diff options
-rw-r--r-- | ML_ADMConstraints/src/ML_ADMConstraints.cc | 169 | ||||
-rw-r--r-- | ML_ADMConstraints_MP/src/ML_ADMConstraints_MP.cc | 194 | ||||
-rw-r--r-- | ML_ADMConstraints_O2/src/ML_ADMConstraints_O2.cc | 169 |
3 files changed, 379 insertions, 153 deletions
diff --git a/ML_ADMConstraints/src/ML_ADMConstraints.cc b/ML_ADMConstraints/src/ML_ADMConstraints.cc index d925f84..54f0864 100644 --- a/ML_ADMConstraints/src/ML_ADMConstraints.cc +++ b/ML_ADMConstraints/src/ML_ADMConstraints.cc @@ -285,53 +285,128 @@ static void ML_ADMConstraints_Body(cGH const * restrict const cctkGH, int const + gu32*(-PDstandardNth2gzz + 2*PDstandardNth3gyz) + gu33*PDstandardNth3gzz); - CCTK_REAL R11 = 0.5*(-2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 - + G311*G322 + G311*G333 + gu32*PDstandardNth11gyz) + - 2*gu32*PDstandardNth12gxz + 2*gu32*PDstandardNth13gxy + - gu22*(-PDstandardNth11gyy + 2*PDstandardNth12gxy - PDstandardNth22gxx) - - 2*gu32*PDstandardNth23gxx + gu33*(-PDstandardNth11gzz + - 2*PDstandardNth13gxz - PDstandardNth33gxx) + 2*SQR(G112) + 2*SQR(G113) - + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); - - CCTK_REAL R12 = 0.5*(2*(G113*G123 + G213*G223 + G313*G323) - - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*PDstandardNth12gxy) + - gu31*(PDstandardNth11gyz - PDstandardNth12gxz - PDstandardNth13gxy) + - gu21*(PDstandardNth11gyy + PDstandardNth22gxx) + - gu32*PDstandardNth22gxz + gu31*PDstandardNth23gxx + - gu32*(-PDstandardNth12gyz + PDstandardNth13gyy - PDstandardNth23gxy) + - gu33*PDstandardNth23gxz + gu33*(-PDstandardNth12gzz + - PDstandardNth13gyz - PDstandardNth33gxy)); - - CCTK_REAL R13 = 0.5*(2*(G112*G123 + G212*G223 + G312*G323) - - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*PDstandardNth13gxz) + - gu21*(PDstandardNth11gyz - PDstandardNth12gxz - PDstandardNth13gxy + - PDstandardNth23gxx) + gu22*(PDstandardNth12gyz - PDstandardNth13gyy - - PDstandardNth22gxz + PDstandardNth23gxy) + gu31*(PDstandardNth11gzz + - PDstandardNth33gxx) + gu32*(PDstandardNth12gzz - PDstandardNth13gyz - - PDstandardNth23gxz + PDstandardNth33gxy)); - - CCTK_REAL R22 = 0.5*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + - G322*(G311 + G333) + gu31*PDstandardNth13gyy) + - gu11*(-PDstandardNth11gyy + 2*PDstandardNth12gxy - PDstandardNth22gxx) - + gu31*(-2*PDstandardNth22gxz + 2*(PDstandardNth12gyz + - PDstandardNth23gxy)) + gu33*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - - PDstandardNth33gyy) + 2*(SQR(G112) + SQR(G123) + SQR(G212) + - SQR(G223) + SQR(G312) + SQR(G323))); - - CCTK_REAL R23 = 0.5*(2*(G112*G113 + G212*G213 + G312*G313) + - gu11*(-PDstandardNth11gyz + PDstandardNth12gxz + PDstandardNth13gxy - - PDstandardNth23gxx) + gu21*(-PDstandardNth12gyz + PDstandardNth13gyy + - PDstandardNth22gxz - PDstandardNth23gxy) - 2*(G111*G123 + G211*G223 + - G311*G323 + gu32*PDstandardNth23gyz) + gu31*(PDstandardNth12gzz - - PDstandardNth13gyz - PDstandardNth23gxz + PDstandardNth33gxy) + - gu32*(PDstandardNth22gzz + PDstandardNth33gyy)); - - CCTK_REAL R33 = 0.5*(gu11*(-PDstandardNth11gzz + 2*PDstandardNth13gxz - - PDstandardNth33gxx) - 2*((G111 + G122)*G133 + (G211 + G222)*G233 + - (G311 + G322)*G333 + gu21*(PDstandardNth12gzz + PDstandardNth33gxy)) + - gu22*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - PDstandardNth33gyy) - + 2*(gu21*(PDstandardNth13gyz + PDstandardNth23gxz) + SQR(G113) + - SQR(G123) + SQR(G213) + SQR(G223) + SQR(G313) + SQR(G323))); + CCTK_REAL R11 = 0.5*(gu32*(4*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) + + 2*(-PDstandardNth11gyz + PDstandardNth12gxz + PDstandardNth13gxy - + PDstandardNth23gxx)) + gu22*(-PDstandardNth11gyy + 2*PDstandardNth12gxy + - PDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-PDstandardNth11gzz + 2*PDstandardNth13gxz - + PDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313))))); + + CCTK_REAL R12 = 0.5*(gu21*(PDstandardNth11gyy - 2*PDstandardNth12gxy + + PDstandardNth22gxx) + gu31*(PDstandardNth11gyz - PDstandardNth12gxz - + PDstandardNth13gxy + PDstandardNth23gxx) + gu32*(-PDstandardNth12gyz + + PDstandardNth13gyy + PDstandardNth22gxz - PDstandardNth23gxy) + + gu33*(-PDstandardNth12gzz + PDstandardNth13gyz + PDstandardNth23gxz - + PDstandardNth33gxy) + 2*(gu31*((G123*G211 - G113*G212)*gxyL + + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + G213*gxyL + G313*gxzL) + + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G212*G213) + + G211*G223)*gyyL + (G223*G311 - G213*G312 - G212*G313)*gyzL + + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + gu32*((-(G123*G212) + + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + G113*(G122*gxxL + + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + (-(G223*G312) + + G222*G313 - G212*G323)*gyzL + (G313*G322 - G312*G323)*gzzL) + + gu33*((-(G133*G212) + G123*G213)*gxyL + (-(G133*G312) + G123*G313)*gxzL + + G113*(G123*gxxL + G223*gxyL + G323*gxzL) - G112*(G133*gxxL + + G233*gxyL + G333*gxzL) + (G213*G223 - G212*G233)*gyyL + G213*G323*gyzL + + (-(G233*G312) + G223*G313 - G212*G333)*gyzL + (G313*G323 - + G312*G333)*gzzL) + gu21*(G122*(G211*gxyL + G311*gxzL) + G111*(G122*gxxL + + G222*gxyL + G322*gxzL) + G222*(G211*gyyL + G311*gyzL) - + 2*(G112*(G212*gxyL + G312*gxzL) + G212*G312*gyzL) + G322*(G211*gyzL + + G311*gzzL) - gxxL*SQR(G112) - gyyL*SQR(G212) - gzzL*SQR(G312)))); + + CCTK_REAL R13 = 0.5*(gu21*(PDstandardNth11gyz - PDstandardNth12gxz - + PDstandardNth13gxy + PDstandardNth23gxx) + gu22*(PDstandardNth12gyz - + PDstandardNth13gyy - PDstandardNth22gxz + PDstandardNth23gxy) + + gu31*(PDstandardNth11gzz - 2*PDstandardNth13gxz + PDstandardNth33gxx) + + gu32*(PDstandardNth12gzz - PDstandardNth13gyz - PDstandardNth23gxz + + PDstandardNth33gxy) + 2*(gu21*((G123*G211 - G113*G212)*gxyL + + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + G213*gxyL + G313*gxzL) + + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G212*G213) + + G211*G223)*gyyL + (G223*G311 - G213*G312 - G212*G313)*gyzL + + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + gu22*((G123*G212 - + G122*G213)*gxyL + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + + G222*gxyL + G322*gxzL) + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (-(G213*G222) + G212*G223)*gyyL + (G223*G312 - G222*G313 - + G213*G322)*gyzL + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + gu32*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu31*(G133*(G211*gxyL + G311*gxzL) + G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G211*gyyL + G311*gyzL) - 2*(G113*(G213*gxyL + + G313*gxzL) + G213*G313*gyzL) + G333*(G211*gyzL + G311*gzzL) - + gxxL*SQR(G113) - gyyL*SQR(G213) - gzzL*SQR(G313)))); + + CCTK_REAL R22 = 0.5*(gu31*(4*((G123*G212 - G122*G213)*gxyL + + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + G222*gxyL + G322*gxzL) + + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G213*G222) + + G212*G223)*gyyL + (G223*G312 - G222*G313 - G213*G322)*gyzL + + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + 2*(PDstandardNth12gyz - PDstandardNth13gyy - PDstandardNth22gxz + + PDstandardNth23gxy)) + gu11*(-PDstandardNth11gyy + 2*PDstandardNth12gxy + - PDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - + PDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); + + CCTK_REAL R23 = 0.5*(gu11*(-PDstandardNth11gyz + PDstandardNth12gxz + + PDstandardNth13gxy - PDstandardNth23gxx) + gu21*(-PDstandardNth12gyz + + PDstandardNth13gyy + PDstandardNth22gxz - PDstandardNth23gxy) + + gu31*(PDstandardNth12gzz - PDstandardNth13gyz - PDstandardNth23gxz + + PDstandardNth33gxy) + gu32*(PDstandardNth22gzz - 2*PDstandardNth23gyz + + PDstandardNth33gyy) + 2*(gu11*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) + gu21*((-(G123*G212) + + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + G113*(G122*gxxL + + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + (-(G223*G312) + + G222*G313 - G212*G323)*gyzL + (G313*G322 - G312*G323)*gzzL) + + gu31*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu32*(G133*(G222*gxyL + G322*gxzL) + G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G222*gyyL + G322*gyzL) - 2*(G123*(G223*gxyL + + G323*gxzL) + G223*G323*gyzL) + G333*(G222*gyzL + G322*gzzL) - + gxxL*SQR(G123) - gyyL*SQR(G223) - gzzL*SQR(G323)))); + + CCTK_REAL R33 = 0.5*(gu21*(4*((-(G133*G212) + G123*G213)*gxyL + + (-(G133*G312) + G123*G313)*gxzL + G113*(G123*gxxL + G223*gxyL + + G323*gxzL) - G112*(G133*gxxL + G233*gxyL + G333*gxzL) + (G213*G223 - + G212*G233)*gyyL + G213*G323*gyzL + (-(G233*G312) + G223*G313 - + G212*G333)*gyzL + (G313*G323 - G312*G333)*gzzL) + + 2*(-PDstandardNth12gzz + PDstandardNth13gyz + PDstandardNth23gxz - + PDstandardNth33gxy)) + gu11*(-PDstandardNth11gzz + 2*PDstandardNth13gxz + - PDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313)))) + gu22*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - + PDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); CCTK_REAL trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; diff --git a/ML_ADMConstraints_MP/src/ML_ADMConstraints_MP.cc b/ML_ADMConstraints_MP/src/ML_ADMConstraints_MP.cc index 3dab86d..572a0d2 100644 --- a/ML_ADMConstraints_MP/src/ML_ADMConstraints_MP.cc +++ b/ML_ADMConstraints_MP/src/ML_ADMConstraints_MP.cc @@ -1068,74 +1068,150 @@ static void ML_ADMConstraints_MP_Body(cGH const * restrict const cctkGH, int con 2*JacPDstandardNth3gxz) + gu32*(-JacPDstandardNth2gzz + 2*JacPDstandardNth3gyz) + gu33*JacPDstandardNth3gzz); - CCTK_REAL R11 = 0.5*(-2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 - + G311*G322 + G311*G333 + gu32*JacPDstandardNth11gyz) + - gu21*(-JacPDstandardNth12gxx + JacPDstandardNth21gxx) + - gu22*(-JacPDstandardNth11gyy + 2*JacPDstandardNth21gxy - - JacPDstandardNth22gxx) + gu31*(-JacPDstandardNth13gxx + - JacPDstandardNth31gxx) + 2*gu32*JacPDstandardNth31gxy + - gu32*(2*JacPDstandardNth21gxz - JacPDstandardNth23gxx - - JacPDstandardNth32gxx) + gu33*(-JacPDstandardNth11gzz + - 2*JacPDstandardNth31gxz - JacPDstandardNth33gxx) + 2*SQR(G112) + - 2*SQR(G113) + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); + CCTK_REAL R11 = 0.5*(gu21*(-JacPDstandardNth12gxx + + JacPDstandardNth21gxx) + gu31*(-JacPDstandardNth13gxx + + JacPDstandardNth31gxx) + gu32*(4*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) - JacPDstandardNth11gyz + + JacPDstandardNth21gxz - JacPDstandardNth23gxx + + JacPDstandardNth31gxy) + gu32*(-JacPDstandardNth11gyz + + JacPDstandardNth21gxz + JacPDstandardNth31gxy - JacPDstandardNth32gxx) + + gu22*(-JacPDstandardNth11gyy + 2*JacPDstandardNth21gxy - + JacPDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-JacPDstandardNth11gzz + 2*JacPDstandardNth31gxz - + JacPDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313))))); - CCTK_REAL R12 = 0.5*(2*(G113*G123 + G213*G223 + G313*G323) - - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*JacPDstandardNth12gxy + - gu32*JacPDstandardNth12gyz) + gu31*(JacPDstandardNth11gyz - - JacPDstandardNth12gxz - JacPDstandardNth13gxy) + - gu22*(-JacPDstandardNth12gyy + JacPDstandardNth21gyy) + - gu21*(JacPDstandardNth11gyy + JacPDstandardNth22gxx) + - gu32*JacPDstandardNth22gxz + gu32*(JacPDstandardNth21gyz - - JacPDstandardNth23gxy) + gu32*JacPDstandardNth31gyy + - gu31*JacPDstandardNth32gxx + gu33*JacPDstandardNth32gxz + - gu33*(-JacPDstandardNth12gzz + JacPDstandardNth31gyz - - JacPDstandardNth33gxy)); + CCTK_REAL R12 = 0.5*(gu22*(-JacPDstandardNth12gyy + + JacPDstandardNth21gyy) + gu21*(JacPDstandardNth11gyy - + 2*JacPDstandardNth12gxy + JacPDstandardNth22gxx) + + gu32*(-2*JacPDstandardNth12gyz + JacPDstandardNth21gyz + + JacPDstandardNth22gxz - JacPDstandardNth23gxy + JacPDstandardNth31gyy) + + gu31*(JacPDstandardNth11gyz - JacPDstandardNth12gxz - + JacPDstandardNth13gxy + JacPDstandardNth32gxx) + + gu33*(-JacPDstandardNth12gzz + JacPDstandardNth31gyz + + JacPDstandardNth32gxz - JacPDstandardNth33gxy) + 2*(gu31*((G123*G211 - + G113*G212)*gxyL + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + + G213*gxyL + G313*gxzL) + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + + (-(G212*G213) + G211*G223)*gyyL + (G223*G311 - G213*G312 - + G212*G313)*gyzL + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + + gu32*((-(G123*G212) + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + + G113*(G122*gxxL + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + + G223*gxyL + G323*gxzL) + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + + (-(G223*G312) + G222*G313 - G212*G323)*gyzL + (G313*G322 - + G312*G323)*gzzL) + gu33*((-(G133*G212) + G123*G213)*gxyL + + (-(G133*G312) + G123*G313)*gxzL + G113*(G123*gxxL + G223*gxyL + + G323*gxzL) - G112*(G133*gxxL + G233*gxyL + G333*gxzL) + (G213*G223 - + G212*G233)*gyyL + G213*G323*gyzL + (-(G233*G312) + G223*G313 - + G212*G333)*gyzL + (G313*G323 - G312*G333)*gzzL) + gu21*(G122*(G211*gxyL + + G311*gxzL) + G111*(G122*gxxL + G222*gxyL + G322*gxzL) + + G222*(G211*gyyL + G311*gyzL) - 2*(G112*(G212*gxyL + G312*gxzL) + + G212*G312*gyzL) + G322*(G211*gyzL + G311*gzzL) - gxxL*SQR(G112) - + gyyL*SQR(G212) - gzzL*SQR(G312)))); - CCTK_REAL R13 = 0.5*(2*(G112*G123 + G212*G223 + G312*G323) - - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*JacPDstandardNth13gxz + - gu32*JacPDstandardNth13gyz) + gu22*(-JacPDstandardNth13gyy + - JacPDstandardNth21gyz - JacPDstandardNth22gxz) + - gu21*(JacPDstandardNth11gyz - JacPDstandardNth12gxz - - JacPDstandardNth13gxy + JacPDstandardNth23gxx) + - gu22*JacPDstandardNth23gxy + gu32*JacPDstandardNth31gyz + + CCTK_REAL R13 = 0.5*(gu21*(JacPDstandardNth11gyz - + JacPDstandardNth12gxz - JacPDstandardNth13gxy + JacPDstandardNth23gxx) + + gu22*(-JacPDstandardNth13gyy + JacPDstandardNth21gyz - + JacPDstandardNth22gxz + JacPDstandardNth23gxy) + gu33*(-JacPDstandardNth13gzz + JacPDstandardNth31gzz) + - gu32*(JacPDstandardNth21gzz - JacPDstandardNth32gxz) + - gu31*(JacPDstandardNth11gzz + JacPDstandardNth33gxx) + - gu32*JacPDstandardNth33gxy); + gu31*(JacPDstandardNth11gzz - 2*JacPDstandardNth13gxz + + JacPDstandardNth33gxx) + gu32*(-2*JacPDstandardNth13gyz + + JacPDstandardNth21gzz + JacPDstandardNth31gyz - JacPDstandardNth32gxz + + JacPDstandardNth33gxy) + 2*(gu21*((G123*G211 - G113*G212)*gxyL + + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + G213*gxyL + G313*gxzL) + + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G212*G213) + + G211*G223)*gyyL + (G223*G311 - G213*G312 - G212*G313)*gyzL + + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + gu22*((G123*G212 - + G122*G213)*gxyL + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + + G222*gxyL + G322*gxzL) + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (-(G213*G222) + G212*G223)*gyyL + (G223*G312 - G222*G313 - + G213*G322)*gyzL + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + gu32*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu31*(G133*(G211*gxyL + G311*gxzL) + G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G211*gyyL + G311*gyzL) - 2*(G113*(G213*gxyL + + G313*gxzL) + G213*G313*gyzL) + G333*(G211*gyzL + G311*gzzL) - + gxxL*SQR(G113) - gyyL*SQR(G213) - gzzL*SQR(G313)))); CCTK_REAL R22 = 0.5*(gu21*(JacPDstandardNth12gyy - - JacPDstandardNth21gyy) + gu11*(-JacPDstandardNth11gyy + - 2*JacPDstandardNth12gxy - JacPDstandardNth22gxx) - 2*(G111*G122 + - G122*G133 + G211*G222 + G222*G233 + G311*G322 + G322*G333 + - gu31*JacPDstandardNth22gxz) + gu31*(2*JacPDstandardNth12gyz - - JacPDstandardNth13gyy - JacPDstandardNth31gyy) + - 2*gu31*JacPDstandardNth32gxy + gu32*(-JacPDstandardNth23gyy + - JacPDstandardNth32gyy) + gu33*(-JacPDstandardNth22gzz + - 2*JacPDstandardNth32gyz - JacPDstandardNth33gyy) + 2*SQR(G112) + - 2*SQR(G123) + 2*SQR(G212) + 2*SQR(G223) + 2*SQR(G312) + 2*SQR(G323)); + JacPDstandardNth21gyy) + gu31*(4*((G123*G212 - G122*G213)*gxyL + + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + G222*gxyL + G322*gxzL) + + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G213*G222) + + G212*G223)*gyyL + (G223*G312 - G222*G313 - G213*G322)*gyzL + + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + JacPDstandardNth12gyz - JacPDstandardNth13gyy - JacPDstandardNth22gxz + + JacPDstandardNth32gxy) + gu31*(JacPDstandardNth12gyz - + JacPDstandardNth22gxz - JacPDstandardNth31gyy + JacPDstandardNth32gxy) + + gu32*(-JacPDstandardNth23gyy + JacPDstandardNth32gyy) + + gu11*(-JacPDstandardNth11gyy + 2*JacPDstandardNth12gxy - + JacPDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-JacPDstandardNth22gzz + 2*JacPDstandardNth32gyz - + JacPDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); - CCTK_REAL R23 = 0.5*(2*(G112*G113 + G212*G213 + G312*G313) + - gu11*(-JacPDstandardNth11gyz + JacPDstandardNth12gxz + - JacPDstandardNth13gxy - JacPDstandardNth23gxx) + - gu21*(JacPDstandardNth13gyy - JacPDstandardNth21gyz + - JacPDstandardNth22gxz - JacPDstandardNth23gxy) - 2*(G111*G123 + - G211*G223 + G311*G323 + gu31*JacPDstandardNth23gxz) + + CCTK_REAL R23 = 0.5*(gu11*(-JacPDstandardNth11gyz + + JacPDstandardNth12gxz + JacPDstandardNth13gxy - JacPDstandardNth23gxx) + + gu21*(JacPDstandardNth13gyy - JacPDstandardNth21gyz + + JacPDstandardNth22gxz - JacPDstandardNth23gxy) + gu33*(-JacPDstandardNth23gzz + JacPDstandardNth32gzz) + - gu31*(JacPDstandardNth12gzz - JacPDstandardNth31gyz + - JacPDstandardNth32gxz + JacPDstandardNth33gxy) + - gu32*(JacPDstandardNth22gzz - 2*JacPDstandardNth23gyz + - JacPDstandardNth33gyy)); + gu31*(JacPDstandardNth12gzz - 2*JacPDstandardNth23gxz - + JacPDstandardNth31gyz + JacPDstandardNth32gxz + JacPDstandardNth33gxy) + + gu32*(JacPDstandardNth22gzz - 2*JacPDstandardNth23gyz + + JacPDstandardNth33gyy) + 2*(gu11*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) + gu21*((-(G123*G212) + + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + G113*(G122*gxxL + + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + (-(G223*G312) + + G222*G313 - G212*G323)*gyzL + (G313*G322 - G312*G323)*gzzL) + + gu31*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu32*(G133*(G222*gxyL + G322*gxzL) + G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G222*gyyL + G322*gyzL) - 2*(G123*(G223*gxyL + + G323*gxzL) + G223*G323*gyzL) + G333*(G222*gyzL + G322*gzzL) - + gxxL*SQR(G123) - gyyL*SQR(G223) - gzzL*SQR(G323)))); - CCTK_REAL R33 = 0.5*(gu21*(-JacPDstandardNth12gzz + - 2*JacPDstandardNth13gyz - JacPDstandardNth21gzz) + - 2*gu21*JacPDstandardNth23gxz + gu31*(JacPDstandardNth13gzz - + CCTK_REAL R33 = 0.5*(gu31*(JacPDstandardNth13gzz - JacPDstandardNth31gzz) + gu32*(JacPDstandardNth23gzz - - JacPDstandardNth32gzz) + gu11*(-JacPDstandardNth11gzz + - 2*JacPDstandardNth13gxz - JacPDstandardNth33gxx) - 2*(G111*G133 + - G122*G133 + G211*G233 + G222*G233 + G311*G333 + G322*G333 + - gu21*JacPDstandardNth33gxy) + gu22*(-JacPDstandardNth22gzz + - 2*JacPDstandardNth23gyz - JacPDstandardNth33gyy) + 2*SQR(G113) + - 2*SQR(G123) + 2*SQR(G213) + 2*SQR(G223) + 2*SQR(G313) + 2*SQR(G323)); + JacPDstandardNth32gzz) + gu21*(4*((-(G133*G212) + G123*G213)*gxyL + + (-(G133*G312) + G123*G313)*gxzL + G113*(G123*gxxL + G223*gxyL + + G323*gxzL) - G112*(G133*gxxL + G233*gxyL + G333*gxzL) + (G213*G223 - + G212*G233)*gyyL + G213*G323*gyzL + (-(G233*G312) + G223*G313 - + G212*G333)*gyzL + (G313*G323 - G312*G333)*gzzL) - JacPDstandardNth12gzz + + JacPDstandardNth13gyz + JacPDstandardNth23gxz - + JacPDstandardNth33gxy) + gu21*(JacPDstandardNth13gyz - + JacPDstandardNth21gzz + JacPDstandardNth23gxz - JacPDstandardNth33gxy) + + gu11*(-JacPDstandardNth11gzz + 2*JacPDstandardNth13gxz - + JacPDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313)))) + gu22*(-JacPDstandardNth22gzz + 2*JacPDstandardNth23gyz - + JacPDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); CCTK_REAL trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; diff --git a/ML_ADMConstraints_O2/src/ML_ADMConstraints_O2.cc b/ML_ADMConstraints_O2/src/ML_ADMConstraints_O2.cc index 452db16..1542371 100644 --- a/ML_ADMConstraints_O2/src/ML_ADMConstraints_O2.cc +++ b/ML_ADMConstraints_O2/src/ML_ADMConstraints_O2.cc @@ -285,53 +285,128 @@ static void ML_ADMConstraints_O2_Body(cGH const * restrict const cctkGH, int con + gu32*(-PDstandardNth2gzz + 2*PDstandardNth3gyz) + gu33*PDstandardNth3gzz); - CCTK_REAL R11 = 0.5*(-2*(G111*G122 + G111*G133 + G211*G222 + G211*G233 - + G311*G322 + G311*G333 + gu32*PDstandardNth11gyz) + - 2*gu32*PDstandardNth12gxz + 2*gu32*PDstandardNth13gxy + - gu22*(-PDstandardNth11gyy + 2*PDstandardNth12gxy - PDstandardNth22gxx) - - 2*gu32*PDstandardNth23gxx + gu33*(-PDstandardNth11gzz + - 2*PDstandardNth13gxz - PDstandardNth33gxx) + 2*SQR(G112) + 2*SQR(G113) - + 2*SQR(G212) + 2*SQR(G213) + 2*SQR(G312) + 2*SQR(G313)); - - CCTK_REAL R12 = 0.5*(2*(G113*G123 + G213*G223 + G313*G323) - - 2*(G112*G133 + G212*G233 + G312*G333 + gu21*PDstandardNth12gxy) + - gu31*(PDstandardNth11gyz - PDstandardNth12gxz - PDstandardNth13gxy) + - gu21*(PDstandardNth11gyy + PDstandardNth22gxx) + - gu32*PDstandardNth22gxz + gu31*PDstandardNth23gxx + - gu32*(-PDstandardNth12gyz + PDstandardNth13gyy - PDstandardNth23gxy) + - gu33*PDstandardNth23gxz + gu33*(-PDstandardNth12gzz + - PDstandardNth13gyz - PDstandardNth33gxy)); - - CCTK_REAL R13 = 0.5*(2*(G112*G123 + G212*G223 + G312*G323) - - 2*(G113*G122 + G213*G222 + G313*G322 + gu31*PDstandardNth13gxz) + - gu21*(PDstandardNth11gyz - PDstandardNth12gxz - PDstandardNth13gxy + - PDstandardNth23gxx) + gu22*(PDstandardNth12gyz - PDstandardNth13gyy - - PDstandardNth22gxz + PDstandardNth23gxy) + gu31*(PDstandardNth11gzz + - PDstandardNth33gxx) + gu32*(PDstandardNth12gzz - PDstandardNth13gyz - - PDstandardNth23gxz + PDstandardNth33gxy)); - - CCTK_REAL R22 = 0.5*(-2*(G122*(G111 + G133) + G222*(G211 + G233) + - G322*(G311 + G333) + gu31*PDstandardNth13gyy) + - gu11*(-PDstandardNth11gyy + 2*PDstandardNth12gxy - PDstandardNth22gxx) - + gu31*(-2*PDstandardNth22gxz + 2*(PDstandardNth12gyz + - PDstandardNth23gxy)) + gu33*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - - PDstandardNth33gyy) + 2*(SQR(G112) + SQR(G123) + SQR(G212) + - SQR(G223) + SQR(G312) + SQR(G323))); - - CCTK_REAL R23 = 0.5*(2*(G112*G113 + G212*G213 + G312*G313) + - gu11*(-PDstandardNth11gyz + PDstandardNth12gxz + PDstandardNth13gxy - - PDstandardNth23gxx) + gu21*(-PDstandardNth12gyz + PDstandardNth13gyy + - PDstandardNth22gxz - PDstandardNth23gxy) - 2*(G111*G123 + G211*G223 + - G311*G323 + gu32*PDstandardNth23gyz) + gu31*(PDstandardNth12gzz - - PDstandardNth13gyz - PDstandardNth23gxz + PDstandardNth33gxy) + - gu32*(PDstandardNth22gzz + PDstandardNth33gyy)); - - CCTK_REAL R33 = 0.5*(gu11*(-PDstandardNth11gzz + 2*PDstandardNth13gxz - - PDstandardNth33gxx) - 2*((G111 + G122)*G133 + (G211 + G222)*G233 + - (G311 + G322)*G333 + gu21*(PDstandardNth12gzz + PDstandardNth33gxy)) + - gu22*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - PDstandardNth33gyy) - + 2*(gu21*(PDstandardNth13gyz + PDstandardNth23gxz) + SQR(G113) + - SQR(G123) + SQR(G213) + SQR(G223) + SQR(G313) + SQR(G323))); + CCTK_REAL R11 = 0.5*(gu32*(4*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) + + 2*(-PDstandardNth11gyz + PDstandardNth12gxz + PDstandardNth13gxy - + PDstandardNth23gxx)) + gu22*(-PDstandardNth11gyy + 2*PDstandardNth12gxy + - PDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-PDstandardNth11gzz + 2*PDstandardNth13gxz - + PDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313))))); + + CCTK_REAL R12 = 0.5*(gu21*(PDstandardNth11gyy - 2*PDstandardNth12gxy + + PDstandardNth22gxx) + gu31*(PDstandardNth11gyz - PDstandardNth12gxz - + PDstandardNth13gxy + PDstandardNth23gxx) + gu32*(-PDstandardNth12gyz + + PDstandardNth13gyy + PDstandardNth22gxz - PDstandardNth23gxy) + + gu33*(-PDstandardNth12gzz + PDstandardNth13gyz + PDstandardNth23gxz - + PDstandardNth33gxy) + 2*(gu31*((G123*G211 - G113*G212)*gxyL + + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + G213*gxyL + G313*gxzL) + + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G212*G213) + + G211*G223)*gyyL + (G223*G311 - G213*G312 - G212*G313)*gyzL + + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + gu32*((-(G123*G212) + + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + G113*(G122*gxxL + + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + (-(G223*G312) + + G222*G313 - G212*G323)*gyzL + (G313*G322 - G312*G323)*gzzL) + + gu33*((-(G133*G212) + G123*G213)*gxyL + (-(G133*G312) + G123*G313)*gxzL + + G113*(G123*gxxL + G223*gxyL + G323*gxzL) - G112*(G133*gxxL + + G233*gxyL + G333*gxzL) + (G213*G223 - G212*G233)*gyyL + G213*G323*gyzL + + (-(G233*G312) + G223*G313 - G212*G333)*gyzL + (G313*G323 - + G312*G333)*gzzL) + gu21*(G122*(G211*gxyL + G311*gxzL) + G111*(G122*gxxL + + G222*gxyL + G322*gxzL) + G222*(G211*gyyL + G311*gyzL) - + 2*(G112*(G212*gxyL + G312*gxzL) + G212*G312*gyzL) + G322*(G211*gyzL + + G311*gzzL) - gxxL*SQR(G112) - gyyL*SQR(G212) - gzzL*SQR(G312)))); + + CCTK_REAL R13 = 0.5*(gu21*(PDstandardNth11gyz - PDstandardNth12gxz - + PDstandardNth13gxy + PDstandardNth23gxx) + gu22*(PDstandardNth12gyz - + PDstandardNth13gyy - PDstandardNth22gxz + PDstandardNth23gxy) + + gu31*(PDstandardNth11gzz - 2*PDstandardNth13gxz + PDstandardNth33gxx) + + gu32*(PDstandardNth12gzz - PDstandardNth13gyz - PDstandardNth23gxz + + PDstandardNth33gxy) + 2*(gu21*((G123*G211 - G113*G212)*gxyL + + (G123*G311 - G113*G312)*gxzL - G112*(G113*gxxL + G213*gxyL + G313*gxzL) + + G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G212*G213) + + G211*G223)*gyyL + (G223*G311 - G213*G312 - G212*G313)*gyzL + + G211*G323*gyzL + (-(G312*G313) + G311*G323)*gzzL) + gu22*((G123*G212 - + G122*G213)*gxyL + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + + G222*gxyL + G322*gxzL) + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (-(G213*G222) + G212*G223)*gyyL + (G223*G312 - G222*G313 - + G213*G322)*gyzL + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + gu32*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu31*(G133*(G211*gxyL + G311*gxzL) + G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G211*gyyL + G311*gyzL) - 2*(G113*(G213*gxyL + + G313*gxzL) + G213*G313*gyzL) + G333*(G211*gyzL + G311*gzzL) - + gxxL*SQR(G113) - gyyL*SQR(G213) - gzzL*SQR(G313)))); + + CCTK_REAL R22 = 0.5*(gu31*(4*((G123*G212 - G122*G213)*gxyL + + (G123*G312 - G122*G313)*gxzL - G113*(G122*gxxL + G222*gxyL + G322*gxzL) + + G112*(G123*gxxL + G223*gxyL + G323*gxzL) + (-(G213*G222) + + G212*G223)*gyyL + (G223*G312 - G222*G313 - G213*G322)*gyzL + + G212*G323*gyzL + (-(G313*G322) + G312*G323)*gzzL) + + 2*(PDstandardNth12gyz - PDstandardNth13gyy - PDstandardNth22gxz + + PDstandardNth23gxy)) + gu11*(-PDstandardNth11gyy + 2*PDstandardNth12gxy + - PDstandardNth22gxx + 2*(G122*(-(G211*gxyL) - G311*gxzL) + + 2*G112*(G212*gxyL + G312*gxzL) - G111*(G122*gxxL + G222*gxyL + + G322*gxzL) + (2*G212*G312 - G211*G322)*gyzL + G222*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G112) + gyyL*SQR(G212) + gzzL*(-(G311*G322) + + SQR(G312)))) + gu33*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - + PDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); + + CCTK_REAL R23 = 0.5*(gu11*(-PDstandardNth11gyz + PDstandardNth12gxz + + PDstandardNth13gxy - PDstandardNth23gxx) + gu21*(-PDstandardNth12gyz + + PDstandardNth13gyy + PDstandardNth22gxz - PDstandardNth23gxy) + + gu31*(PDstandardNth12gzz - PDstandardNth13gyz - PDstandardNth23gxz + + PDstandardNth33gxy) + gu32*(PDstandardNth22gzz - 2*PDstandardNth23gyz + + PDstandardNth33gyy) + 2*(gu11*((-(G123*G211) + G113*G212)*gxyL + + (-(G123*G311) + G113*G312)*gxzL + G112*(G113*gxxL + G213*gxyL + + G313*gxzL) - G111*(G123*gxxL + G223*gxyL + G323*gxzL) + (G212*G213 - + G211*G223)*gyyL + G212*G313*gyzL + (-(G223*G311) + G213*G312 - + G211*G323)*gyzL + (G312*G313 - G311*G323)*gzzL) + gu21*((-(G123*G212) + + G122*G213)*gxyL + (-(G123*G312) + G122*G313)*gxzL + G113*(G122*gxxL + + G222*gxyL + G322*gxzL) - G112*(G123*gxxL + G223*gxyL + G323*gxzL) + + (G213*G222 - G212*G223)*gyyL + G213*G322*gyzL + (-(G223*G312) + + G222*G313 - G212*G323)*gyzL + (G313*G322 - G312*G323)*gzzL) + + gu31*((G133*G212 - G123*G213)*gxyL + (G133*G312 - G123*G313)*gxzL - + G113*(G123*gxxL + G223*gxyL + G323*gxzL) + G112*(G133*gxxL + G233*gxyL + + G333*gxzL) + (-(G213*G223) + G212*G233)*gyyL + (G233*G312 - G223*G313 + - G213*G323)*gyzL + G212*G333*gyzL + (-(G313*G323) + G312*G333)*gzzL) + + gu32*(G133*(G222*gxyL + G322*gxzL) + G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + G233*(G222*gyyL + G322*gyzL) - 2*(G123*(G223*gxyL + + G323*gxzL) + G223*G323*gyzL) + G333*(G222*gyzL + G322*gzzL) - + gxxL*SQR(G123) - gyyL*SQR(G223) - gzzL*SQR(G323)))); + + CCTK_REAL R33 = 0.5*(gu21*(4*((-(G133*G212) + G123*G213)*gxyL + + (-(G133*G312) + G123*G313)*gxzL + G113*(G123*gxxL + G223*gxyL + + G323*gxzL) - G112*(G133*gxxL + G233*gxyL + G333*gxzL) + (G213*G223 - + G212*G233)*gyyL + G213*G323*gyzL + (-(G233*G312) + G223*G313 - + G212*G333)*gyzL + (G313*G323 - G312*G333)*gzzL) + + 2*(-PDstandardNth12gzz + PDstandardNth13gyz + PDstandardNth23gxz - + PDstandardNth33gxy)) + gu11*(-PDstandardNth11gzz + 2*PDstandardNth13gxz + - PDstandardNth33gxx + 2*(G133*(-(G211*gxyL) - G311*gxzL) + + 2*G113*(G213*gxyL + G313*gxzL) - G111*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G213*G313 - G211*G333)*gyzL + G233*(-(G211*gyyL) - + G311*gyzL) + gxxL*SQR(G113) + gyyL*SQR(G213) + gzzL*(-(G311*G333) + + SQR(G313)))) + gu22*(-PDstandardNth22gzz + 2*PDstandardNth23gyz - + PDstandardNth33gyy + 2*(G133*(-(G222*gxyL) - G322*gxzL) + + 2*G123*(G223*gxyL + G323*gxzL) - G122*(G133*gxxL + G233*gxyL + + G333*gxzL) + (2*G223*G323 - G222*G333)*gyzL + G233*(-(G222*gyyL) - + G322*gyzL) + gxxL*SQR(G123) + gyyL*SQR(G223) + gzzL*(-(G322*G333) + + SQR(G323))))); CCTK_REAL trR = gu11*R11 + gu22*R22 + 2*(gu21*R12 + gu31*R13 + gu32*R23) + gu33*R33; |