diff options
| author | Erik Schnetter <schnetter@cct.lsu.edu> | 2009-04-28 13:38:57 -0500 |
|---|---|---|
| committer | Erik Schnetter <schnetter@cct.lsu.edu> | 2009-04-28 13:38:57 -0500 |
| commit | 10ee905e681cedb97d8a2e4d4f7b4445d74ee7bc (patch) | |
| tree | 21cf8b52fb83a88acf0b72088244a8e881092560 /ML_ADM | |
| parent | 51a068080ddd36d89943b754c46fd7b0e265c1ff (diff) | |
Regenerate code
Diffstat (limited to 'ML_ADM')
| -rw-r--r-- | ML_ADM/src/ML_ADM_RHS.c | 368 | ||||
| -rw-r--r-- | ML_ADM/src/ML_ADM_constraints.c | 380 |
2 files changed, 239 insertions, 509 deletions
diff --git a/ML_ADM/src/ML_ADM_RHS.c b/ML_ADM/src/ML_ADM_RHS.c index 586551f..5f0f51c 100644 --- a/ML_ADM/src/ML_ADM_RHS.c +++ b/ML_ADM/src/ML_ADM_RHS.c @@ -297,195 +297,118 @@ void ML_ADM_RHS_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT cons /* Precompute derivatives (old style) */ /* Calculate temporaries and grid functions */ - CCTK_REAL const T1000001 = SQR(g23L); + detg = 2*g12L*g13L*g23L + g33L*(g11L*g22L - SQR(g12L)) - g22L*SQR(g13L) - g11L*SQR(g23L); - CCTK_REAL const T1000003 = g13L*g23L; + gu11 = INV(detg)*(g22L*g33L - SQR(g23L)); - CCTK_REAL const T1000004 = -(g12L*g33L); + gu12 = (g13L*g23L - g12L*g33L)*INV(detg); - CCTK_REAL const T1000007 = SQR(g13L); + gu13 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - CCTK_REAL const T1000008 = -(g13L*g22L); + gu21 = (g13L*g23L - g12L*g33L)*INV(detg); - CCTK_REAL const T1000009 = g12L*g23L; + gu22 = INV(detg)*(g11L*g33L - SQR(g13L)); - CCTK_REAL const T1000012 = g12L*g13L; + gu23 = (g12L*g13L - g11L*g23L)*INV(detg); - CCTK_REAL const T1000013 = -(g11L*g23L); + gu31 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - CCTK_REAL const T1000016 = SQR(g12L); + gu32 = (g12L*g13L - g11L*g23L)*INV(detg); - CCTK_REAL const T1000017 = -PDstandardNth3g12; + gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - CCTK_REAL const T1000019 = -PDstandardNth2g13; + G111 = khalf*(gu11*PDstandardNth1g11 + 2*(gu12*PDstandardNth1g12 + gu13*PDstandardNth1g13) - gu12*PDstandardNth2g11 - + gu13*PDstandardNth3g11); - CCTK_REAL const T1000021 = -PDstandardNth1g23; + G211 = khalf*(gu21*PDstandardNth1g11 + 2*(gu22*PDstandardNth1g12 + gu23*PDstandardNth1g13) - gu22*PDstandardNth2g11 - + gu23*PDstandardNth3g11); - CCTK_REAL const T1000023 = -PDstandardNth11g23; + G311 = khalf*(gu31*PDstandardNth1g11 + 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - gu32*PDstandardNth2g11 - + gu33*PDstandardNth3g11); - CCTK_REAL const T1000024 = -PDstandardNth23g11; + G112 = khalf*(gu12*PDstandardNth1g22 + gu11*PDstandardNth2g11 + + gu13*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000029 = -2*PDstandardNth12g12; + G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + + gu23*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000031 = -PDstandardNth13g22; + G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + + gu33*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000032 = -PDstandardNth22g13; + G113 = khalf*(gu13*PDstandardNth1g33 + gu11*PDstandardNth3g11 + + gu12*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000034 = -2*PDstandardNth13g13; + G213 = khalf*(gu23*PDstandardNth1g33 + gu21*PDstandardNth3g11 + + gu22*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000036 = -PDstandardNth12g33; + G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + + gu32*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000037 = -PDstandardNth33g12; + G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu12*PDstandardNth2g22 + + gu13*(2*PDstandardNth2g23 - PDstandardNth3g22)); - CCTK_REAL const T1000039 = -2*PDstandardNth23g23; + G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu22*PDstandardNth2g22 + + gu23*(2*PDstandardNth2g23 - PDstandardNth3g22)); - g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandardNth1beta1 + - g12L*PDstandardNth1beta2 + g13L*PDstandardNth1beta3) + - beta1L*PDstandardNth1g11 + beta2L*PDstandardNth2g11 + - beta3L*PDstandardNth3g11; + G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu32*PDstandardNth2g22 + + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - g12rhsL = -2*alphaL*K12L + g22L*PDstandardNth1beta2 + - g23L*PDstandardNth1beta3 + beta1L*PDstandardNth1g12 + - g11L*PDstandardNth2beta1 + g12L* - (PDstandardNth1beta1 + PDstandardNth2beta2) + g13L*PDstandardNth2beta3 + - beta2L*PDstandardNth2g12 + beta3L*PDstandardNth3g12; - - g13rhsL = -2*alphaL*K13L + g23L*PDstandardNth1beta2 + - g33L*PDstandardNth1beta3 + beta1L*PDstandardNth1g13 + - beta2L*PDstandardNth2g13 + g11L*PDstandardNth3beta1 + - g12L*PDstandardNth3beta2 + g13L* - (PDstandardNth1beta1 + PDstandardNth3beta3) + beta3L*PDstandardNth3g13; - - g22rhsL = -2*alphaL*K22L + beta1L*PDstandardNth1g22 + - 2*(g12L*PDstandardNth2beta1 + g22L*PDstandardNth2beta2 + - g23L*PDstandardNth2beta3) + beta2L*PDstandardNth2g22 + - beta3L*PDstandardNth3g22; - - g23rhsL = -2*alphaL*K23L + beta1L*PDstandardNth1g23 + - g13L*PDstandardNth2beta1 + g33L*PDstandardNth2beta3 + - beta2L*PDstandardNth2g23 + g12L*PDstandardNth3beta1 + - g22L*PDstandardNth3beta2 + g23L* - (PDstandardNth2beta2 + PDstandardNth3beta3) + beta3L*PDstandardNth3g23; - - g33rhsL = -2*alphaL*K33L + beta1L*PDstandardNth1g33 + - beta2L*PDstandardNth2g33 + 2* - (g13L*PDstandardNth3beta1 + g23L*PDstandardNth3beta2 + - g33L*PDstandardNth3beta3) + beta3L*PDstandardNth3g33; - - alpharhsL = 0; - - beta1rhsL = 0; - - beta2rhsL = 0; - - beta3rhsL = 0; - - CCTK_REAL const T1000005 = T1000003 + T1000004; - - CCTK_REAL const T1000010 = T1000008 + T1000009; - - CCTK_REAL const T1000014 = T1000012 + T1000013; - - CCTK_REAL const T1000018 = PDstandardNth1g23 + PDstandardNth2g13 + T1000017; - - CCTK_REAL const T1000020 = PDstandardNth1g23 + PDstandardNth3g12 + T1000019; - - CCTK_REAL const T1000022 = PDstandardNth2g13 + PDstandardNth3g12 + T1000021; - - CCTK_REAL const T1000025 = - PDstandardNth12g13 + PDstandardNth13g12 + T1000023 + T1000024; - - CCTK_REAL const T1000030 = PDstandardNth11g22 + PDstandardNth22g11 + T1000029; - - CCTK_REAL const T1000033 = - PDstandardNth12g23 + PDstandardNth23g12 + T1000031 + T1000032; - - CCTK_REAL const T1000035 = PDstandardNth11g33 + PDstandardNth33g11 + T1000034; - - CCTK_REAL const T1000038 = - PDstandardNth13g23 + PDstandardNth23g13 + T1000036 + T1000037; - - CCTK_REAL const T1000040 = PDstandardNth22g33 + PDstandardNth33g22 + T1000039; - - detg = 2*g12L*g13L*g23L + g11L*(g22L*g33L - T1000001) - g22L*T1000007 - - g33L*T1000016; - - CCTK_REAL const T1000002 = INV(detg); - - CCTK_REAL const T1000006 = T1000002*T1000005; - - CCTK_REAL const T1000011 = T1000002*T1000010; - - CCTK_REAL const T1000015 = T1000002*T1000014; - - gu11 = (g22L*g33L - T1000001)*T1000002; - - gu22 = T1000002*(g11L*g33L - T1000007); - - gu33 = T1000002*(g11L*g22L - T1000016); - - gu12 = T1000006; - - gu13 = T1000011; - - gu21 = T1000006; + G123 = khalf*(gu13*PDstandardNth2g33 + gu11*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu12*PDstandardNth3g22); - gu23 = T1000015; + G223 = khalf*(gu23*PDstandardNth2g33 + gu21*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu22*PDstandardNth3g22); - gu31 = T1000011; + G323 = khalf*(gu33*PDstandardNth2g33 + gu31*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu32*PDstandardNth3g22); - gu32 = T1000015; + G133 = khalf*(-(gu11*PDstandardNth1g33) - gu12*PDstandardNth2g33 + 2*gu11*PDstandardNth3g13 + + 2*gu12*PDstandardNth3g23 + gu13*PDstandardNth3g33); - G111 = khalf*(gu11*PDstandardNth1g11 + - 2*(gu12*PDstandardNth1g12 + gu13*PDstandardNth1g13) - - gu12*PDstandardNth2g11 - gu13*PDstandardNth3g11); + G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + 2*gu21*PDstandardNth3g13 + + 2*gu22*PDstandardNth3g23 + gu23*PDstandardNth3g33); - G211 = khalf*(gu21*PDstandardNth1g11 + - 2*(gu22*PDstandardNth1g12 + gu23*PDstandardNth1g13) - - gu22*PDstandardNth2g11 - gu23*PDstandardNth3g11); + G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + 2*gu31*PDstandardNth3g13 + + 2*gu32*PDstandardNth3g23 + gu33*PDstandardNth3g33); - G311 = khalf*(gu31*PDstandardNth1g11 + - 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - - gu32*PDstandardNth2g11 - gu33*PDstandardNth3g11); + R11 = 2*(G112*G211 + G113*G311 + G213*G312) - G111*(G111 + G212 + G313) - G211*(G112 + G222 + G323) - + G311*(G113 + G223 + G333) + khalf*(-(gu22*(PDstandardNth11g22 - 2*PDstandardNth12g12 + PDstandardNth22g11)) + + gu23*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu32*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) - + gu33*(PDstandardNth11g33 - 2*PDstandardNth13g13 + PDstandardNth33g11)) + SQR(G111) + SQR(G212) + SQR(G313); - G112 = khalf*(gu12*PDstandardNth1g22 + gu11*PDstandardNth2g11 + gu13*T1000018); - - G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + gu23*T1000018); - - G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + gu33*T1000018); - - G113 = khalf*(gu13*PDstandardNth1g33 + gu11*PDstandardNth3g11 + gu12*T1000020); - - G213 = khalf*(gu23*PDstandardNth1g33 + gu21*PDstandardNth3g11 + gu22*T1000020); - - G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + gu32*T1000020); - - G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu12*PDstandardNth2g22 + gu13*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu22*PDstandardNth2g22 + gu23*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu32*PDstandardNth2g22 + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G123 = khalf*(gu13*PDstandardNth2g33 + gu12*PDstandardNth3g22 + gu11*T1000022); - - G223 = khalf*(gu23*PDstandardNth2g33 + gu22*PDstandardNth3g22 + gu21*T1000022); - - G323 = khalf*(gu33*PDstandardNth2g33 + gu32*PDstandardNth3g22 + gu31*T1000022); - - G133 = khalf*(-(gu11*PDstandardNth1g33) - gu12*PDstandardNth2g33 + - 2*gu11*PDstandardNth3g13 + 2*gu12*PDstandardNth3g23 + - gu13*PDstandardNth3g33); + R12 = khalf*(2*(G122*G211 + G123*G311 + G213*G322 + G313*G323) - + 2*(G112*G212 + G112*G313 + G212*G323 + G312*G333 + gu12*PDstandardNth12g12) - gu32*PDstandardNth12g23 - + gu33*PDstandardNth12g33 + gu13*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + + gu32*PDstandardNth13g22 + gu33*PDstandardNth13g23 + gu12*(PDstandardNth11g22 + PDstandardNth22g11) + + gu32*PDstandardNth22g13 + gu13*PDstandardNth23g11 - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - + gu33*PDstandardNth33g12); - G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + - 2*gu21*PDstandardNth3g13 + 2*gu22*PDstandardNth3g23 + - gu23*PDstandardNth3g33); + R13 = khalf*(2*(G123*G211 + G212*G223 + G133*G311 + G233*G312) - + 2*(G213*G222 + G223*G313 + G113*(G212 + G313) + gu13*PDstandardNth13g13) + + gu12*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + PDstandardNth23g11) + + gu22*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu13*(PDstandardNth11g33 + PDstandardNth33g11) + + gu23*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12)); + + R22 = -(G122*(G111 + G212 + G313)) + 2*(G122*G212 + G123*G312 + G223*G322) - G222*(G112 + G222 + G323) - + G322*(G113 + G223 + G333) + khalf*(-(gu11*(PDstandardNth11g22 - 2*PDstandardNth12g12 + PDstandardNth22g11)) + + gu13*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu31*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) - + gu33*(PDstandardNth22g33 - 2*PDstandardNth23g23 + PDstandardNth33g22)) + SQR(G112) + SQR(G222) + SQR(G323); - G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + - 2*gu31*PDstandardNth3g13 + 2*gu32*PDstandardNth3g23 + - gu33*PDstandardNth3g33); + R23 = khalf*(2*(G112*G113 + G122*G213 + G133*G312 + G233*G322) + + gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu21*(-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - PDstandardNth23g12) - + 2*(G111*G123 + G113*G323 + G223*(G112 + G323) + gu23*PDstandardNth23g23) + + gu13*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12) + + gu23*(PDstandardNth22g33 + PDstandardNth33g22)); + + R33 = -(G133*(G111 + G212 + G313)) + 2*(G123*G213 + G133*G313) + 2*G233*G323 - G233*(G112 + G222 + G323) - + G333*(G113 + G223 + G333) + khalf*(-(gu11*(PDstandardNth11g33 - 2*PDstandardNth13g13 + PDstandardNth33g11)) + + gu12*(-PDstandardNth12g33 + PDstandardNth13g23 + PDstandardNth23g13 - PDstandardNth33g12) + + gu21*(-PDstandardNth12g33 + PDstandardNth13g23 + PDstandardNth23g13 - PDstandardNth33g12) - + gu22*(PDstandardNth22g33 - 2*PDstandardNth23g23 + PDstandardNth33g22)) + SQR(G113) + SQR(G223) + SQR(G333); Km11 = gu11*K11L + gu12*K12L + gu13*K13L; @@ -505,104 +428,69 @@ void ML_ADM_RHS_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_INT cons Km33 = gu31*K13L + gu32*K23L + gu33*K33L; - CCTK_REAL const T1000026 = G111 + G212 + G313; - - CCTK_REAL const T1000027 = G112 + G222 + G323; + trK = Km11 + Km22 + Km33; - CCTK_REAL const T1000028 = G113 + G223 + G333; + g11rhsL = -2*alphaL*K11L + 2*(g11L*PDstandardNth1beta1 + g12L*PDstandardNth1beta2 + g13L*PDstandardNth1beta3) + + beta1L*PDstandardNth1g11 + beta2L*PDstandardNth2g11 + beta3L*PDstandardNth3g11; - R12 = khalf*(2*(G122*G211 + G123*G311 + G213*G322 + G313*G323) - - 2*(G112*G212 + G112*G313 + G212*G323 + G312*G333 + - gu12*PDstandardNth12g12) - gu32*PDstandardNth12g23 - - gu33*PDstandardNth12g33 + gu13* - (PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + - gu32*PDstandardNth13g22 + gu33*PDstandardNth13g23 + - gu12*(PDstandardNth11g22 + PDstandardNth22g11) + - gu32*PDstandardNth22g13 + gu13*PDstandardNth23g11 - - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - - gu33*PDstandardNth33g12); + g12rhsL = -2*alphaL*K12L + g22L*PDstandardNth1beta2 + g23L*PDstandardNth1beta3 + beta1L*PDstandardNth1g12 + + g11L*PDstandardNth2beta1 + g12L*(PDstandardNth1beta1 + PDstandardNth2beta2) + g13L*PDstandardNth2beta3 + + beta2L*PDstandardNth2g12 + beta3L*PDstandardNth3g12; - R13 = khalf*(2*(G123*G211 + G212*G223 + G133*G311 + G233*G312) - - 2*(G213*G222 + G223*G313 + G113*(G212 + G313) + - gu13*PDstandardNth13g13) + - gu12*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + - PDstandardNth23g11) + gu22* - (PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + - PDstandardNth23g12) + gu13*(PDstandardNth11g33 + PDstandardNth33g11) + - gu23*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + - PDstandardNth33g12)); + g13rhsL = -2*alphaL*K13L + g23L*PDstandardNth1beta2 + g33L*PDstandardNth1beta3 + beta1L*PDstandardNth1g13 + + beta2L*PDstandardNth2g13 + g11L*PDstandardNth3beta1 + g12L*PDstandardNth3beta2 + + g13L*(PDstandardNth1beta1 + PDstandardNth3beta3) + beta3L*PDstandardNth3g13; - R23 = khalf*(2*(G112*G113 + G122*G213 + G133*G312 + G233*G322) + - gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - - PDstandardNth23g11) + gu21* - (-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - - PDstandardNth23g12) - 2* - (G111*G123 + G113*G323 + G223*(G112 + G323) + gu23*PDstandardNth23g23) + - gu13*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + - PDstandardNth33g12) + gu23*(PDstandardNth22g33 + PDstandardNth33g22)); + g22rhsL = -2*alphaL*K22L + beta1L*PDstandardNth1g22 + + 2*(g12L*PDstandardNth2beta1 + g22L*PDstandardNth2beta2 + g23L*PDstandardNth2beta3) + beta2L*PDstandardNth2g22 + + beta3L*PDstandardNth3g22; - trK = Km11 + Km22 + Km33; + g23rhsL = -2*alphaL*K23L + beta1L*PDstandardNth1g23 + g13L*PDstandardNth2beta1 + g33L*PDstandardNth2beta3 + + beta2L*PDstandardNth2g23 + g12L*PDstandardNth3beta1 + g22L*PDstandardNth3beta2 + + g23L*(PDstandardNth2beta2 + PDstandardNth3beta3) + beta3L*PDstandardNth3g23; - R11 = 2*(G112*G211 + G113*G311 + G213*G312) - G111*T1000026 - G211*T1000027 - - G311*T1000028 + khalf*(gu23*T1000025 + gu32*T1000025 - gu22*T1000030 - - gu33*T1000035) + SQR(G111) + SQR(G212) + SQR(G313); - - R22 = 2*(G122*G212 + G123*G312 + G223*G322) - G122*T1000026 - G222*T1000027 - - G322*T1000028 + khalf*(-(gu11*T1000030) + gu13*T1000033 + gu31*T1000033 - - gu33*T1000040) + SQR(G112) + SQR(G222) + SQR(G323); - - R33 = 2*(G123*G213 + G133*G313 + G233*G323) - G133*T1000026 - G233*T1000027 - - G333*T1000028 + khalf*(-(gu11*T1000035) + gu12*T1000038 + gu21*T1000038 - - gu22*T1000040) + SQR(G113) + SQR(G223) + SQR(G333); - - K12rhsL = -PDstandardNth12alpha + G112*PDstandardNth1alpha + - K22L*PDstandardNth1beta2 + K23L*PDstandardNth1beta3 + - beta1L*PDstandardNth1K12 + G212*PDstandardNth2alpha + - K11L*PDstandardNth2beta1 + K12L* - (PDstandardNth1beta1 + PDstandardNth2beta2) + K13L*PDstandardNth2beta3 + - beta2L*PDstandardNth2K12 + G312*PDstandardNth3alpha + - beta3L*PDstandardNth3K12 + alphaL* - (-2*(K11L*Km12 + K12L*Km22 + K13L*Km32) + R12 + K12L*trK); - - K13rhsL = -PDstandardNth13alpha + G113*PDstandardNth1alpha + - K23L*PDstandardNth1beta2 + K33L*PDstandardNth1beta3 + - beta1L*PDstandardNth1K13 + G213*PDstandardNth2alpha + - beta2L*PDstandardNth2K13 + G313*PDstandardNth3alpha + - K11L*PDstandardNth3beta1 + K12L*PDstandardNth3beta2 + - K13L*(PDstandardNth1beta1 + PDstandardNth3beta3) + - beta3L*PDstandardNth3K13 + alphaL* - (-2*(K11L*Km13 + K12L*Km23 + K13L*Km33) + R13 + K13L*trK); - - K23rhsL = G123*PDstandardNth1alpha + beta1L*PDstandardNth1K23 - - PDstandardNth23alpha + G223*PDstandardNth2alpha + - K13L*PDstandardNth2beta1 + K33L*PDstandardNth2beta3 + - beta2L*PDstandardNth2K23 + G323*PDstandardNth3alpha + - K12L*PDstandardNth3beta1 + K22L*PDstandardNth3beta2 + - K23L*(PDstandardNth2beta2 + PDstandardNth3beta3) + - beta3L*PDstandardNth3K23 + alphaL* - (-2*(K12L*Km13 + K22L*Km23 + K23L*Km33) + R23 + K23L*trK); + g33rhsL = -2*alphaL*K33L + beta1L*PDstandardNth1g33 + beta2L*PDstandardNth2g33 + + 2*(g13L*PDstandardNth3beta1 + g23L*PDstandardNth3beta2 + g33L*PDstandardNth3beta3) + beta3L*PDstandardNth3g33; K11rhsL = -PDstandardNth11alpha + G111*PDstandardNth1alpha + - 2*(K11L*PDstandardNth1beta1 + K12L*PDstandardNth1beta2 + - K13L*PDstandardNth1beta3) + beta1L*PDstandardNth1K11 + - G211*PDstandardNth2alpha + beta2L*PDstandardNth2K11 + - G311*PDstandardNth3alpha + beta3L*PDstandardNth3K11 + + 2*(K11L*PDstandardNth1beta1 + K12L*PDstandardNth1beta2 + K13L*PDstandardNth1beta3) + beta1L*PDstandardNth1K11 + + G211*PDstandardNth2alpha + beta2L*PDstandardNth2K11 + G311*PDstandardNth3alpha + beta3L*PDstandardNth3K11 + alphaL*(-2*(K11L*Km11 + K12L*Km21 + K13L*Km31) + R11 + K11L*trK); - K22rhsL = G122*PDstandardNth1alpha + beta1L*PDstandardNth1K22 - - PDstandardNth22alpha + G222*PDstandardNth2alpha + - 2*(K12L*PDstandardNth2beta1 + K22L*PDstandardNth2beta2 + - K23L*PDstandardNth2beta3) + beta2L*PDstandardNth2K22 + + K12rhsL = -PDstandardNth12alpha + G112*PDstandardNth1alpha + K22L*PDstandardNth1beta2 + K23L*PDstandardNth1beta3 + + beta1L*PDstandardNth1K12 + G212*PDstandardNth2alpha + K11L*PDstandardNth2beta1 + + K12L*(PDstandardNth1beta1 + PDstandardNth2beta2) + K13L*PDstandardNth2beta3 + beta2L*PDstandardNth2K12 + + G312*PDstandardNth3alpha + beta3L*PDstandardNth3K12 + + alphaL*(-2*(K11L*Km12 + K12L*Km22 + K13L*Km32) + R12 + K12L*trK); + + K13rhsL = -PDstandardNth13alpha + G113*PDstandardNth1alpha + K23L*PDstandardNth1beta2 + K33L*PDstandardNth1beta3 + + beta1L*PDstandardNth1K13 + G213*PDstandardNth2alpha + beta2L*PDstandardNth2K13 + G313*PDstandardNth3alpha + + K11L*PDstandardNth3beta1 + K12L*PDstandardNth3beta2 + K13L*(PDstandardNth1beta1 + PDstandardNth3beta3) + + beta3L*PDstandardNth3K13 + alphaL*(-2*(K11L*Km13 + K12L*Km23 + K13L*Km33) + R13 + K13L*trK); + + K22rhsL = G122*PDstandardNth1alpha + beta1L*PDstandardNth1K22 - PDstandardNth22alpha + G222*PDstandardNth2alpha + + 2*(K12L*PDstandardNth2beta1 + K22L*PDstandardNth2beta2 + K23L*PDstandardNth2beta3) + beta2L*PDstandardNth2K22 + G322*PDstandardNth3alpha + beta3L*PDstandardNth3K22 + alphaL*(-2*(K12L*Km12 + K22L*Km22 + K23L*Km32) + R22 + K22L*trK); - K33rhsL = G133*PDstandardNth1alpha + beta1L*PDstandardNth1K33 + - G233*PDstandardNth2alpha + beta2L*PDstandardNth2K33 - + K23rhsL = G123*PDstandardNth1alpha + beta1L*PDstandardNth1K23 - PDstandardNth23alpha + G223*PDstandardNth2alpha + + K13L*PDstandardNth2beta1 + K33L*PDstandardNth2beta3 + beta2L*PDstandardNth2K23 + G323*PDstandardNth3alpha + + K12L*PDstandardNth3beta1 + K22L*PDstandardNth3beta2 + K23L*(PDstandardNth2beta2 + PDstandardNth3beta3) + + beta3L*PDstandardNth3K23 + alphaL*(-2*(K12L*Km13 + K22L*Km23 + K23L*Km33) + R23 + K23L*trK); + + K33rhsL = G133*PDstandardNth1alpha + beta1L*PDstandardNth1K33 + G233*PDstandardNth2alpha + beta2L*PDstandardNth2K33 - PDstandardNth33alpha + G333*PDstandardNth3alpha + - 2*(K13L*PDstandardNth3beta1 + K23L*PDstandardNth3beta2 + - K33L*PDstandardNth3beta3) + beta3L*PDstandardNth3K33 + + 2*(K13L*PDstandardNth3beta1 + K23L*PDstandardNth3beta2 + K33L*PDstandardNth3beta3) + beta3L*PDstandardNth3K33 + alphaL*(-2*(K13L*Km13 + K23L*Km23 + K33L*Km33) + R33 + K33L*trK); + alpharhsL = 0; + + beta1rhsL = 0; + + beta2rhsL = 0; + + beta3rhsL = 0; + /* Copy local copies back to grid functions */ alpharhs[index] = alpharhsL; diff --git a/ML_ADM/src/ML_ADM_constraints.c b/ML_ADM/src/ML_ADM_constraints.c index 17f24d7..fe54f0d 100644 --- a/ML_ADM/src/ML_ADM_constraints.c +++ b/ML_ADM/src/ML_ADM_constraints.c @@ -250,160 +250,121 @@ void ML_ADM_constraints_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_ /* Precompute derivatives (old style) */ /* Calculate temporaries and grid functions */ - CCTK_REAL const T1000001 = SQR(g23L); + detg = 2*g12L*g13L*g23L + g33L*(g11L*g22L - SQR(g12L)) - g22L*SQR(g13L) - g11L*SQR(g23L); - CCTK_REAL const T1000003 = g13L*g23L; + gu11 = INV(detg)*(g22L*g33L - SQR(g23L)); - CCTK_REAL const T1000004 = -(g12L*g33L); + gu12 = (g13L*g23L - g12L*g33L)*INV(detg); - CCTK_REAL const T1000007 = SQR(g13L); + gu13 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - CCTK_REAL const T1000008 = -(g13L*g22L); + gu21 = (g13L*g23L - g12L*g33L)*INV(detg); - CCTK_REAL const T1000009 = g12L*g23L; + gu22 = INV(detg)*(g11L*g33L - SQR(g13L)); - CCTK_REAL const T1000012 = g12L*g13L; + gu23 = (g12L*g13L - g11L*g23L)*INV(detg); - CCTK_REAL const T1000013 = -(g11L*g23L); + gu31 = (-(g13L*g22L) + g12L*g23L)*INV(detg); - CCTK_REAL const T1000016 = SQR(g12L); + gu32 = (g12L*g13L - g11L*g23L)*INV(detg); - CCTK_REAL const T1000017 = -PDstandardNth3g12; + gu33 = INV(detg)*(g11L*g22L - SQR(g12L)); - CCTK_REAL const T1000019 = -PDstandardNth2g13; + G111 = khalf*(gu11*PDstandardNth1g11 + 2*(gu12*PDstandardNth1g12 + gu13*PDstandardNth1g13) - gu12*PDstandardNth2g11 - + gu13*PDstandardNth3g11); - CCTK_REAL const T1000021 = -PDstandardNth1g23; + G211 = khalf*(gu21*PDstandardNth1g11 + 2*(gu22*PDstandardNth1g12 + gu23*PDstandardNth1g13) - gu22*PDstandardNth2g11 - + gu23*PDstandardNth3g11); - CCTK_REAL const T1000023 = -PDstandardNth11g23; + G311 = khalf*(gu31*PDstandardNth1g11 + 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - gu32*PDstandardNth2g11 - + gu33*PDstandardNth3g11); - CCTK_REAL const T1000024 = -PDstandardNth23g11; + G112 = khalf*(gu12*PDstandardNth1g22 + gu11*PDstandardNth2g11 + + gu13*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000032 = -2*PDstandardNth12g12; + G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + + gu23*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000034 = -PDstandardNth13g22; + G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + + gu33*(PDstandardNth1g23 + PDstandardNth2g13 - PDstandardNth3g12)); - CCTK_REAL const T1000035 = -PDstandardNth22g13; + G113 = khalf*(gu13*PDstandardNth1g33 + gu11*PDstandardNth3g11 + + gu12*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000043 = -2*PDstandardNth13g13; + G213 = khalf*(gu23*PDstandardNth1g33 + gu21*PDstandardNth3g11 + + gu22*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000045 = -PDstandardNth12g33; + G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + + gu32*(PDstandardNth1g23 - PDstandardNth2g13 + PDstandardNth3g12)); - CCTK_REAL const T1000046 = -PDstandardNth33g12; + G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu12*PDstandardNth2g22 + + gu13*(2*PDstandardNth2g23 - PDstandardNth3g22)); - CCTK_REAL const T1000048 = -2*PDstandardNth23g23; + G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu22*PDstandardNth2g22 + + gu23*(2*PDstandardNth2g23 - PDstandardNth3g22)); - CCTK_REAL const T1000053 = -PDstandardNth1K23; + G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + gu32*PDstandardNth2g22 + + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - CCTK_REAL const T1000060 = -PDstandardNth2K13; + G123 = khalf*(gu13*PDstandardNth2g33 + gu11*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu12*PDstandardNth3g22); - CCTK_REAL const T1000070 = -PDstandardNth3K12; + G223 = khalf*(gu23*PDstandardNth2g33 + gu21*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu22*PDstandardNth3g22); - CCTK_REAL const T1000005 = T1000003 + T1000004; + G323 = khalf*(gu33*PDstandardNth2g33 + gu31*(-PDstandardNth1g23 + PDstandardNth2g13 + PDstandardNth3g12) + + gu32*PDstandardNth3g22); - CCTK_REAL const T1000010 = T1000008 + T1000009; + G133 = khalf*(-(gu11*PDstandardNth1g33) - gu12*PDstandardNth2g33 + 2*gu11*PDstandardNth3g13 + + 2*gu12*PDstandardNth3g23 + gu13*PDstandardNth3g33); - CCTK_REAL const T1000014 = T1000012 + T1000013; + G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + 2*gu21*PDstandardNth3g13 + + 2*gu22*PDstandardNth3g23 + gu23*PDstandardNth3g33); - CCTK_REAL const T1000018 = PDstandardNth1g23 + PDstandardNth2g13 + T1000017; + G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + 2*gu31*PDstandardNth3g13 + + 2*gu32*PDstandardNth3g23 + gu33*PDstandardNth3g33); - CCTK_REAL const T1000020 = PDstandardNth1g23 + PDstandardNth3g12 + T1000019; + R11 = -(G111*(G111 + G122 + G133)) - G211*(G211 + G222 + G233) - G311*(G311 + G322 + G333) + + khalf*(-(gu22*(PDstandardNth11g22 - 2*PDstandardNth12g12 + PDstandardNth22g11)) + + gu23*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu32*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) - + gu33*(PDstandardNth11g33 - 2*PDstandardNth13g13 + PDstandardNth33g11)) + SQR(G111) + SQR(G112) + SQR(G113) + + SQR(G211) + SQR(G212) + SQR(G213) + SQR(G311) + SQR(G312) + SQR(G313); - CCTK_REAL const T1000022 = PDstandardNth2g13 + PDstandardNth3g12 + T1000021; - - CCTK_REAL const T1000025 = - PDstandardNth12g13 + PDstandardNth13g12 + T1000023 + T1000024; - - CCTK_REAL const T1000033 = PDstandardNth11g22 + PDstandardNth22g11 + T1000032; - - CCTK_REAL const T1000036 = - PDstandardNth12g23 + PDstandardNth23g12 + T1000034 + T1000035; - - CCTK_REAL const T1000044 = PDstandardNth11g33 + PDstandardNth33g11 + T1000043; - - CCTK_REAL const T1000047 = - PDstandardNth13g23 + PDstandardNth23g13 + T1000045 + T1000046; - - CCTK_REAL const T1000049 = PDstandardNth22g33 + PDstandardNth33g22 + T1000048; - - detg = 2*g12L*g13L*g23L + g11L*(g22L*g33L - T1000001) - g22L*T1000007 - - g33L*T1000016; - - CCTK_REAL const T1000002 = INV(detg); - - CCTK_REAL const T1000006 = T1000002*T1000005; - - CCTK_REAL const T1000011 = T1000002*T1000010; - - CCTK_REAL const T1000015 = T1000002*T1000014; - - gu11 = (g22L*g33L - T1000001)*T1000002; - - gu22 = T1000002*(g11L*g33L - T1000007); - - gu33 = T1000002*(g11L*g22L - T1000016); - - gu12 = T1000006; - - gu13 = T1000011; - - gu21 = T1000006; - - gu23 = T1000015; - - gu31 = T1000011; - - gu32 = T1000015; - - G111 = khalf*(gu11*PDstandardNth1g11 + - 2*(gu12*PDstandardNth1g12 + gu13*PDstandardNth1g13) - - gu12*PDstandardNth2g11 - gu13*PDstandardNth3g11); - - G211 = khalf*(gu21*PDstandardNth1g11 + - 2*(gu22*PDstandardNth1g12 + gu23*PDstandardNth1g13) - - gu22*PDstandardNth2g11 - gu23*PDstandardNth3g11); - - G311 = khalf*(gu31*PDstandardNth1g11 + - 2*(gu32*PDstandardNth1g12 + gu33*PDstandardNth1g13) - - gu32*PDstandardNth2g11 - gu33*PDstandardNth3g11); - - G112 = khalf*(gu12*PDstandardNth1g22 + gu11*PDstandardNth2g11 + gu13*T1000018); - - G212 = khalf*(gu22*PDstandardNth1g22 + gu21*PDstandardNth2g11 + gu23*T1000018); - - G312 = khalf*(gu32*PDstandardNth1g22 + gu31*PDstandardNth2g11 + gu33*T1000018); - - G113 = khalf*(gu13*PDstandardNth1g33 + gu11*PDstandardNth3g11 + gu12*T1000020); - - G213 = khalf*(gu23*PDstandardNth1g33 + gu21*PDstandardNth3g11 + gu22*T1000020); - - G313 = khalf*(gu33*PDstandardNth1g33 + gu31*PDstandardNth3g11 + gu32*T1000020); - - G122 = khalf*(gu11*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu12*PDstandardNth2g22 + gu13*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G222 = khalf*(gu21*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu22*PDstandardNth2g22 + gu23*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G322 = khalf*(gu31*(-PDstandardNth1g22 + 2*PDstandardNth2g12) + - gu32*PDstandardNth2g22 + gu33*(2*PDstandardNth2g23 - PDstandardNth3g22)); - - G123 = khalf*(gu13*PDstandardNth2g33 + gu12*PDstandardNth3g22 + gu11*T1000022); - - G223 = khalf*(gu23*PDstandardNth2g33 + gu22*PDstandardNth3g22 + gu21*T1000022); - - G323 = khalf*(gu33*PDstandardNth2g33 + gu32*PDstandardNth3g22 + gu31*T1000022); + R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) - 2*(G112*G133 + G212*G233 + G312*G333 + gu12*PDstandardNth12g12) - + gu32*PDstandardNth12g23 - gu33*PDstandardNth12g33 + + gu13*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + gu32*PDstandardNth13g22 + + gu33*PDstandardNth13g23 + gu12*(PDstandardNth11g22 + PDstandardNth22g11) + gu32*PDstandardNth22g13 + + gu13*PDstandardNth23g11 - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - gu33*PDstandardNth33g12); + + R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) - 2*(G113*G122 + G213*G222 + G313*G322 + gu13*PDstandardNth13g13) + + gu12*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + PDstandardNth23g11) + + gu22*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu13*(PDstandardNth11g33 + PDstandardNth33g11) + + gu23*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12)); + + R22 = -(G122*(G111 + G122 + G133)) - G222*(G211 + G222 + G233) - G322*(G311 + G322 + G333) + + khalf*(-(gu11*(PDstandardNth11g22 - 2*PDstandardNth12g12 + PDstandardNth22g11)) + + gu13*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) + + gu31*(PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + PDstandardNth23g12) - + gu33*(PDstandardNth22g33 - 2*PDstandardNth23g23 + PDstandardNth33g22)) + SQR(G112) + SQR(G122) + SQR(G123) + + SQR(G212) + SQR(G222) + SQR(G223) + SQR(G312) + SQR(G322) + SQR(G323); - G133 = khalf*(-(gu11*PDstandardNth1g33) - gu12*PDstandardNth2g33 + - 2*gu11*PDstandardNth3g13 + 2*gu12*PDstandardNth3g23 + - gu13*PDstandardNth3g33); + R23 = khalf*(2*(G112*G113 + G212*G213 + G312*G313) + + gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - PDstandardNth23g11) + + gu21*(-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - PDstandardNth23g12) - + 2*(G111*G123 + G211*G223 + G311*G323 + gu23*PDstandardNth23g23) + + gu13*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + PDstandardNth33g12) + + gu23*(PDstandardNth22g33 + PDstandardNth33g22)); - G233 = khalf*(-(gu21*PDstandardNth1g33) - gu22*PDstandardNth2g33 + - 2*gu21*PDstandardNth3g13 + 2*gu22*PDstandardNth3g23 + - gu23*PDstandardNth3g33); + R33 = -(G133*(G111 + G122 + G133)) - G233*(G211 + G222 + G233) - G333*(G311 + G322 + G333) + + khalf*(-(gu11*(PDstandardNth11g33 - 2*PDstandardNth13g13 + PDstandardNth33g11)) + + gu12*(-PDstandardNth12g33 + PDstandardNth13g23 + PDstandardNth23g13 - PDstandardNth33g12) + + gu21*(-PDstandardNth12g33 + PDstandardNth13g23 + PDstandardNth23g13 - PDstandardNth33g12) - + gu22*(PDstandardNth22g33 - 2*PDstandardNth23g23 + PDstandardNth33g22)) + SQR(G113) + SQR(G123) + SQR(G133) + + SQR(G213) + SQR(G223) + SQR(G233) + SQR(G313) + SQR(G323) + SQR(G333); - G333 = khalf*(-(gu31*PDstandardNth1g33) - gu32*PDstandardNth2g33 + - 2*gu31*PDstandardNth3g13 + 2*gu32*PDstandardNth3g23 + - gu33*PDstandardNth3g33); + trR = gu11*R11 + (gu12 + gu21)*R12 + (gu13 + gu31)*R13 + gu22*R22 + (gu23 + gu32)*R23 + gu33*R33; Km11 = gu11*K11L + gu12*K12L + gu13*K13L; @@ -423,155 +384,36 @@ void ML_ADM_constraints_Body(cGH const * const cctkGH, CCTK_INT const dir, CCTK_ Km33 = gu31*K13L + gu32*K23L + gu33*K33L; - CCTK_REAL const T1000026 = SQR(G112); - - CCTK_REAL const T1000027 = G111 + G122 + G133; - - CCTK_REAL const T1000028 = SQR(G212); - - CCTK_REAL const T1000029 = G211 + G222 + G233; - - CCTK_REAL const T1000030 = SQR(G312); - - CCTK_REAL const T1000031 = G311 + G322 + G333; - - CCTK_REAL const T1000037 = SQR(G113); - - CCTK_REAL const T1000038 = SQR(G123); - - CCTK_REAL const T1000039 = SQR(G213); - - CCTK_REAL const T1000040 = SQR(G223); - - CCTK_REAL const T1000041 = SQR(G313); - - CCTK_REAL const T1000042 = SQR(G323); - - CCTK_REAL const T1000050 = -(G123*K11L); - - CCTK_REAL const T1000051 = -(G223*K12L); - - CCTK_REAL const T1000052 = -(G323*K13L); - - CCTK_REAL const T1000054 = -(G113*K12L); - - CCTK_REAL const T1000055 = G112*K13L; - - CCTK_REAL const T1000056 = -(G213*K22L); - - CCTK_REAL const T1000057 = G212*K23L; - - CCTK_REAL const T1000058 = -(G313*K23L); - - CCTK_REAL const T1000059 = G312*K33L; - - CCTK_REAL const T1000061 = G123*K11L; - - CCTK_REAL const T1000062 = G223*K12L; - - CCTK_REAL const T1000063 = G323*K13L; - - CCTK_REAL const T1000064 = G113*K12L; - - CCTK_REAL const T1000065 = -(G112*K13L); - - CCTK_REAL const T1000066 = G213*K22L; - - CCTK_REAL const T1000067 = -(G212*K23L); - - CCTK_REAL const T1000068 = G313*K23L; - - CCTK_REAL const T1000069 = -(G312*K33L); - - R12 = khalf*(2*(G113*G123 + G213*G223 + G313*G323) - - 2*(G112*G133 + G212*G233 + G312*G333 + gu12*PDstandardNth12g12) - - gu32*PDstandardNth12g23 - gu33*PDstandardNth12g33 + - gu13*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12) + - gu32*PDstandardNth13g22 + gu33*PDstandardNth13g23 + - gu12*(PDstandardNth11g22 + PDstandardNth22g11) + - gu32*PDstandardNth22g13 + gu13*PDstandardNth23g11 - - gu32*PDstandardNth23g12 + gu33*PDstandardNth23g13 - - gu33*PDstandardNth33g12); - - R13 = khalf*(2*(G112*G123 + G212*G223 + G312*G323) - - 2*(G113*G122 + G213*G222 + G313*G322 + gu13*PDstandardNth13g13) + - gu12*(PDstandardNth11g23 - PDstandardNth12g13 - PDstandardNth13g12 + - PDstandardNth23g11) + gu22* - (PDstandardNth12g23 - PDstandardNth13g22 - PDstandardNth22g13 + - PDstandardNth23g12) + gu13*(PDstandardNth11g33 + PDstandardNth33g11) + - gu23*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + - PDstandardNth33g12)); - - R23 = khalf*(2*(G112*G113 + G212*G213 + G312*G313) + - gu11*(-PDstandardNth11g23 + PDstandardNth12g13 + PDstandardNth13g12 - - PDstandardNth23g11) + gu21* - (-PDstandardNth12g23 + PDstandardNth13g22 + PDstandardNth22g13 - - PDstandardNth23g12) - 2* - (G111*G123 + G211*G223 + G311*G323 + gu23*PDstandardNth23g23) + - gu13*(PDstandardNth12g33 - PDstandardNth13g23 - PDstandardNth23g13 + - PDstandardNth33g12) + gu23*(PDstandardNth22g33 + PDstandardNth33g22)); - trK = Km11 + Km22 + Km33; - R11 = T1000026 - G111*T1000027 + T1000028 - G211*T1000029 + T1000030 - - G311*T1000031 + T1000037 + T1000039 + T1000041 + - khalf*(gu23*T1000025 + gu32*T1000025 - gu22*T1000033 - gu33*T1000044) + - SQR(G111) + SQR(G211) + SQR(G311); - - R22 = T1000026 - G122*T1000027 + T1000028 - G222*T1000029 + T1000030 - - G322*T1000031 + T1000038 + T1000040 + T1000042 + - khalf*(-(gu11*T1000033) + gu13*T1000036 + gu31*T1000036 - gu33*T1000049) + - SQR(G122) + SQR(G222) + SQR(G322); - - R33 = -(G133*T1000027) - G233*T1000029 - G333*T1000031 + T1000037 + T1000038 + - T1000039 + T1000040 + T1000041 + T1000042 + - khalf*(-(gu11*T1000044) + gu12*T1000047 + gu21*T1000047 - gu22*T1000049) + - SQR(G133) + SQR(G233) + SQR(G333); - - M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L + G211*K22L + - G311*K23L - PDstandardNth1K12 + PDstandardNth2K11) + - gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L + - G312*K23L - PDstandardNth1K22 + PDstandardNth2K12) + - gu31*(-(G113*K11L) - G213*K12L + G111*K13L - G313*K13L + G211*K23L + - G311*K33L - PDstandardNth1K13 + PDstandardNth3K11) + - gu33*(-(G133*K11L) - G233*K12L + G113*K13L - G333*K13L + G213*K23L + - G313*K33L - PDstandardNth1K33 + PDstandardNth3K13) + - gu32*(PDstandardNth3K12 + T1000050 + T1000051 + T1000052 + T1000053 + - T1000055 + T1000057 + T1000059) + - gu23*(PDstandardNth2K13 + T1000050 + T1000051 + T1000052 + T1000053 + - T1000064 + T1000066 + T1000068); - - M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L - G211*K22L - - G311*K23L + PDstandardNth1K12 - PDstandardNth2K11) + - gu12*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L - G312*K23L + - PDstandardNth1K22 - PDstandardNth2K12) + - gu32*(-(G123*K12L) + G122*K13L - G223*K22L + G222*K23L - G323*K23L + - G322*K33L - PDstandardNth2K23 + PDstandardNth3K22) + - gu33*(-(G133*K12L) + G123*K13L - G233*K22L + G223*K23L - G333*K23L + - G323*K33L - PDstandardNth2K33 + PDstandardNth3K23) + - gu31*(PDstandardNth3K12 + T1000054 + T1000055 + T1000056 + T1000057 + - T1000058 + T1000059 + T1000060) + - gu13*(PDstandardNth1K23 + T1000054 + T1000056 + T1000058 + T1000060 + - T1000061 + T1000062 + T1000063); - - M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L - G211*K23L - - G311*K33L + PDstandardNth1K13 - PDstandardNth3K11) + - gu13*(G133*K11L + G233*K12L + (-G113 + G333)*K13L - G213*K23L - G313*K33L + - PDstandardNth1K33 - PDstandardNth3K13) + - gu22*(G123*K12L - G122*K13L + G223*K22L - G222*K23L + G323*K23L - - G322*K33L + PDstandardNth2K23 - PDstandardNth3K22) + - gu23*(G133*K12L - G123*K13L + G233*K22L - G223*K23L + G333*K23L - - G323*K33L + PDstandardNth2K33 - PDstandardNth3K23) + - gu12*(PDstandardNth1K23 + T1000061 + T1000062 + T1000063 + T1000065 + - T1000067 + T1000069 + T1000070) + - gu21*(PDstandardNth2K13 + T1000064 + T1000065 + T1000066 + T1000067 + - T1000068 + T1000069 + T1000070); - - trR = gu11*R11 + (gu12 + gu21)*R12 + (gu13 + gu31)*R13 + gu22*R22 + - (gu23 + gu32)*R23 + gu33*R33; - - HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR - SQR(Km11) - SQR(Km22) - - SQR(Km33) + SQR(trK); + HL = -2*(Km12*Km21 + Km13*Km31 + Km23*Km32) + trR - SQR(Km11) - SQR(Km22) - SQR(Km33) + SQR(trK); + + M1L = gu21*(-(G112*K11L) + G111*K12L - G212*K12L - G312*K13L + G211*K22L + G311*K23L - PDstandardNth1K12 + + PDstandardNth2K11) + gu22*(-(G122*K11L) + G112*K12L - G222*K12L - G322*K13L + G212*K22L + G312*K23L - + PDstandardNth1K22 + PDstandardNth2K12) + gu23* + (-(G123*K11L) + G113*K12L - G223*K12L - G323*K13L + G213*K22L + G313*K23L - PDstandardNth1K23 + PDstandardNth2K13)\ + + gu31*(-(G113*K11L) - G213*K12L + G111*K13L - G313*K13L + G211*K23L + G311*K33L - PDstandardNth1K13 + + PDstandardNth3K11) + gu32*(-(G123*K11L) - G223*K12L + G112*K13L - G323*K13L + G212*K23L + G312*K33L - + PDstandardNth1K23 + PDstandardNth3K12) + gu33* + (-(G133*K11L) - G233*K12L + G113*K13L - G333*K13L + G213*K23L + G313*K33L - PDstandardNth1K33 + PDstandardNth3K13); + + M2L = gu11*(G112*K11L + (-G111 + G212)*K12L + G312*K13L - G211*K22L - G311*K23L + PDstandardNth1K12 - + PDstandardNth2K11) + gu12*(G122*K11L + (-G112 + G222)*K12L + G322*K13L - G212*K22L - G312*K23L + + PDstandardNth1K22 - PDstandardNth2K12) + gu13* + (G123*K11L + (-G113 + G223)*K12L + G323*K13L - G213*K22L - G313*K23L + PDstandardNth1K23 - PDstandardNth2K13) + + gu31*(-(G113*K12L) + G112*K13L - G213*K22L + G212*K23L - G313*K23L + G312*K33L - PDstandardNth2K13 + + PDstandardNth3K12) + gu32*(-(G123*K12L) + G122*K13L - G223*K22L + G222*K23L - G323*K23L + G322*K33L - + PDstandardNth2K23 + PDstandardNth3K22) + gu33* + (-(G133*K12L) + G123*K13L - G233*K22L + G223*K23L - G333*K23L + G323*K33L - PDstandardNth2K33 + PDstandardNth3K23); + + M3L = gu11*(G113*K11L + G213*K12L + (-G111 + G313)*K13L - G211*K23L - G311*K33L + PDstandardNth1K13 - + PDstandardNth3K11) + gu12*(G123*K11L + G223*K12L + (-G112 + G323)*K13L - G212*K23L - G312*K33L + + PDstandardNth1K23 - PDstandardNth3K12) + gu21* + (G113*K12L - G112*K13L + G213*K22L - G212*K23L + G313*K23L - G312*K33L + PDstandardNth2K13 - PDstandardNth3K12) + + gu13*(G133*K11L + G233*K12L + (-G113 + G333)*K13L - G213*K23L - G313*K33L + PDstandardNth1K33 - + PDstandardNth3K13) + gu22*(G123*K12L - G122*K13L + G223*K22L - G222*K23L + G323*K23L - G322*K33L + + PDstandardNth2K23 - PDstandardNth3K22) + gu23* + (G133*K12L - G123*K13L + G233*K22L - G223*K23L + G333*K23L - G323*K33L + PDstandardNth2K33 - PDstandardNth3K23); /* Copy local copies back to grid functions */ |