandardNth1phi + Atu32*PDstandardNth2phi + Atu33*PDstandardNth3phi) - + ktwothird*(gtu31*PDstandardNth1trK + gtu32*PDstandardNth2trK + gtu33*PDstandardNth3trK))) + + beta3L*PDstandardNth3Xt3; trKrhsL = -(gu11*PDstandardNth11alpha) - 2*gu21*PDstandardNth12alpha - 2*gu31*PDstandardNth13alpha + (G111*gu11 + 2*G112*gu21 + G122*gu22 + 2*G113*gu31 + 2*G123*gu32 + G133*gu33)*PDstandardNth1alpha + diff --git a/m/McLachlan.m b/m/McLachlan.m index 8ace4a8..246dd80 100644 --- a/m/McLachlan.m +++ b/m/McLachlan.m @@ -454,7 +454,7 @@ evolCalcBSSN = dot[gt[la,lb]] -> - 2 alpha At[la,lb] + Lie[gt[la,lb], beta] - (2/3) gt[la,lb] PD[beta[uc],lc], (* PRD 62, 044034 (2000), eqn. (20) *) - dot[Xt[ui]] -> - 2 Atu[ui,uj] PD[alpha,lj] +(* dot[Xt[ui]] -> - 2 Atu[ui,uj] PD[alpha,lj] + 2 alpha (+ Gt[ui,lj,lk] Atu[uk,uj] - (2/3) gtu[ui,uj] PD[trK,lj] + 6 Atu[ui,uj] PD[phi,lj]) @@ -465,17 +465,17 @@ evolCalcBSSN = + gtu[um,uj] PD[beta[ui],lm,lj] + gtu[um,ui] PD[beta[uj],lm,lj]) + (2/3) (+ dgtu[ui,uj,lj] PD[beta[ul],ll] - + gtu[ui,uj] PD[beta[ul],ll,lj])), - -(* dot[Xt[ui]] -> - 2 Atu[ui,uj] PD[alpha,lj] + + gtu[ui,uj] PD[beta[ul],ll,lj])), *) + (* PRD 67 084023 (2003), eqn (26) *) + dot[Xt[ui]] -> - 2 Atu[ui,uj] PD[alpha,lj] + 2 alpha (+ Gt[ui,lj,lk] Atu[uk,uj] - (2/3) gtu[ui,uj] PD[trK,lj] + 6 Atu[ui,uj] PD[phi,lj]) + gtu[uj,ul] PD[beta[ui],lj,ll] + (1/3) gtu[ui,uj] PD[beta[ul],lj,ll] + beta[uj] PD[Xt[ui],lj] - + PD[gtu[ul,uj],ll] PD[beta[ui],lj] - - (2/3) PD[gtu[ui,uj],lj] PD[beta[ul],ll], *) + + dgtu[ul,uj,ll] PD[beta[ui],lj] + - (2/3) dgtu[ui,uj,lj] PD[beta[ul],ll], (* PRD 62, 044034 (2000), eqn. (11) *) dot[trK] -> - gu[ua,ub] CD[alpha,la,lb] |