diff options
Diffstat (limited to 'ML_BSSN/src/ML_BSSN_constraints.c')
| -rw-r--r-- | ML_BSSN/src/ML_BSSN_constraints.c | 184 |
1 files changed, 49 insertions, 135 deletions
diff --git a/ML_BSSN/src/ML_BSSN_constraints.c b/ML_BSSN/src/ML_BSSN_constraints.c index fc1c71e..9d8b388 100644 --- a/ML_BSSN/src/ML_BSSN_constraints.c +++ b/ML_BSSN/src/ML_BSSN_constraints.c @@ -1,5 +1,5 @@ -/* File produced by user eschnett */ -/* Produced with Mathematica Version 6.0 for Mac OS X x86 (32-bit) (April 20, 2007) */ +/* File produced by user diener */ +/* Produced with Mathematica Version 6.0 for Linux x86 (32-bit) (April 20, 2007) */ /* Mathematica script written by Ian Hinder and Sascha Husa */ @@ -96,27 +96,9 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Declare shorthands */ CCTK_REAL Atm11 = INITVALUE, Atm12 = INITVALUE, Atm13 = INITVALUE, Atm21 = INITVALUE, Atm22 = INITVALUE, Atm23 = INITVALUE; CCTK_REAL Atm31 = INITVALUE, Atm32 = INITVALUE, Atm33 = INITVALUE; - CCTK_REAL ddetg1 = INITVALUE, ddetg2 = INITVALUE, ddetg3 = INITVALUE; - CCTK_REAL ddetgt1 = INITVALUE, ddetgt2 = INITVALUE, ddetgt3 = INITVALUE; - CCTK_REAL detg = INITVALUE; CCTK_REAL detgt = INITVALUE; CCTK_REAL e4phi = INITVALUE; CCTK_REAL em4phi = INITVALUE; - CCTK_REAL g11 = INITVALUE; - CCTK_REAL G111 = INITVALUE, G112 = INITVALUE, G113 = INITVALUE; - CCTK_REAL g12 = INITVALUE; - CCTK_REAL G122 = INITVALUE, G123 = INITVALUE; - CCTK_REAL g13 = INITVALUE; - CCTK_REAL G133 = INITVALUE, G211 = INITVALUE, G212 = INITVALUE, G213 = INITVALUE; - CCTK_REAL g22 = INITVALUE; - CCTK_REAL G222 = INITVALUE, G223 = INITVALUE; - CCTK_REAL g23 = INITVALUE; - CCTK_REAL G233 = INITVALUE, G311 = INITVALUE, G312 = INITVALUE, G313 = INITVALUE, G322 = INITVALUE, G323 = INITVALUE; - CCTK_REAL g33 = INITVALUE; - CCTK_REAL G333 = INITVALUE; - CCTK_REAL gK112 = INITVALUE, gK113 = INITVALUE, gK121 = INITVALUE, gK122 = INITVALUE, gK123 = INITVALUE, gK131 = INITVALUE; - CCTK_REAL gK132 = INITVALUE, gK133 = INITVALUE, gK221 = INITVALUE, gK223 = INITVALUE, gK231 = INITVALUE, gK232 = INITVALUE; - CCTK_REAL gK233 = INITVALUE, gK331 = INITVALUE, gK332 = INITVALUE; CCTK_REAL Gt111 = INITVALUE, Gt112 = INITVALUE, Gt113 = INITVALUE, Gt122 = INITVALUE, Gt123 = INITVALUE, Gt133 = INITVALUE; CCTK_REAL Gt211 = INITVALUE, Gt212 = INITVALUE, Gt213 = INITVALUE, Gt222 = INITVALUE, Gt223 = INITVALUE, Gt233 = INITVALUE; CCTK_REAL Gt311 = INITVALUE, Gt312 = INITVALUE, Gt313 = INITVALUE, Gt322 = INITVALUE, Gt323 = INITVALUE, Gt333 = INITVALUE; @@ -141,6 +123,7 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Declare precomputed derivatives*/ /* Declare derivatives */ + CCTK_REAL PDstandard4th1At11 = INITVALUE; CCTK_REAL PDstandard4th2At11 = INITVALUE; CCTK_REAL PDstandard4th3At11 = INITVALUE; CCTK_REAL PDstandard4th1At12 = INITVALUE; @@ -150,12 +133,14 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA CCTK_REAL PDstandard4th2At13 = INITVALUE; CCTK_REAL PDstandard4th3At13 = INITVALUE; CCTK_REAL PDstandard4th1At22 = INITVALUE; + CCTK_REAL PDstandard4th2At22 = INITVALUE; CCTK_REAL PDstandard4th3At22 = INITVALUE; CCTK_REAL PDstandard4th1At23 = INITVALUE; CCTK_REAL PDstandard4th2At23 = INITVALUE; CCTK_REAL PDstandard4th3At23 = INITVALUE; CCTK_REAL PDstandard4th1At33 = INITVALUE; CCTK_REAL PDstandard4th2At33 = INITVALUE; + CCTK_REAL PDstandard4th3At33 = INITVALUE; CCTK_REAL PDstandard4th1gt11 = INITVALUE; CCTK_REAL PDstandard4th2gt11 = INITVALUE; CCTK_REAL PDstandard4th3gt11 = INITVALUE; @@ -277,6 +262,7 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Include user supplied include files */ /* Precompute derivatives (new style) */ + PDstandard4th1At11 = PDstandard4th1(At11, i, j, k); PDstandard4th2At11 = PDstandard4th2(At11, i, j, k); PDstandard4th3At11 = PDstandard4th3(At11, i, j, k); PDstandard4th1At12 = PDstandard4th1(At12, i, j, k); @@ -286,12 +272,14 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA PDstandard4th2At13 = PDstandard4th2(At13, i, j, k); PDstandard4th3At13 = PDstandard4th3(At13, i, j, k); PDstandard4th1At22 = PDstandard4th1(At22, i, j, k); + PDstandard4th2At22 = PDstandard4th2(At22, i, j, k); PDstandard4th3At22 = PDstandard4th3(At22, i, j, k); PDstandard4th1At23 = PDstandard4th1(At23, i, j, k); PDstandard4th2At23 = PDstandard4th2(At23, i, j, k); PDstandard4th3At23 = PDstandard4th3(At23, i, j, k); PDstandard4th1At33 = PDstandard4th1(At33, i, j, k); PDstandard4th2At33 = PDstandard4th2(At33, i, j, k); + PDstandard4th3At33 = PDstandard4th3(At33, i, j, k); PDstandard4th1gt11 = PDstandard4th1(gt11, i, j, k); PDstandard4th2gt11 = PDstandard4th2(gt11, i, j, k); PDstandard4th3gt11 = PDstandard4th3(gt11, i, j, k); @@ -373,12 +361,6 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA /* Calculate temporaries and grid functions */ detgt = 1; - ddetgt1 = 0; - - ddetgt2 = 0; - - ddetgt3 = 0; - gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); gtu21 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); @@ -773,20 +755,6 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA em4phi = INV(e4phi); - g11 = e4phi*gt11L; - - g12 = e4phi*gt12L; - - g13 = e4phi*gt13L; - - g22 = e4phi*gt22L; - - g23 = e4phi*gt23L; - - g33 = e4phi*gt33L; - - detg = CUB(e4phi); - gu11 = em4phi*gtu11; gu21 = em4phi*gtu21; @@ -799,48 +767,6 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA gu33 = em4phi*gtu33; - ddetg1 = e4phi*(ddetgt1 + 4*detgt*PDstandard4th1phi); - - ddetg2 = e4phi*(ddetgt2 + 4*detgt*PDstandard4th2phi); - - ddetg3 = e4phi*(ddetgt3 + 4*detgt*PDstandard4th3phi); - - G111 = -((-6*detg*Gt111 + ddetg1*(-6 + g11*gu11) + g11*(ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - - G211 = ((6*detg*Gt211 - g11*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - - G311 = ((6*detg*Gt311 - g11*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - - G112 = -((-6*detg*Gt112 + ddetg2*(-3 + g12*gu21) + g12*(ddetg1*gu11 + ddetg3*gu31))*INV(detg))/6.; - - G212 = -((-6*detg*Gt212 + ddetg1*(-3 + g12*gu21) + g12*(ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - - G312 = ((6*detg*Gt312 - g12*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - - G113 = -((-6*detg*Gt113 + g13*(ddetg1*gu11 + ddetg2*gu21) + ddetg3*(-3 + g13*gu31))*INV(detg))/6.; - - G213 = ((6*detg*Gt213 - g13*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - - G313 = -((-6*detg*Gt313 + ddetg1*(-3 + g13*gu31) + g13*(ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - - G122 = ((6*detg*Gt122 - g22*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - - G222 = -((-6*detg*Gt222 + ddetg2*(-6 + g22*gu22) + g22*(ddetg1*gu21 + ddetg3*gu32))*INV(detg))/6.; - - G322 = ((6*detg*Gt322 - g22*(ddetg1*gu31 + ddetg2*gu32 + ddetg3*gu33))*INV(detg))/6.; - - G123 = ((6*detg*Gt123 - g23*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - - G223 = -((-6*detg*Gt223 + g23*(ddetg1*gu21 + ddetg2*gu22) + ddetg3*(-3 + g23*gu32))*INV(detg))/6.; - - G323 = -((-6*detg*Gt323 + ddetg2*(-3 + g23*gu32) + g23*(ddetg1*gu31 + ddetg3*gu33))*INV(detg))/6.; - - G133 = ((6*detg*Gt133 - g33*(ddetg1*gu11 + ddetg2*gu21 + ddetg3*gu31))*INV(detg))/6.; - - G233 = ((6*detg*Gt233 - g33*(ddetg1*gu21 + ddetg2*gu22 + ddetg3*gu32))*INV(detg))/6.; - - G333 = -((-6*detg*Gt333 + g33*(ddetg1*gu31 + ddetg2*gu32) + ddetg3*(-6 + g33*gu33))*INV(detg))/6.; - R11 = Rphi11 + Rt11; R12 = Rphi12 + Rt12; @@ -875,59 +801,47 @@ void ML_BSSN_constraints_Body(cGH *cctkGH, CCTK_INT dir, CCTK_INT face, CCTK_REA HL = -2*(Atm12*Atm21 + Atm13*Atm31 + Atm23*Atm32) + trR - SQR(Atm11) - SQR(Atm22) - SQR(Atm33) + ktwothird*SQR(trKL); - gK112 = e4phi*(-2*(At11L*G112 + At12L*G212 + At13L*G312) + PDstandard4th2At11 + 4*At11L*PDstandard4th2phi) + - g11*kthird*PDstandard4th2trK; - - gK113 = e4phi*(-2*(At11L*G113 + At12L*G213 + At13L*G313) + PDstandard4th3At11 + 4*At11L*PDstandard4th3phi) + - g11*kthird*PDstandard4th3trK; - - gK121 = e4phi*(-(At11L*G112) - At22L*G211 - At12L*(G111 + G212) - At23L*G311 - At13L*G312 + PDstandard4th1At12 + - 4*At12L*PDstandard4th1phi) + g12*kthird*PDstandard4th1trK; - - gK122 = e4phi*(-(At11L*G122) - At22L*G212 - At12L*(G112 + G222) - At23L*G312 - At13L*G322 + PDstandard4th2At12 + - 4*At12L*PDstandard4th2phi) + g12*kthird*PDstandard4th2trK; - - gK123 = e4phi*(-(At11L*G123) - At22L*G213 - At12L*(G113 + G223) - At23L*G313 - At13L*G323 + PDstandard4th3At12 + - 4*At12L*PDstandard4th3phi) + g12*kthird*PDstandard4th3trK; - - gK131 = e4phi*(-(At11L*G113) - At23L*G211 - At12L*G213 - At33L*G311 - At13L*(G111 + G313) + PDstandard4th1At13 + - 4*At13L*PDstandard4th1phi) + g13*kthird*PDstandard4th1trK; - - gK132 = e4phi*(-(At11L*G123) - At23L*G212 - At12L*G223 - At33L*G312 - At13L*(G112 + G323) + PDstandard4th2At13 + - 4*At13L*PDstandard4th2phi) + g13*kthird*PDstandard4th2trK; - - gK133 = e4phi*(-(At11L*G133) - At23L*G213 - At12L*G233 - At33L*G313 - At13L*(G113 + G333) + PDstandard4th3At13 + - 4*At13L*PDstandard4th3phi) + g13*kthird*PDstandard4th3trK; - - gK221 = e4phi*(-2*(At12L*G112 + At22L*G212 + At23L*G312) + PDstandard4th1At22 + 4*At22L*PDstandard4th1phi) + - g22*kthird*PDstandard4th1trK; - - gK223 = e4phi*(-2*(At12L*G123 + At22L*G223 + At23L*G323) + PDstandard4th3At22 + 4*At22L*PDstandard4th3phi) + - g22*kthird*PDstandard4th3trK; - - gK231 = e4phi*(-(At13L*G112) - At12L*G113 - At23L*G212 - At22L*G213 - At33L*G312 - At23L*G313 + PDstandard4th1At23 + - 4*At23L*PDstandard4th1phi) + g23*kthird*PDstandard4th1trK; - - gK232 = e4phi*(-(At13L*G122) - At12L*G123 - At23L*G222 - At22L*G223 - At33L*G322 - At23L*G323 + PDstandard4th2At23 + - 4*At23L*PDstandard4th2phi) + g23*kthird*PDstandard4th2trK; - - gK233 = e4phi*(-(At13L*G123) - At12L*G133 - At23L*G223 - At22L*G233 - At33L*G323 - At23L*G333 + PDstandard4th3At23 + - 4*At23L*PDstandard4th3phi) + g23*kthird*PDstandard4th3trK; - - gK331 = e4phi*(-2*(At13L*G113 + At23L*G213 + At33L*G313) + PDstandard4th1At33 + 4*At33L*PDstandard4th1phi) + - g33*kthird*PDstandard4th1trK; - - gK332 = e4phi*(-2*(At13L*G123 + At23L*G223 + At33L*G323) + PDstandard4th2At33 + 4*At33L*PDstandard4th2phi) + - g33*kthird*PDstandard4th2trK; - - M1L = (gK112 - gK121)*gu21 + (gK122 - gK221)*gu22 + (gK113 - gK131)*gu31 + (gK123 + gK132 - 2*gK231)*gu32 + - (gK133 - gK331)*gu33; - - M2L = (-gK112 + gK121)*gu11 + (-gK122 + gK221)*gu21 + (gK123 - 2*gK132 + gK231)*gu31 + (gK223 - gK232)*gu32 + - (gK233 - gK332)*gu33; - - M3L = (-gK113 + gK131)*gu11 + (-2*gK123 + gK132 + gK231)*gu21 + (-gK223 + gK232)*gu22 + (-gK133 + gK331)*gu31 + - (-gK233 + gK332)*gu32; + M1L = -(At12L*Gt112*gtu22) - At11L*Gt122*gtu22 - At22L*Gt212*gtu22 - At12L*Gt222*gtu22 - At23L*Gt312*gtu22 - + At13L*Gt322*gtu22 - At13L*Gt111*gtu31 - 3*At11L*Gt113*gtu31 - At23L*Gt211*gtu31 - 3*At12L*Gt213*gtu31 - + At33L*Gt311*gtu31 - 3*At13L*Gt313*gtu31 - At13L*Gt112*gtu32 - At12L*Gt113*gtu32 - At23L*Gt212*gtu32 - + At22L*Gt213*gtu32 - 2*At12L*Gt223*gtu32 - At33L*Gt312*gtu32 - At23L*Gt313*gtu32 - 2*At13L*Gt323*gtu32 - + 2*(At11L*Gt111*gtu11 + At12L*Gt211*gtu11 + At13L*Gt311*gtu11 + At11L*Gt123*gtu32) - At13L*Gt113*gtu33 - + At11L*Gt133*gtu33 - At23L*Gt213*gtu33 - At12L*Gt233*gtu33 - At33L*Gt313*gtu33 - At13L*Gt333*gtu33 + + gtu11*PDstandard4th1At11 + gtu21*(-(At12L*Gt111) - 3*At11L*Gt112 - At22L*Gt211 - 3*At12L*Gt212 - At23L*Gt311 - + 3*At13L*Gt312 + PDstandard4th1At12) + gtu31*PDstandard4th1At13 + 6*At11L*gtu11*PDstandard4th1phi + + 6*At12L*gtu21*PDstandard4th1phi + 6*At13L*gtu31*PDstandard4th1phi - ktwothird*PDstandard4th1trK + + gtu21*PDstandard4th2At11 + gtu22*PDstandard4th2At12 + gtu32*PDstandard4th2At13 + 6*At11L*gtu21*PDstandard4th2phi + + 6*At12L*gtu22*PDstandard4th2phi + 6*At13L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At11 + + gtu32*PDstandard4th3At12 + gtu33*PDstandard4th3At13 + 6*At11L*gtu31*PDstandard4th3phi + + 6*At12L*gtu32*PDstandard4th3phi + 6*At13L*gtu33*PDstandard4th3phi; + + M2L = -(At12L*Gt111*gtu11) - At11L*Gt112*gtu11 - At22L*Gt211*gtu11 - At12L*Gt212*gtu11 - At23L*Gt311*gtu11 - + At13L*Gt312*gtu11 - 3*At12L*Gt112*gtu21 - At11L*Gt122*gtu21 - 3*At22L*Gt212*gtu21 - At12L*Gt222*gtu21 - + 3*At23L*Gt312*gtu21 - At13L*Gt322*gtu21 - 2*At12L*Gt122*gtu22 - 2*At22L*Gt222*gtu22 - 2*At23L*Gt322*gtu22 - + At13L*Gt112*gtu31 - 2*At12L*Gt113*gtu31 - At11L*Gt123*gtu31 - At23L*Gt212*gtu31 - 2*At22L*Gt213*gtu31 - + At12L*Gt223*gtu31 - At33L*Gt312*gtu31 - 2*At23L*Gt313*gtu31 - At13L*Gt323*gtu31 - At13L*Gt122*gtu32 - + 3*At12L*Gt123*gtu32 - At23L*Gt222*gtu32 - 3*At22L*Gt223*gtu32 - At33L*Gt322*gtu32 - 3*At23L*Gt323*gtu32 - + At13L*Gt123*gtu33 - At12L*Gt133*gtu33 - At23L*Gt223*gtu33 - At22L*Gt233*gtu33 - At33L*Gt323*gtu33 - + At23L*Gt333*gtu33 + gtu11*PDstandard4th1At12 + gtu21*PDstandard4th1At22 + gtu31*PDstandard4th1At23 + + 6*At12L*gtu11*PDstandard4th1phi + 6*At22L*gtu21*PDstandard4th1phi + 6*At23L*gtu31*PDstandard4th1phi + + gtu21*PDstandard4th2At12 + gtu22*PDstandard4th2At22 + gtu32*PDstandard4th2At23 + 6*At12L*gtu21*PDstandard4th2phi + + 6*At22L*gtu22*PDstandard4th2phi + 6*At23L*gtu32*PDstandard4th2phi - ktwothird*PDstandard4th2trK + + gtu31*PDstandard4th3At12 + gtu32*PDstandard4th3At22 + gtu33*PDstandard4th3At23 + 6*At12L*gtu31*PDstandard4th3phi + + 6*At22L*gtu32*PDstandard4th3phi + 6*At23L*gtu33*PDstandard4th3phi; + + M3L = -(At13L*Gt111*gtu11) - At11L*Gt113*gtu11 - At23L*Gt211*gtu11 - At12L*Gt213*gtu11 - At33L*Gt311*gtu11 - + At13L*Gt313*gtu11 - 2*At13L*Gt112*gtu21 - At12L*Gt113*gtu21 - At11L*Gt123*gtu21 - 2*At23L*Gt212*gtu21 - + At22L*Gt213*gtu21 - At12L*Gt223*gtu21 - 2*At33L*Gt312*gtu21 - At23L*Gt313*gtu21 - At13L*Gt323*gtu21 - + At13L*Gt122*gtu22 - At12L*Gt123*gtu22 - At23L*Gt222*gtu22 - At22L*Gt223*gtu22 - At33L*Gt322*gtu22 - + At23L*Gt323*gtu22 - 3*At13L*Gt113*gtu31 - At11L*Gt133*gtu31 - 3*At23L*Gt213*gtu31 - At12L*Gt233*gtu31 - + 3*At33L*Gt313*gtu31 - At13L*Gt333*gtu31 - 3*At13L*Gt123*gtu32 - At12L*Gt133*gtu32 - 3*At23L*Gt223*gtu32 - + At22L*Gt233*gtu32 - 3*At33L*Gt323*gtu32 - At23L*Gt333*gtu32 - 2*At13L*Gt133*gtu33 - 2*At23L*Gt233*gtu33 - + 2*At33L*Gt333*gtu33 + gtu11*PDstandard4th1At13 + gtu21*PDstandard4th1At23 + gtu31*PDstandard4th1At33 + + 6*At13L*gtu11*PDstandard4th1phi + 6*At23L*gtu21*PDstandard4th1phi + 6*At33L*gtu31*PDstandard4th1phi + + gtu21*PDstandard4th2At13 + gtu22*PDstandard4th2At23 + gtu32*PDstandard4th2At33 + 6*At13L*gtu21*PDstandard4th2phi + + 6*At23L*gtu22*PDstandard4th2phi + 6*At33L*gtu32*PDstandard4th2phi + gtu31*PDstandard4th3At13 + + gtu32*PDstandard4th3At23 + gtu33*PDstandard4th3At33 + 6*At13L*gtu31*PDstandard4th3phi + + 6*At23L*gtu32*PDstandard4th3phi + 6*At33L*gtu33*PDstandard4th3phi - ktwothird*PDstandard4th3trK; cSL = trR; |