/* File produced by Kranc */ #define KRANC_C #include #include #include #include #include "cctk.h" #include "cctk_Arguments.h" #include "cctk_Parameters.h" #include "GenericFD.h" #include "Differencing.h" #include "loopcontrol.h" /* Define macros used in calculations */ #define INITVALUE (42) #define INV(x) ((1.0) / (x)) #define SQR(x) ((x) * (x)) #define CUB(x) ((x) * (x) * (x)) #define QAD(x) ((x) * (x) * (x) * (x)) void ML_BSSN_MP_O8_constraints1_SelectBCs(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; CCTK_INT ierr = 0; ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GenericFD_GetBoundaryWidth(cctkGH), -1 /* no table */, "ML_BSSN_MP_O8::ML_Ham","flat"); if (ierr < 0) CCTK_WARN(1, "Failed to register flat BC for ML_BSSN_MP_O8::ML_Ham."); return; } void ML_BSSN_MP_O8_constraints1_Body(cGH const * restrict const cctkGH, int const dir, int const face, CCTK_REAL const normal[3], CCTK_REAL const tangentA[3], CCTK_REAL const tangentB[3], int const min[3], int const max[3], int const n_subblock_gfs, CCTK_REAL * restrict const subblock_gfs[]) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; /* Declare finite differencing variables */ if (verbose > 1) { CCTK_VInfo(CCTK_THORNSTRING,"Entering ML_BSSN_MP_O8_constraints1_Body"); } if (cctk_iteration % ML_BSSN_MP_O8_constraints1_calc_every != ML_BSSN_MP_O8_constraints1_calc_offset) { return; } /* Include user-supplied include files */ /* Initialise finite differencing variables */ CCTK_REAL const dx = CCTK_DELTA_SPACE(0); CCTK_REAL const dy = CCTK_DELTA_SPACE(1); CCTK_REAL const dz = CCTK_DELTA_SPACE(2); int const di = 1; int const dj = CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0); int const dk = CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0); CCTK_REAL const dxi = 1.0 / dx; CCTK_REAL const dyi = 1.0 / dy; CCTK_REAL const dzi = 1.0 / dz; CCTK_REAL const khalf = 0.5; CCTK_REAL const kthird = 1/3.0; CCTK_REAL const ktwothird = 2.0/3.0; CCTK_REAL const kfourthird = 4.0/3.0; CCTK_REAL const keightthird = 8.0/3.0; CCTK_REAL const hdxi = 0.5 * dxi; CCTK_REAL const hdyi = 0.5 * dyi; CCTK_REAL const hdzi = 0.5 * dzi; /* Initialize predefined quantities */ CCTK_REAL const p1o1024dx = INV(dx)/1024.; CCTK_REAL const p1o1024dy = INV(dy)/1024.; CCTK_REAL const p1o1024dz = INV(dz)/1024.; CCTK_REAL const p1o1680dx = INV(dx)/1680.; CCTK_REAL const p1o1680dy = INV(dy)/1680.; CCTK_REAL const p1o1680dz = INV(dz)/1680.; CCTK_REAL const p1o5040dx2 = pow(dx,-2)/5040.; CCTK_REAL const p1o5040dy2 = pow(dy,-2)/5040.; CCTK_REAL const p1o5040dz2 = pow(dz,-2)/5040.; CCTK_REAL const p1o560dx = INV(dx)/560.; CCTK_REAL const p1o560dy = INV(dy)/560.; CCTK_REAL const p1o560dz = INV(dz)/560.; CCTK_REAL const p1o705600dxdy = (INV(dx)*INV(dy))/705600.; CCTK_REAL const p1o705600dxdz = (INV(dx)*INV(dz))/705600.; CCTK_REAL const p1o705600dydz = (INV(dy)*INV(dz))/705600.; CCTK_REAL const p1o840dx = INV(dx)/840.; CCTK_REAL const p1o840dy = INV(dy)/840.; CCTK_REAL const p1o840dz = INV(dz)/840.; CCTK_REAL const p1odx = INV(dx); CCTK_REAL const p1ody = INV(dy); CCTK_REAL const p1odz = INV(dz); CCTK_REAL const pm1o840dx = -INV(dx)/840.; CCTK_REAL const pm1o840dy = -INV(dy)/840.; CCTK_REAL const pm1o840dz = -INV(dz)/840.; /* Loop over the grid points */ #pragma omp parallel LC_LOOP3 (ML_BSSN_MP_O8_constraints1, i,j,k, min[0],min[1],min[2], max[0],max[1],max[2], cctk_lsh[0],cctk_lsh[1],cctk_lsh[2]) { // int index = INITVALUE; int const index = CCTK_GFINDEX3D(cctkGH,i,j,k); /* Declare derivatives */ // CCTK_REAL PDstandardNth1gt11 = INITVALUE; // CCTK_REAL PDstandardNth2gt11 = INITVALUE; // CCTK_REAL PDstandardNth3gt11 = INITVALUE; // CCTK_REAL PDstandardNth11gt11 = INITVALUE; // CCTK_REAL PDstandardNth22gt11 = INITVALUE; // CCTK_REAL PDstandardNth33gt11 = INITVALUE; // CCTK_REAL PDstandardNth12gt11 = INITVALUE; // CCTK_REAL PDstandardNth13gt11 = INITVALUE; // CCTK_REAL PDstandardNth23gt11 = INITVALUE; // CCTK_REAL PDstandardNth1gt12 = INITVALUE; // CCTK_REAL PDstandardNth2gt12 = INITVALUE; // CCTK_REAL PDstandardNth3gt12 = INITVALUE; // CCTK_REAL PDstandardNth11gt12 = INITVALUE; // CCTK_REAL PDstandardNth22gt12 = INITVALUE; // CCTK_REAL PDstandardNth33gt12 = INITVALUE; // CCTK_REAL PDstandardNth12gt12 = INITVALUE; // CCTK_REAL PDstandardNth13gt12 = INITVALUE; // CCTK_REAL PDstandardNth23gt12 = INITVALUE; // CCTK_REAL PDstandardNth1gt13 = INITVALUE; // CCTK_REAL PDstandardNth2gt13 = INITVALUE; // CCTK_REAL PDstandardNth3gt13 = INITVALUE; // CCTK_REAL PDstandardNth11gt13 = INITVALUE; // CCTK_REAL PDstandardNth22gt13 = INITVALUE; // CCTK_REAL PDstandardNth33gt13 = INITVALUE; // CCTK_REAL PDstandardNth12gt13 = INITVALUE; // CCTK_REAL PDstandardNth13gt13 = INITVALUE; // CCTK_REAL PDstandardNth23gt13 = INITVALUE; // CCTK_REAL PDstandardNth1gt22 = INITVALUE; // CCTK_REAL PDstandardNth2gt22 = INITVALUE; // CCTK_REAL PDstandardNth3gt22 = INITVALUE; // CCTK_REAL PDstandardNth11gt22 = INITVALUE; // CCTK_REAL PDstandardNth22gt22 = INITVALUE; // CCTK_REAL PDstandardNth33gt22 = INITVALUE; // CCTK_REAL PDstandardNth12gt22 = INITVALUE; // CCTK_REAL PDstandardNth13gt22 = INITVALUE; // CCTK_REAL PDstandardNth23gt22 = INITVALUE; // CCTK_REAL PDstandardNth1gt23 = INITVALUE; // CCTK_REAL PDstandardNth2gt23 = INITVALUE; // CCTK_REAL PDstandardNth3gt23 = INITVALUE; // CCTK_REAL PDstandardNth11gt23 = INITVALUE; // CCTK_REAL PDstandardNth22gt23 = INITVALUE; // CCTK_REAL PDstandardNth33gt23 = INITVALUE; // CCTK_REAL PDstandardNth12gt23 = INITVALUE; // CCTK_REAL PDstandardNth13gt23 = INITVALUE; // CCTK_REAL PDstandardNth23gt23 = INITVALUE; // CCTK_REAL PDstandardNth1gt33 = INITVALUE; // CCTK_REAL PDstandardNth2gt33 = INITVALUE; // CCTK_REAL PDstandardNth3gt33 = INITVALUE; // CCTK_REAL PDstandardNth11gt33 = INITVALUE; // CCTK_REAL PDstandardNth22gt33 = INITVALUE; // CCTK_REAL PDstandardNth33gt33 = INITVALUE; // CCTK_REAL PDstandardNth12gt33 = INITVALUE; // CCTK_REAL PDstandardNth13gt33 = INITVALUE; // CCTK_REAL PDstandardNth23gt33 = INITVALUE; // CCTK_REAL PDstandardNth1phi = INITVALUE; // CCTK_REAL PDstandardNth2phi = INITVALUE; // CCTK_REAL PDstandardNth3phi = INITVALUE; // CCTK_REAL PDstandardNth11phi = INITVALUE; // CCTK_REAL PDstandardNth22phi = INITVALUE; // CCTK_REAL PDstandardNth33phi = INITVALUE; // CCTK_REAL PDstandardNth12phi = INITVALUE; // CCTK_REAL PDstandardNth13phi = INITVALUE; // CCTK_REAL PDstandardNth23phi = INITVALUE; // CCTK_REAL PDstandardNth1Xt1 = INITVALUE; // CCTK_REAL PDstandardNth2Xt1 = INITVALUE; // CCTK_REAL PDstandardNth3Xt1 = INITVALUE; // CCTK_REAL PDstandardNth1Xt2 = INITVALUE; // CCTK_REAL PDstandardNth2Xt2 = INITVALUE; // CCTK_REAL PDstandardNth3Xt2 = INITVALUE; // CCTK_REAL PDstandardNth1Xt3 = INITVALUE; // CCTK_REAL PDstandardNth2Xt3 = INITVALUE; // CCTK_REAL PDstandardNth3Xt3 = INITVALUE; /* Assign local copies of grid functions */ CCTK_REAL alphaL = alpha[index]; CCTK_REAL At11L = At11[index]; CCTK_REAL At12L = At12[index]; CCTK_REAL At13L = At13[index]; CCTK_REAL At22L = At22[index]; CCTK_REAL At23L = At23[index]; CCTK_REAL At33L = At33[index]; CCTK_REAL beta1L = beta1[index]; CCTK_REAL beta2L = beta2[index]; CCTK_REAL beta3L = beta3[index]; CCTK_REAL dJ111L = dJ111[index]; CCTK_REAL dJ112L = dJ112[index]; CCTK_REAL dJ113L = dJ113[index]; CCTK_REAL dJ122L = dJ122[index]; CCTK_REAL dJ123L = dJ123[index]; CCTK_REAL dJ133L = dJ133[index]; CCTK_REAL dJ211L = dJ211[index]; CCTK_REAL dJ212L = dJ212[index]; CCTK_REAL dJ213L = dJ213[index]; CCTK_REAL dJ222L = dJ222[index]; CCTK_REAL dJ223L = dJ223[index]; CCTK_REAL dJ233L = dJ233[index]; CCTK_REAL dJ311L = dJ311[index]; CCTK_REAL dJ312L = dJ312[index]; CCTK_REAL dJ313L = dJ313[index]; CCTK_REAL dJ322L = dJ322[index]; CCTK_REAL dJ323L = dJ323[index]; CCTK_REAL dJ333L = dJ333[index]; CCTK_REAL eTttL = (*stress_energy_state) ? (eTtt[index]) : 0.0; CCTK_REAL eTtxL = (*stress_energy_state) ? (eTtx[index]) : 0.0; CCTK_REAL eTtyL = (*stress_energy_state) ? (eTty[index]) : 0.0; CCTK_REAL eTtzL = (*stress_energy_state) ? (eTtz[index]) : 0.0; CCTK_REAL eTxxL = (*stress_energy_state) ? (eTxx[index]) : 0.0; CCTK_REAL eTxyL = (*stress_energy_state) ? (eTxy[index]) : 0.0; CCTK_REAL eTxzL = (*stress_energy_state) ? (eTxz[index]) : 0.0; CCTK_REAL eTyyL = (*stress_energy_state) ? (eTyy[index]) : 0.0; CCTK_REAL eTyzL = (*stress_energy_state) ? (eTyz[index]) : 0.0; CCTK_REAL eTzzL = (*stress_energy_state) ? (eTzz[index]) : 0.0; CCTK_REAL gt11L = gt11[index]; CCTK_REAL gt12L = gt12[index]; CCTK_REAL gt13L = gt13[index]; CCTK_REAL gt22L = gt22[index]; CCTK_REAL gt23L = gt23[index]; CCTK_REAL gt33L = gt33[index]; CCTK_REAL J11L = J11[index]; CCTK_REAL J12L = J12[index]; CCTK_REAL J13L = J13[index]; CCTK_REAL J21L = J21[index]; CCTK_REAL J22L = J22[index]; CCTK_REAL J23L = J23[index]; CCTK_REAL J31L = J31[index]; CCTK_REAL J32L = J32[index]; CCTK_REAL J33L = J33[index]; CCTK_REAL phiL = phi[index]; CCTK_REAL trKL = trK[index]; CCTK_REAL Xt1L = Xt1[index]; CCTK_REAL Xt2L = Xt2[index]; CCTK_REAL Xt3L = Xt3[index]; /* Include user supplied include files */ /* Precompute derivatives */ CCTK_REAL const PDstandardNth1gt11 = PDstandardNth1(gt11, i, j, k); CCTK_REAL const PDstandardNth2gt11 = PDstandardNth2(gt11, i, j, k); CCTK_REAL const PDstandardNth3gt11 = PDstandardNth3(gt11, i, j, k); CCTK_REAL const PDstandardNth11gt11 = PDstandardNth11(gt11, i, j, k); CCTK_REAL const PDstandardNth22gt11 = PDstandardNth22(gt11, i, j, k); CCTK_REAL const PDstandardNth33gt11 = PDstandardNth33(gt11, i, j, k); CCTK_REAL const PDstandardNth12gt11 = PDstandardNth12(gt11, i, j, k); CCTK_REAL const PDstandardNth13gt11 = PDstandardNth13(gt11, i, j, k); CCTK_REAL const PDstandardNth23gt11 = PDstandardNth23(gt11, i, j, k); CCTK_REAL const PDstandardNth1gt12 = PDstandardNth1(gt12, i, j, k); CCTK_REAL const PDstandardNth2gt12 = PDstandardNth2(gt12, i, j, k); CCTK_REAL const PDstandardNth3gt12 = PDstandardNth3(gt12, i, j, k); CCTK_REAL const PDstandardNth11gt12 = PDstandardNth11(gt12, i, j, k); CCTK_REAL const PDstandardNth22gt12 = PDstandardNth22(gt12, i, j, k); CCTK_REAL const PDstandardNth33gt12 = PDstandardNth33(gt12, i, j, k); CCTK_REAL const PDstandardNth12gt12 = PDstandardNth12(gt12, i, j, k); CCTK_REAL const PDstandardNth13gt12 = PDstandardNth13(gt12, i, j, k); CCTK_REAL const PDstandardNth23gt12 = PDstandardNth23(gt12, i, j, k); CCTK_REAL const PDstandardNth1gt13 = PDstandardNth1(gt13, i, j, k); CCTK_REAL const PDstandardNth2gt13 = PDstandardNth2(gt13, i, j, k); CCTK_REAL const PDstandardNth3gt13 = PDstandardNth3(gt13, i, j, k); CCTK_REAL const PDstandardNth11gt13 = PDstandardNth11(gt13, i, j, k); CCTK_REAL const PDstandardNth22gt13 = PDstandardNth22(gt13, i, j, k); CCTK_REAL const PDstandardNth33gt13 = PDstandardNth33(gt13, i, j, k); CCTK_REAL const PDstandardNth12gt13 = PDstandardNth12(gt13, i, j, k); CCTK_REAL const PDstandardNth13gt13 = PDstandardNth13(gt13, i, j, k); CCTK_REAL const PDstandardNth23gt13 = PDstandardNth23(gt13, i, j, k); CCTK_REAL const PDstandardNth1gt22 = PDstandardNth1(gt22, i, j, k); CCTK_REAL const PDstandardNth2gt22 = PDstandardNth2(gt22, i, j, k); CCTK_REAL const PDstandardNth3gt22 = PDstandardNth3(gt22, i, j, k); CCTK_REAL const PDstandardNth11gt22 = PDstandardNth11(gt22, i, j, k); CCTK_REAL const PDstandardNth22gt22 = PDstandardNth22(gt22, i, j, k); CCTK_REAL const PDstandardNth33gt22 = PDstandardNth33(gt22, i, j, k); CCTK_REAL const PDstandardNth12gt22 = PDstandardNth12(gt22, i, j, k); CCTK_REAL const PDstandardNth13gt22 = PDstandardNth13(gt22, i, j, k); CCTK_REAL const PDstandardNth23gt22 = PDstandardNth23(gt22, i, j, k); CCTK_REAL const PDstandardNth1gt23 = PDstandardNth1(gt23, i, j, k); CCTK_REAL const PDstandardNth2gt23 = PDstandardNth2(gt23, i, j, k); CCTK_REAL const PDstandardNth3gt23 = PDstandardNth3(gt23, i, j, k); CCTK_REAL const PDstandardNth11gt23 = PDstandardNth11(gt23, i, j, k); CCTK_REAL const PDstandardNth22gt23 = PDstandardNth22(gt23, i, j, k); CCTK_REAL const PDstandardNth33gt23 = PDstandardNth33(gt23, i, j, k); CCTK_REAL const PDstandardNth12gt23 = PDstandardNth12(gt23, i, j, k); CCTK_REAL const PDstandardNth13gt23 = PDstandardNth13(gt23, i, j, k); CCTK_REAL const PDstandardNth23gt23 = PDstandardNth23(gt23, i, j, k); CCTK_REAL const PDstandardNth1gt33 = PDstandardNth1(gt33, i, j, k); CCTK_REAL const PDstandardNth2gt33 = PDstandardNth2(gt33, i, j, k); CCTK_REAL const PDstandardNth3gt33 = PDstandardNth3(gt33, i, j, k); CCTK_REAL const PDstandardNth11gt33 = PDstandardNth11(gt33, i, j, k); CCTK_REAL const PDstandardNth22gt33 = PDstandardNth22(gt33, i, j, k); CCTK_REAL const PDstandardNth33gt33 = PDstandardNth33(gt33, i, j, k); CCTK_REAL const PDstandardNth12gt33 = PDstandardNth12(gt33, i, j, k); CCTK_REAL const PDstandardNth13gt33 = PDstandardNth13(gt33, i, j, k); CCTK_REAL const PDstandardNth23gt33 = PDstandardNth23(gt33, i, j, k); CCTK_REAL const PDstandardNth1phi = PDstandardNth1(phi, i, j, k); CCTK_REAL const PDstandardNth2phi = PDstandardNth2(phi, i, j, k); CCTK_REAL const PDstandardNth3phi = PDstandardNth3(phi, i, j, k); CCTK_REAL const PDstandardNth11phi = PDstandardNth11(phi, i, j, k); CCTK_REAL const PDstandardNth22phi = PDstandardNth22(phi, i, j, k); CCTK_REAL const PDstandardNth33phi = PDstandardNth33(phi, i, j, k); CCTK_REAL const PDstandardNth12phi = PDstandardNth12(phi, i, j, k); CCTK_REAL const PDstandardNth13phi = PDstandardNth13(phi, i, j, k); CCTK_REAL const PDstandardNth23phi = PDstandardNth23(phi, i, j, k); CCTK_REAL const PDstandardNth1Xt1 = PDstandardNth1(Xt1, i, j, k); CCTK_REAL const PDstandardNth2Xt1 = PDstandardNth2(Xt1, i, j, k); CCTK_REAL const PDstandardNth3Xt1 = PDstandardNth3(Xt1, i, j, k); CCTK_REAL const PDstandardNth1Xt2 = PDstandardNth1(Xt2, i, j, k); CCTK_REAL const PDstandardNth2Xt2 = PDstandardNth2(Xt2, i, j, k); CCTK_REAL const PDstandardNth3Xt2 = PDstandardNth3(Xt2, i, j, k); CCTK_REAL const PDstandardNth1Xt3 = PDstandardNth1(Xt3, i, j, k); CCTK_REAL const PDstandardNth2Xt3 = PDstandardNth2(Xt3, i, j, k); CCTK_REAL const PDstandardNth3Xt3 = PDstandardNth3(Xt3, i, j, k); /* Calculate temporaries and grid functions */ CCTK_REAL detgt = 1; CCTK_REAL gtu11 = INV(detgt)*(gt22L*gt33L - SQR(gt23L)); CCTK_REAL gtu12 = (gt13L*gt23L - gt12L*gt33L)*INV(detgt); CCTK_REAL gtu13 = (-(gt13L*gt22L) + gt12L*gt23L)*INV(detgt); CCTK_REAL gtu22 = INV(detgt)*(gt11L*gt33L - SQR(gt13L)); CCTK_REAL gtu23 = (gt12L*gt13L - gt11L*gt23L)*INV(detgt); CCTK_REAL gtu33 = INV(detgt)*(gt11L*gt22L - SQR(gt12L)); CCTK_REAL Gtl111 = khalf*(J11L*PDstandardNth1gt11 + J21L*PDstandardNth2gt11 + J31L*PDstandardNth3gt11); CCTK_REAL Gtl112 = khalf*(J12L*PDstandardNth1gt11 + J22L*PDstandardNth2gt11 + J32L*PDstandardNth3gt11); CCTK_REAL Gtl113 = khalf*(J13L*PDstandardNth1gt11 + J23L*PDstandardNth2gt11 + J33L*PDstandardNth3gt11); CCTK_REAL Gtl122 = J12L*PDstandardNth1gt12 - J11L*khalf*PDstandardNth1gt22 + J22L*PDstandardNth2gt12 - J21L*khalf*PDstandardNth2gt22 + J32L*PDstandardNth3gt12 - J31L*khalf*PDstandardNth3gt22; CCTK_REAL Gtl123 = khalf*(J13L*PDstandardNth1gt12 + J12L*PDstandardNth1gt13 - J11L*PDstandardNth1gt23 + J23L*PDstandardNth2gt12 + J22L*PDstandardNth2gt13 - J21L*PDstandardNth2gt23 + J33L*PDstandardNth3gt12 + J32L*PDstandardNth3gt13 - J31L*PDstandardNth3gt23); CCTK_REAL Gtl133 = J13L*PDstandardNth1gt13 - J11L*khalf*PDstandardNth1gt33 + J23L*PDstandardNth2gt13 - J21L*khalf*PDstandardNth2gt33 + J33L*PDstandardNth3gt13 - J31L*khalf*PDstandardNth3gt33; CCTK_REAL Gtl211 = -(J12L*khalf*PDstandardNth1gt11) + J11L*PDstandardNth1gt12 - J22L*khalf*PDstandardNth2gt11 + J21L*PDstandardNth2gt12 - J32L*khalf*PDstandardNth3gt11 + J31L*PDstandardNth3gt12; CCTK_REAL Gtl212 = khalf*(J11L*PDstandardNth1gt22 + J21L*PDstandardNth2gt22 + J31L*PDstandardNth3gt22); CCTK_REAL Gtl213 = khalf*(J13L*PDstandardNth1gt12 - J12L*PDstandardNth1gt13 + J11L*PDstandardNth1gt23 + J23L*PDstandardNth2gt12 - J22L*PDstandardNth2gt13 + J21L*PDstandardNth2gt23 + J33L*PDstandardNth3gt12 - J32L*PDstandardNth3gt13 + J31L*PDstandardNth3gt23); CCTK_REAL Gtl222 = khalf*(J12L*PDstandardNth1gt22 + J22L*PDstandardNth2gt22 + J32L*PDstandardNth3gt22); CCTK_REAL Gtl223 = khalf*(J13L*PDstandardNth1gt22 + J23L*PDstandardNth2gt22 + J33L*PDstandardNth3gt22); CCTK_REAL Gtl233 = J13L*PDstandardNth1gt23 - J12L*khalf*PDstandardNth1gt33 + J23L*PDstandardNth2gt23 - J22L*khalf*PDstandardNth2gt33 + J33L*PDstandardNth3gt23 - J32L*khalf*PDstandardNth3gt33; CCTK_REAL Gtl311 = -(J13L*khalf*PDstandardNth1gt11) + J11L*PDstandardNth1gt13 - J23L*khalf*PDstandardNth2gt11 + J21L*PDstandardNth2gt13 - J33L*khalf*PDstandardNth3gt11 + J31L*PDstandardNth3gt13; CCTK_REAL Gtl312 = khalf*(-(J13L*PDstandardNth1gt12) + J12L*PDstandardNth1gt13 + J11L*PDstandardNth1gt23 - J23L*PDstandardNth2gt12 + J22L*PDstandardNth2gt13 + J21L*PDstandardNth2gt23 - J33L*PDstandardNth3gt12 + J32L*PDstandardNth3gt13 + J31L*PDstandardNth3gt23); CCTK_REAL Gtl313 = khalf*(J11L*PDstandardNth1gt33 + J21L*PDstandardNth2gt33 + J31L*PDstandardNth3gt33); CCTK_REAL Gtl322 = -(J13L*khalf*PDstandardNth1gt22) + J12L*PDstandardNth1gt23 - J23L*khalf*PDstandardNth2gt22 + J22L*PDstandardNth2gt23 - J33L*khalf*PDstandardNth3gt22 + J32L*PDstandardNth3gt23; CCTK_REAL Gtl323 = khalf*(J12L*PDstandardNth1gt33 + J22L*PDstandardNth2gt33 + J32L*PDstandardNth3gt33); CCTK_REAL Gtl333 = khalf*(J13L*PDstandardNth1gt33 + J23L*PDstandardNth2gt33 + J33L*PDstandardNth3gt33); CCTK_REAL Gtlu111 = Gtl111*gtu11 + Gtl112*gtu12 + Gtl113*gtu13; CCTK_REAL Gtlu112 = Gtl111*gtu12 + Gtl112*gtu22 + Gtl113*gtu23; CCTK_REAL Gtlu113 = Gtl111*gtu13 + Gtl112*gtu23 + Gtl113*gtu33; CCTK_REAL Gtlu121 = Gtl112*gtu11 + Gtl122*gtu12 + Gtl123*gtu13; CCTK_REAL Gtlu122 = Gtl112*gtu12 + Gtl122*gtu22 + Gtl123*gtu23; CCTK_REAL Gtlu123 = Gtl112*gtu13 + Gtl122*gtu23 + Gtl123*gtu33; CCTK_REAL Gtlu131 = Gtl113*gtu11 + Gtl123*gtu12 + Gtl133*gtu13; CCTK_REAL Gtlu132 = Gtl113*gtu12 + Gtl123*gtu22 + Gtl133*gtu23; CCTK_REAL Gtlu133 = Gtl113*gtu13 + Gtl123*gtu23 + Gtl133*gtu33; CCTK_REAL Gtlu211 = Gtl211*gtu11 + Gtl212*gtu12 + Gtl213*gtu13; CCTK_REAL Gtlu212 = Gtl211*gtu12 + Gtl212*gtu22 + Gtl213*gtu23; CCTK_REAL Gtlu213 = Gtl211*gtu13 + Gtl212*gtu23 + Gtl213*gtu33; CCTK_REAL Gtlu221 = Gtl212*gtu11 + Gtl222*gtu12 + Gtl223*gtu13; CCTK_REAL Gtlu222 = Gtl212*gtu12 + Gtl222*gtu22 + Gtl223*gtu23; CCTK_REAL Gtlu223 = Gtl212*gtu13 + Gtl222*gtu23 + Gtl223*gtu33; CCTK_REAL Gtlu231 = Gtl213*gtu11 + Gtl223*gtu12 + Gtl233*gtu13; CCTK_REAL Gtlu232 = Gtl213*gtu12 + Gtl223*gtu22 + Gtl233*gtu23; CCTK_REAL Gtlu233 = Gtl213*gtu13 + Gtl223*gtu23 + Gtl233*gtu33; CCTK_REAL Gtlu311 = Gtl311*gtu11 + Gtl312*gtu12 + Gtl313*gtu13; CCTK_REAL Gtlu312 = Gtl311*gtu12 + Gtl312*gtu22 + Gtl313*gtu23; CCTK_REAL Gtlu313 = Gtl311*gtu13 + Gtl312*gtu23 + Gtl313*gtu33; CCTK_REAL Gtlu321 = Gtl312*gtu11 + Gtl322*gtu12 + Gtl323*gtu13; CCTK_REAL Gtlu322 = Gtl312*gtu12 + Gtl322*gtu22 + Gtl323*gtu23; CCTK_REAL Gtlu323 = Gtl312*gtu13 + Gtl322*gtu23 + Gtl323*gtu33; CCTK_REAL Gtlu331 = Gtl313*gtu11 + Gtl323*gtu12 + Gtl333*gtu13; CCTK_REAL Gtlu332 = Gtl313*gtu12 + Gtl323*gtu22 + Gtl333*gtu23; CCTK_REAL Gtlu333 = Gtl313*gtu13 + Gtl323*gtu23 + Gtl333*gtu33; CCTK_REAL Gt111 = Gtl111*gtu11 + Gtl211*gtu12 + Gtl311*gtu13; CCTK_REAL Gt211 = Gtl111*gtu12 + Gtl211*gtu22 + Gtl311*gtu23; CCTK_REAL Gt311 = Gtl111*gtu13 + Gtl211*gtu23 + Gtl311*gtu33; CCTK_REAL Gt112 = Gtl112*gtu11 + Gtl212*gtu12 + Gtl312*gtu13; CCTK_REAL Gt212 = Gtl112*gtu12 + Gtl212*gtu22 + Gtl312*gtu23; CCTK_REAL Gt312 = Gtl112*gtu13 + Gtl212*gtu23 + Gtl312*gtu33; CCTK_REAL Gt113 = Gtl113*gtu11 + Gtl213*gtu12 + Gtl313*gtu13; CCTK_REAL Gt213 = Gtl113*gtu12 + Gtl213*gtu22 + Gtl313*gtu23; CCTK_REAL Gt313 = Gtl113*gtu13 + Gtl213*gtu23 + Gtl313*gtu33; CCTK_REAL Gt122 = Gtl122*gtu11 + Gtl222*gtu12 + Gtl322*gtu13; CCTK_REAL Gt222 = Gtl122*gtu12 + Gtl222*gtu22 + Gtl322*gtu23; CCTK_REAL Gt322 = Gtl122*gtu13 + Gtl222*gtu23 + Gtl322*gtu33; CCTK_REAL Gt123 = Gtl123*gtu11 + Gtl223*gtu12 + Gtl323*gtu13; CCTK_REAL Gt223 = Gtl123*gtu12 + Gtl223*gtu22 + Gtl323*gtu23; CCTK_REAL Gt323 = Gtl123*gtu13 + Gtl223*gtu23 + Gtl323*gtu33; CCTK_REAL Gt133 = Gtl133*gtu11 + Gtl233*gtu12 + Gtl333*gtu13; CCTK_REAL Gt233 = Gtl133*gtu12 + Gtl233*gtu22 + Gtl333*gtu23; CCTK_REAL Gt333 = Gtl133*gtu13 + Gtl233*gtu23 + Gtl333*gtu33; CCTK_REAL Xtn1 = Gt111*gtu11 + Gt122*gtu22 + 2*(Gt112*gtu12 + Gt113*gtu13 + Gt123*gtu23) + Gt133*gtu33; CCTK_REAL Xtn2 = Gt211*gtu11 + Gt222*gtu22 + 2*(Gt212*gtu12 + Gt213*gtu13 + Gt223*gtu23) + Gt233*gtu33; CCTK_REAL Xtn3 = Gt311*gtu11 + Gt322*gtu22 + 2*(Gt312*gtu12 + Gt313*gtu13 + Gt323*gtu23) + Gt333*gtu33; CCTK_REAL Rt11 = 3*(Gt111*Gtlu111 + Gt112*Gtlu112 + Gt113*Gtlu113) + 2*(Gt211*Gtlu121 + Gt212*Gtlu122 + Gt213*Gtlu123 + Gt311*Gtlu131 + Gt312*Gtlu132 + Gt313*Gtlu133) + Gt211*Gtlu211 + Gt212*Gtlu212 + Gt213*Gtlu213 + Gt311*Gtlu311 + Gt312*Gtlu312 + Gt313*Gtlu313 + J11L*(gt11L*PDstandardNth1Xt1 + gt12L*PDstandardNth1Xt2 + gt13L*PDstandardNth1Xt3) + J21L*(gt11L*PDstandardNth2Xt1 + gt12L*PDstandardNth2Xt2 + gt13L*PDstandardNth2Xt3) + J31L*(gt11L*PDstandardNth3Xt1 + gt12L*PDstandardNth3Xt2 + gt13L*PDstandardNth3Xt3) + Gtl111*Xtn1 + Gtl112*Xtn2 + Gtl113*Xtn3 + khalf*(-2*(gtu12*(J11L*J12L*PDstandardNth11gt11 + J12L*J21L*PDstandardNth12gt11 + J11L*J22L*PDstandardNth12gt11 + J12L*J31L*PDstandardNth13gt11 + J11L*J32L*PDstandardNth13gt11 + dJ112L*PDstandardNth1gt11 + J21L*J22L*PDstandardNth22gt11 + J22L*J31L*PDstandardNth23gt11 + J21L*J32L*PDstandardNth23gt11 + dJ212L*PDstandardNth2gt11 + J31L*J32L*PDstandardNth33gt11 + dJ312L*PDstandardNth3gt11) + gtu13*(J11L*J13L*PDstandardNth11gt11 + J13L*J21L*PDstandardNth12gt11 + J11L*J23L*PDstandardNth12gt11 + J13L*J31L*PDstandardNth13gt11 + J11L*J33L*PDstandardNth13gt11 + dJ113L*PDstandardNth1gt11 + J21L*J23L*PDstandardNth22gt11 + J23L*J31L*PDstandardNth23gt11 + J21L*J33L*PDstandardNth23gt11 + dJ213L*PDstandardNth2gt11 + J31L*J33L*PDstandardNth33gt11 + dJ313L*PDstandardNth3gt11) + gtu23*(J12L*J13L*PDstandardNth11gt11 + J13L*J22L*PDstandardNth12gt11 + J12L*J23L*PDstandardNth12gt11 + J13L*J32L*PDstandardNth13gt11 + J12L*J33L*PDstandardNth13gt11 + dJ123L*PDstandardNth1gt11 + J22L*J23L*PDstandardNth22gt11 + J23L*J32L*PDstandardNth23gt11 + J22L*J33L*PDstandardNth23gt11 + dJ223L*PDstandardNth2gt11 + J32L*J33L*PDstandardNth33gt11 + dJ323L*PDstandardNth3gt11)) - gtu11*(2*J11L*J21L*PDstandardNth12gt11 + 2*J11L*J31L*PDstandardNth13gt11 + dJ111L*PDstandardNth1gt11 + 2*J21L*J31L*PDstandardNth23gt11 + dJ211L*PDstandardNth2gt11 + dJ311L*PDstandardNth3gt11 + PDstandardNth11gt11*SQR(J11L) + PDstandardNth22gt11*SQR(J21L) + PDstandardNth33gt11*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt11 + 2*J12L*J32L*PDstandardNth13gt11 + dJ122L*PDstandardNth1gt11 + 2*J22L*J32L*PDstandardNth23gt11 + dJ222L*PDstandardNth2gt11 + dJ322L*PDstandardNth3gt11 + PDstandardNth11gt11*SQR(J12L) + PDstandardNth22gt11*SQR(J22L) + PDstandardNth33gt11*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt11 + 2*J13L*J33L*PDstandardNth13gt11 + dJ133L*PDstandardNth1gt11 + 2*J23L*J33L*PDstandardNth23gt11 + dJ233L*PDstandardNth2gt11 + dJ333L*PDstandardNth3gt11 + PDstandardNth11gt11*SQR(J13L) + PDstandardNth22gt11*SQR(J23L) + PDstandardNth33gt11*SQR(J33L))); CCTK_REAL Rt12 = Gt122*Gtlu112 + Gt123*Gtlu113 + (Gt111 + Gt212)*Gtlu121 + Gt222*Gtlu122 + (Gt113 + Gt223)*Gtlu123 + Gt322*Gtlu132 + Gt323*Gtlu133 + Gt111*Gtlu211 + Gt112*(Gtlu111 + Gtlu122 + Gtlu212) + Gt113*Gtlu213 + 2*(Gt211*Gtlu221 + Gt212*Gtlu222 + Gt213*Gtlu223) + Gt311*(Gtlu231 + Gtlu321) + Gt312*(Gtlu131 + Gtlu232 + Gtlu322) + Gt313*(Gtlu233 + Gtlu323) + khalf*((gt12L*J11L + gt11L*J12L)*PDstandardNth1Xt1 + (gt22L*J11L + gt12L*J12L)*PDstandardNth1Xt2 + (gt23L*J11L + gt13L*J12L)*PDstandardNth1Xt3 + (gt12L*J21L + gt11L*J22L)*PDstandardNth2Xt1 + (gt22L*J21L + gt12L*J22L)*PDstandardNth2Xt2 + (gt23L*J21L + gt13L*J22L)*PDstandardNth2Xt3 - 2*(gtu12*(J11L*J12L*PDstandardNth11gt12 + J12L*J21L*PDstandardNth12gt12 + J11L*J22L*PDstandardNth12gt12 + J12L*J31L*PDstandardNth13gt12 + J11L*J32L*PDstandardNth13gt12 + dJ112L*PDstandardNth1gt12 + J21L*J22L*PDstandardNth22gt12 + J22L*J31L*PDstandardNth23gt12 + J21L*J32L*PDstandardNth23gt12 + dJ212L*PDstandardNth2gt12 + J31L*J32L*PDstandardNth33gt12 + dJ312L*PDstandardNth3gt12) + gtu13*(J11L*J13L*PDstandardNth11gt12 + J13L*J21L*PDstandardNth12gt12 + J11L*J23L*PDstandardNth12gt12 + J13L*J31L*PDstandardNth13gt12 + J11L*J33L*PDstandardNth13gt12 + dJ113L*PDstandardNth1gt12 + J21L*J23L*PDstandardNth22gt12 + J23L*J31L*PDstandardNth23gt12 + J21L*J33L*PDstandardNth23gt12 + dJ213L*PDstandardNth2gt12 + J31L*J33L*PDstandardNth33gt12 + dJ313L*PDstandardNth3gt12) + gtu23*(J12L*J13L*PDstandardNth11gt12 + J13L*J22L*PDstandardNth12gt12 + J12L*J23L*PDstandardNth12gt12 + J13L*J32L*PDstandardNth13gt12 + J12L*J33L*PDstandardNth13gt12 + dJ123L*PDstandardNth1gt12 + J22L*J23L*PDstandardNth22gt12 + J23L*J32L*PDstandardNth23gt12 + J22L*J33L*PDstandardNth23gt12 + dJ223L*PDstandardNth2gt12 + J32L*J33L*PDstandardNth33gt12 + dJ323L*PDstandardNth3gt12)) + (gt12L*J31L + gt11L*J32L)*PDstandardNth3Xt1 + (gt22L*J31L + gt12L*J32L)*PDstandardNth3Xt2 + (gt23L*J31L + gt13L*J32L)*PDstandardNth3Xt3 + (Gtl112 + Gtl211)*Xtn1 + (Gtl122 + Gtl212)*Xtn2 + (Gtl123 + Gtl213)*Xtn3 - gtu11*(2*J11L*J21L*PDstandardNth12gt12 + 2*J11L*J31L*PDstandardNth13gt12 + dJ111L*PDstandardNth1gt12 + 2*J21L*J31L*PDstandardNth23gt12 + dJ211L*PDstandardNth2gt12 + dJ311L*PDstandardNth3gt12 + PDstandardNth11gt12*SQR(J11L) + PDstandardNth22gt12*SQR(J21L) + PDstandardNth33gt12*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt12 + 2*J12L*J32L*PDstandardNth13gt12 + dJ122L*PDstandardNth1gt12 + 2*J22L*J32L*PDstandardNth23gt12 + dJ222L*PDstandardNth2gt12 + dJ322L*PDstandardNth3gt12 + PDstandardNth11gt12*SQR(J12L) + PDstandardNth22gt12*SQR(J22L) + PDstandardNth33gt12*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt12 + 2*J13L*J33L*PDstandardNth13gt12 + dJ133L*PDstandardNth1gt12 + 2*J23L*J33L*PDstandardNth23gt12 + dJ233L*PDstandardNth2gt12 + dJ333L*PDstandardNth3gt12 + PDstandardNth11gt12*SQR(J13L) + PDstandardNth22gt12*SQR(J23L) + PDstandardNth33gt12*SQR(J33L))); CCTK_REAL Rt13 = Gt123*Gtlu112 + Gt133*Gtlu113 + Gt223*Gtlu122 + Gt233*Gtlu123 + (Gt111 + Gt313)*Gtlu131 + (Gt112 + Gt323)*Gtlu132 + Gt333*Gtlu133 + Gt111*Gtlu311 + Gt112*Gtlu312 + Gt113*(Gtlu111 + Gtlu133 + Gtlu313) + Gt211*(Gtlu231 + Gtlu321) + Gt212*(Gtlu232 + Gtlu322) + Gt213*(Gtlu121 + Gtlu233 + Gtlu323) + 2*(Gt311*Gtlu331 + Gt312*Gtlu332 + Gt313*Gtlu333) + khalf*((gt13L*J11L + gt11L*J13L)*PDstandardNth1Xt1 + (gt23L*J11L + gt12L*J13L)*PDstandardNth1Xt2 + (gt33L*J11L + gt13L*J13L)*PDstandardNth1Xt3 + (gt13L*J21L + gt11L*J23L)*PDstandardNth2Xt1 + (gt23L*J21L + gt12L*J23L)*PDstandardNth2Xt2 + (gt33L*J21L + gt13L*J23L)*PDstandardNth2Xt3 - 2*(gtu12*(J11L*J12L*PDstandardNth11gt13 + J12L*J21L*PDstandardNth12gt13 + J11L*J22L*PDstandardNth12gt13 + J12L*J31L*PDstandardNth13gt13 + J11L*J32L*PDstandardNth13gt13 + dJ112L*PDstandardNth1gt13 + J21L*J22L*PDstandardNth22gt13 + J22L*J31L*PDstandardNth23gt13 + J21L*J32L*PDstandardNth23gt13 + dJ212L*PDstandardNth2gt13 + J31L*J32L*PDstandardNth33gt13 + dJ312L*PDstandardNth3gt13) + gtu13*(J11L*J13L*PDstandardNth11gt13 + J13L*J21L*PDstandardNth12gt13 + J11L*J23L*PDstandardNth12gt13 + J13L*J31L*PDstandardNth13gt13 + J11L*J33L*PDstandardNth13gt13 + dJ113L*PDstandardNth1gt13 + J21L*J23L*PDstandardNth22gt13 + J23L*J31L*PDstandardNth23gt13 + J21L*J33L*PDstandardNth23gt13 + dJ213L*PDstandardNth2gt13 + J31L*J33L*PDstandardNth33gt13 + dJ313L*PDstandardNth3gt13) + gtu23*(J12L*J13L*PDstandardNth11gt13 + J13L*J22L*PDstandardNth12gt13 + J12L*J23L*PDstandardNth12gt13 + J13L*J32L*PDstandardNth13gt13 + J12L*J33L*PDstandardNth13gt13 + dJ123L*PDstandardNth1gt13 + J22L*J23L*PDstandardNth22gt13 + J23L*J32L*PDstandardNth23gt13 + J22L*J33L*PDstandardNth23gt13 + dJ223L*PDstandardNth2gt13 + J32L*J33L*PDstandardNth33gt13 + dJ323L*PDstandardNth3gt13)) + (gt13L*J31L + gt11L*J33L)*PDstandardNth3Xt1 + (gt23L*J31L + gt12L*J33L)*PDstandardNth3Xt2 + (gt33L*J31L + gt13L*J33L)*PDstandardNth3Xt3 + (Gtl113 + Gtl311)*Xtn1 + (Gtl123 + Gtl312)*Xtn2 + (Gtl133 + Gtl313)*Xtn3 - gtu11*(2*J11L*J21L*PDstandardNth12gt13 + 2*J11L*J31L*PDstandardNth13gt13 + dJ111L*PDstandardNth1gt13 + 2*J21L*J31L*PDstandardNth23gt13 + dJ211L*PDstandardNth2gt13 + dJ311L*PDstandardNth3gt13 + PDstandardNth11gt13*SQR(J11L) + PDstandardNth22gt13*SQR(J21L) + PDstandardNth33gt13*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt13 + 2*J12L*J32L*PDstandardNth13gt13 + dJ122L*PDstandardNth1gt13 + 2*J22L*J32L*PDstandardNth23gt13 + dJ222L*PDstandardNth2gt13 + dJ322L*PDstandardNth3gt13 + PDstandardNth11gt13*SQR(J12L) + PDstandardNth22gt13*SQR(J22L) + PDstandardNth33gt13*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt13 + 2*J13L*J33L*PDstandardNth13gt13 + dJ133L*PDstandardNth1gt13 + 2*J23L*J33L*PDstandardNth23gt13 + dJ233L*PDstandardNth2gt13 + dJ333L*PDstandardNth3gt13 + PDstandardNth11gt13*SQR(J13L) + PDstandardNth22gt13*SQR(J23L) + PDstandardNth33gt13*SQR(J33L))); CCTK_REAL Rt22 = Gt112*(Gtlu121 + 2*Gtlu211) + Gt122*(Gtlu122 + 2*Gtlu212) + Gt123*(Gtlu123 + 2*Gtlu213) + 3*(Gt212*Gtlu221 + Gt222*Gtlu222 + Gt223*Gtlu223) + 2*(Gt312*Gtlu231 + Gt322*Gtlu232 + Gt323*Gtlu233) + Gt312*Gtlu321 + Gt322*Gtlu322 + Gt323*Gtlu323 + J12L*(gt12L*PDstandardNth1Xt1 + gt22L*PDstandardNth1Xt2 + gt23L*PDstandardNth1Xt3) + J22L*(gt12L*PDstandardNth2Xt1 + gt22L*PDstandardNth2Xt2 + gt23L*PDstandardNth2Xt3) + J32L*(gt12L*PDstandardNth3Xt1 + gt22L*PDstandardNth3Xt2 + gt23L*PDstandardNth3Xt3) + Gtl212*Xtn1 + Gtl222*Xtn2 + Gtl223*Xtn3 + khalf*(-2*(gtu12*(J11L*J12L*PDstandardNth11gt22 + J12L*J21L*PDstandardNth12gt22 + J11L*J22L*PDstandardNth12gt22 + J12L*J31L*PDstandardNth13gt22 + J11L*J32L*PDstandardNth13gt22 + dJ112L*PDstandardNth1gt22 + J21L*J22L*PDstandardNth22gt22 + J22L*J31L*PDstandardNth23gt22 + J21L*J32L*PDstandardNth23gt22 + dJ212L*PDstandardNth2gt22 + J31L*J32L*PDstandardNth33gt22 + dJ312L*PDstandardNth3gt22) + gtu13*(J11L*J13L*PDstandardNth11gt22 + J13L*J21L*PDstandardNth12gt22 + J11L*J23L*PDstandardNth12gt22 + J13L*J31L*PDstandardNth13gt22 + J11L*J33L*PDstandardNth13gt22 + dJ113L*PDstandardNth1gt22 + J21L*J23L*PDstandardNth22gt22 + J23L*J31L*PDstandardNth23gt22 + J21L*J33L*PDstandardNth23gt22 + dJ213L*PDstandardNth2gt22 + J31L*J33L*PDstandardNth33gt22 + dJ313L*PDstandardNth3gt22) + gtu23*(J12L*J13L*PDstandardNth11gt22 + J13L*J22L*PDstandardNth12gt22 + J12L*J23L*PDstandardNth12gt22 + J13L*J32L*PDstandardNth13gt22 + J12L*J33L*PDstandardNth13gt22 + dJ123L*PDstandardNth1gt22 + J22L*J23L*PDstandardNth22gt22 + J23L*J32L*PDstandardNth23gt22 + J22L*J33L*PDstandardNth23gt22 + dJ223L*PDstandardNth2gt22 + J32L*J33L*PDstandardNth33gt22 + dJ323L*PDstandardNth3gt22)) - gtu11*(2*J11L*J21L*PDstandardNth12gt22 + 2*J11L*J31L*PDstandardNth13gt22 + dJ111L*PDstandardNth1gt22 + 2*J21L*J31L*PDstandardNth23gt22 + dJ211L*PDstandardNth2gt22 + dJ311L*PDstandardNth3gt22 + PDstandardNth11gt22*SQR(J11L) + PDstandardNth22gt22*SQR(J21L) + PDstandardNth33gt22*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt22 + 2*J12L*J32L*PDstandardNth13gt22 + dJ122L*PDstandardNth1gt22 + 2*J22L*J32L*PDstandardNth23gt22 + dJ222L*PDstandardNth2gt22 + dJ322L*PDstandardNth3gt22 + PDstandardNth11gt22*SQR(J12L) + PDstandardNth22gt22*SQR(J22L) + PDstandardNth33gt22*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt22 + 2*J13L*J33L*PDstandardNth13gt22 + dJ133L*PDstandardNth1gt22 + 2*J23L*J33L*PDstandardNth23gt22 + dJ233L*PDstandardNth2gt22 + dJ333L*PDstandardNth3gt22 + PDstandardNth11gt22*SQR(J13L) + PDstandardNth22gt22*SQR(J23L) + PDstandardNth33gt22*SQR(J33L))); CCTK_REAL Rt23 = Gt113*Gtlu211 + Gt133*Gtlu213 + Gt213*Gtlu221 + Gt233*Gtlu223 + (Gt212 + Gt313)*Gtlu231 + (Gt222 + Gt323)*Gtlu232 + Gt333*Gtlu233 + Gt112*(Gtlu131 + Gtlu311) + Gt122*(Gtlu132 + Gtlu312) + Gt123*(Gtlu133 + Gtlu212 + Gtlu313) + Gt212*Gtlu321 + Gt222*Gtlu322 + Gt223*(Gtlu222 + Gtlu233 + Gtlu323) + 2*(Gt312*Gtlu331 + Gt322*Gtlu332 + Gt323*Gtlu333) + khalf*((gt13L*J12L + gt12L*J13L)*PDstandardNth1Xt1 + (gt23L*J12L + gt22L*J13L)*PDstandardNth1Xt2 + (gt33L*J12L + gt23L*J13L)*PDstandardNth1Xt3 + (gt13L*J22L + gt12L*J23L)*PDstandardNth2Xt1 + (gt23L*J22L + gt22L*J23L)*PDstandardNth2Xt2 + (gt33L*J22L + gt23L*J23L)*PDstandardNth2Xt3 - 2*(gtu12*(J11L*J12L*PDstandardNth11gt23 + J12L*J21L*PDstandardNth12gt23 + J11L*J22L*PDstandardNth12gt23 + J12L*J31L*PDstandardNth13gt23 + J11L*J32L*PDstandardNth13gt23 + dJ112L*PDstandardNth1gt23 + J21L*J22L*PDstandardNth22gt23 + J22L*J31L*PDstandardNth23gt23 + J21L*J32L*PDstandardNth23gt23 + dJ212L*PDstandardNth2gt23 + J31L*J32L*PDstandardNth33gt23 + dJ312L*PDstandardNth3gt23) + gtu13*(J11L*J13L*PDstandardNth11gt23 + J13L*J21L*PDstandardNth12gt23 + J11L*J23L*PDstandardNth12gt23 + J13L*J31L*PDstandardNth13gt23 + J11L*J33L*PDstandardNth13gt23 + dJ113L*PDstandardNth1gt23 + J21L*J23L*PDstandardNth22gt23 + J23L*J31L*PDstandardNth23gt23 + J21L*J33L*PDstandardNth23gt23 + dJ213L*PDstandardNth2gt23 + J31L*J33L*PDstandardNth33gt23 + dJ313L*PDstandardNth3gt23) + gtu23*(J12L*J13L*PDstandardNth11gt23 + J13L*J22L*PDstandardNth12gt23 + J12L*J23L*PDstandardNth12gt23 + J13L*J32L*PDstandardNth13gt23 + J12L*J33L*PDstandardNth13gt23 + dJ123L*PDstandardNth1gt23 + J22L*J23L*PDstandardNth22gt23 + J23L*J32L*PDstandardNth23gt23 + J22L*J33L*PDstandardNth23gt23 + dJ223L*PDstandardNth2gt23 + J32L*J33L*PDstandardNth33gt23 + dJ323L*PDstandardNth3gt23)) + (gt13L*J32L + gt12L*J33L)*PDstandardNth3Xt1 + (gt23L*J32L + gt22L*J33L)*PDstandardNth3Xt2 + (gt33L*J32L + gt23L*J33L)*PDstandardNth3Xt3 + (Gtl213 + Gtl312)*Xtn1 + (Gtl223 + Gtl322)*Xtn2 + (Gtl233 + Gtl323)*Xtn3 - gtu11*(2*J11L*J21L*PDstandardNth12gt23 + 2*J11L*J31L*PDstandardNth13gt23 + dJ111L*PDstandardNth1gt23 + 2*J21L*J31L*PDstandardNth23gt23 + dJ211L*PDstandardNth2gt23 + dJ311L*PDstandardNth3gt23 + PDstandardNth11gt23*SQR(J11L) + PDstandardNth22gt23*SQR(J21L) + PDstandardNth33gt23*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt23 + 2*J12L*J32L*PDstandardNth13gt23 + dJ122L*PDstandardNth1gt23 + 2*J22L*J32L*PDstandardNth23gt23 + dJ222L*PDstandardNth2gt23 + dJ322L*PDstandardNth3gt23 + PDstandardNth11gt23*SQR(J12L) + PDstandardNth22gt23*SQR(J22L) + PDstandardNth33gt23*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt23 + 2*J13L*J33L*PDstandardNth13gt23 + dJ133L*PDstandardNth1gt23 + 2*J23L*J33L*PDstandardNth23gt23 + dJ233L*PDstandardNth2gt23 + dJ333L*PDstandardNth3gt23 + PDstandardNth11gt23*SQR(J13L) + PDstandardNth22gt23*SQR(J23L) + PDstandardNth33gt23*SQR(J33L))); CCTK_REAL Rt33 = Gt113*(Gtlu131 + 2*Gtlu311) + Gt123*(Gtlu132 + 2*Gtlu312) + Gt133*(Gtlu133 + 2*Gtlu313) + Gt213*(Gtlu231 + 2*Gtlu321) + Gt223*(Gtlu232 + 2*Gtlu322) + Gt233*(Gtlu233 + 2*Gtlu323) + 3*(Gt313*Gtlu331 + Gt323*Gtlu332 + Gt333*Gtlu333) + J13L*(gt13L*PDstandardNth1Xt1 + gt23L*PDstandardNth1Xt2 + gt33L*PDstandardNth1Xt3) + J23L*(gt13L*PDstandardNth2Xt1 + gt23L*PDstandardNth2Xt2 + gt33L*PDstandardNth2Xt3) + J33L*(gt13L*PDstandardNth3Xt1 + gt23L*PDstandardNth3Xt2 + gt33L*PDstandardNth3Xt3) + Gtl313*Xtn1 + Gtl323*Xtn2 + Gtl333*Xtn3 + khalf*(-2*(gtu12*(J11L*J12L*PDstandardNth11gt33 + J12L*J21L*PDstandardNth12gt33 + J11L*J22L*PDstandardNth12gt33 + J12L*J31L*PDstandardNth13gt33 + J11L*J32L*PDstandardNth13gt33 + dJ112L*PDstandardNth1gt33 + J21L*J22L*PDstandardNth22gt33 + J22L*J31L*PDstandardNth23gt33 + J21L*J32L*PDstandardNth23gt33 + dJ212L*PDstandardNth2gt33 + J31L*J32L*PDstandardNth33gt33 + dJ312L*PDstandardNth3gt33) + gtu13*(J11L*J13L*PDstandardNth11gt33 + J13L*J21L*PDstandardNth12gt33 + J11L*J23L*PDstandardNth12gt33 + J13L*J31L*PDstandardNth13gt33 + J11L*J33L*PDstandardNth13gt33 + dJ113L*PDstandardNth1gt33 + J21L*J23L*PDstandardNth22gt33 + J23L*J31L*PDstandardNth23gt33 + J21L*J33L*PDstandardNth23gt33 + dJ213L*PDstandardNth2gt33 + J31L*J33L*PDstandardNth33gt33 + dJ313L*PDstandardNth3gt33) + gtu23*(J12L*J13L*PDstandardNth11gt33 + J13L*J22L*PDstandardNth12gt33 + J12L*J23L*PDstandardNth12gt33 + J13L*J32L*PDstandardNth13gt33 + J12L*J33L*PDstandardNth13gt33 + dJ123L*PDstandardNth1gt33 + J22L*J23L*PDstandardNth22gt33 + J23L*J32L*PDstandardNth23gt33 + J22L*J33L*PDstandardNth23gt33 + dJ223L*PDstandardNth2gt33 + J32L*J33L*PDstandardNth33gt33 + dJ323L*PDstandardNth3gt33)) - gtu11*(2*J11L*J21L*PDstandardNth12gt33 + 2*J11L*J31L*PDstandardNth13gt33 + dJ111L*PDstandardNth1gt33 + 2*J21L*J31L*PDstandardNth23gt33 + dJ211L*PDstandardNth2gt33 + dJ311L*PDstandardNth3gt33 + PDstandardNth11gt33*SQR(J11L) + PDstandardNth22gt33*SQR(J21L) + PDstandardNth33gt33*SQR(J31L)) - gtu22*(2*J12L*J22L*PDstandardNth12gt33 + 2*J12L*J32L*PDstandardNth13gt33 + dJ122L*PDstandardNth1gt33 + 2*J22L*J32L*PDstandardNth23gt33 + dJ222L*PDstandardNth2gt33 + dJ322L*PDstandardNth3gt33 + PDstandardNth11gt33*SQR(J12L) + PDstandardNth22gt33*SQR(J22L) + PDstandardNth33gt33*SQR(J32L)) - gtu33*(2*J13L*J23L*PDstandardNth12gt33 + 2*J13L*J33L*PDstandardNth13gt33 + dJ133L*PDstandardNth1gt33 + 2*J23L*J33L*PDstandardNth23gt33 + dJ233L*PDstandardNth2gt33 + dJ333L*PDstandardNth3gt33 + PDstandardNth11gt33*SQR(J13L) + PDstandardNth22gt33*SQR(J23L) + PDstandardNth33gt33*SQR(J33L))); CCTK_REAL fac1 = IfThen(conformalMethod,-(khalf*INV(phiL)),1); CCTK_REAL cdphi1 = fac1*(J11L*PDstandardNth1phi + J21L*PDstandardNth2phi + J31L*PDstandardNth3phi); CCTK_REAL cdphi2 = fac1*(J12L*PDstandardNth1phi + J22L*PDstandardNth2phi + J32L*PDstandardNth3phi); CCTK_REAL cdphi3 = fac1*(J13L*PDstandardNth1phi + J23L*PDstandardNth2phi + J33L*PDstandardNth3phi); CCTK_REAL fac2 = IfThen(conformalMethod,khalf*pow(phiL,-2),0); CCTK_REAL cdphi211 = fac1*((dJ111L - Gt111*J11L - Gt211*J12L - Gt311*J13L)*PDstandardNth1phi + 2*(J11L*(J21L*PDstandardNth12phi + J31L*PDstandardNth13phi) + J21L*J31L*PDstandardNth23phi) + (dJ211L - Gt111*J21L - Gt211*J22L - Gt311*J23L)*PDstandardNth2phi + (dJ311L - Gt111*J31L - Gt211*J32L - Gt311*J33L)*PDstandardNth3phi + PDstandardNth11phi*SQR(J11L) + PDstandardNth22phi*SQR(J21L) + PDstandardNth33phi*SQR(J31L)) + fac2*SQR(J11L*PDstandardNth1phi + J21L*PDstandardNth2phi + J31L*PDstandardNth3phi); CCTK_REAL cdphi212 = fac2*(J11L*PDstandardNth1phi + J21L*PDstandardNth2phi + J31L*PDstandardNth3phi)*(J12L*PDstandardNth1phi + J22L*PDstandardNth2phi + J32L*PDstandardNth3phi) + fac1*(J12L*(J11L*PDstandardNth11phi + J21L*PDstandardNth12phi + J31L*PDstandardNth13phi) + J11L*(J22L*PDstandardNth12phi + J32L*PDstandardNth13phi) + (dJ112L - Gt112*J11L - Gt212*J12L - Gt312*J13L)*PDstandardNth1phi + J22L*(J21L*PDstandardNth22phi + J31L*PDstandardNth23phi) + (dJ212L - Gt112*J21L - Gt212*J22L - Gt312*J23L)*PDstandardNth2phi + J32L*(J21L*PDstandardNth23phi + J31L*PDstandardNth33phi) + (dJ312L - Gt112*J31L - Gt212*J32L - Gt312*J33L)*PDstandardNth3phi); CCTK_REAL cdphi213 = fac2*(J11L*PDstandardNth1phi + J21L*PDstandardNth2phi + J31L*PDstandardNth3phi)*(J13L*PDstandardNth1phi + J23L*PDstandardNth2phi + J33L*PDstandardNth3phi) + fac1*(J13L*(J11L*PDstandardNth11phi + J21L*PDstandardNth12phi + J31L*PDstandardNth13phi) + J11L*(J23L*PDstandardNth12phi + J33L*PDstandardNth13phi) + (dJ113L - Gt113*J11L - Gt213*J12L - Gt313*J13L)*PDstandardNth1phi + J23L*(J21L*PDstandardNth22phi + J31L*PDstandardNth23phi) + (dJ213L - Gt113*J21L - Gt213*J22L - Gt313*J23L)*PDstandardNth2phi + J33L*(J21L*PDstandardNth23phi + J31L*PDstandardNth33phi) + (dJ313L - Gt113*J31L - Gt213*J32L - Gt313*J33L)*PDstandardNth3phi); CCTK_REAL cdphi222 = fac1*((dJ122L - Gt122*J11L - Gt222*J12L - Gt322*J13L)*PDstandardNth1phi + 2*(J12L*(J22L*PDstandardNth12phi + J32L*PDstandardNth13phi) + J22L*J32L*PDstandardNth23phi) + (dJ222L - Gt122*J21L - Gt222*J22L - Gt322*J23L)*PDstandardNth2phi + (dJ322L - Gt122*J31L - Gt222*J32L - Gt322*J33L)*PDstandardNth3phi + PDstandardNth11phi*SQR(J12L) + PDstandardNth22phi*SQR(J22L) + PDstandardNth33phi*SQR(J32L)) + fac2*SQR(J12L*PDstandardNth1phi + J22L*PDstandardNth2phi + J32L*PDstandardNth3phi); CCTK_REAL cdphi223 = fac2*(J12L*PDstandardNth1phi + J22L*PDstandardNth2phi + J32L*PDstandardNth3phi)*(J13L*PDstandardNth1phi + J23L*PDstandardNth2phi + J33L*PDstandardNth3phi) + fac1*(J13L*(J12L*PDstandardNth11phi + J22L*PDstandardNth12phi + J32L*PDstandardNth13phi) + J12L*(J23L*PDstandardNth12phi + J33L*PDstandardNth13phi) + (dJ123L - Gt123*J11L - Gt223*J12L - Gt323*J13L)*PDstandardNth1phi + J23L*(J22L*PDstandardNth22phi + J32L*PDstandardNth23phi) + (dJ223L - Gt123*J21L - Gt223*J22L - Gt323*J23L)*PDstandardNth2phi + J33L*(J22L*PDstandardNth23phi + J32L*PDstandardNth33phi) + (dJ323L - Gt123*J31L - Gt223*J32L - Gt323*J33L)*PDstandardNth3phi); CCTK_REAL cdphi233 = fac1*((dJ133L - Gt133*J11L - Gt233*J12L - Gt333*J13L)*PDstandardNth1phi + 2*(J13L*(J23L*PDstandardNth12phi + J33L*PDstandardNth13phi) + J23L*J33L*PDstandardNth23phi) + (dJ233L - Gt133*J21L - Gt233*J22L - Gt333*J23L)*PDstandardNth2phi + (dJ333L - Gt133*J31L - Gt233*J32L - Gt333*J33L)*PDstandardNth3phi + PDstandardNth11phi*SQR(J13L) + PDstandardNth22phi*SQR(J23L) + PDstandardNth33phi*SQR(J33L)) + fac2*SQR(J13L*PDstandardNth1phi + J23L*PDstandardNth2phi + J33L*PDstandardNth3phi); CCTK_REAL Rphi11 = -2*(cdphi211 + 2*(-1 + gt11L*gtu11)*SQR(cdphi1) + gt11L*(cdphi211*gtu11 + 4*(cdphi1*(cdphi2*gtu12 + cdphi3*gtu13) + cdphi2*cdphi3*gtu23) + cdphi233*gtu33 + gtu22*(cdphi222 + 2*SQR(cdphi2)) + 2*(cdphi212*gtu12 + cdphi213*gtu13 + cdphi223*gtu23 + gtu33*SQR(cdphi3)))); CCTK_REAL Rphi12 = -2*(cdphi212 + cdphi1*(cdphi2*(-2 + 4*gt12L*gtu12) + 4*cdphi3*gt12L*gtu13) + gt12L*(cdphi211*gtu11 + 4*cdphi2*cdphi3*gtu23 + 2*(cdphi212*gtu12 + cdphi213*gtu13 + cdphi223*gtu23 + gtu11*SQR(cdphi1)) + gtu22*(cdphi222 + 2*SQR(cdphi2)) + gtu33*(cdphi233 + 2*SQR(cdphi3)))); CCTK_REAL Rphi13 = -2*(cdphi213 + cdphi1*(4*cdphi2*gt13L*gtu12 + cdphi3*(-2 + 4*gt13L*gtu13)) + gt13L*(cdphi211*gtu11 + 4*cdphi2*cdphi3*gtu23 + 2*(cdphi212*gtu12 + cdphi213*gtu13 + cdphi223*gtu23 + gtu11*SQR(cdphi1)) + gtu22*(cdphi222 + 2*SQR(cdphi2)) + gtu33*(cdphi233 + 2*SQR(cdphi3)))); CCTK_REAL Rphi22 = -2*(cdphi222 + 2*(-1 + gt22L*gtu22)*SQR(cdphi2) + gt22L*(cdphi222*gtu22 + 4*(cdphi1*cdphi3*gtu13 + cdphi2*(cdphi1*gtu12 + cdphi3*gtu23)) + cdphi233*gtu33 + gtu11*(cdphi211 + 2*SQR(cdphi1)) + 2*(cdphi212*gtu12 + cdphi213*gtu13 + cdphi223*gtu23 + gtu33*SQR(cdphi3)))); CCTK_REAL Rphi23 = -2*(cdphi223 + cdphi2*(4*cdphi1*gt23L*gtu12 + cdphi3*(-2 + 4*gt23L*gtu23)) + gt23L*(4*cdphi1*cdphi3*gtu13 + cdphi222*gtu22 + gtu11*(cdphi211 + 2*SQR(cdphi1)) + 2*(cdphi212*gtu12 + cdphi213*gtu13 + cdphi223*gtu23 + gtu22*SQR(cdphi2)) + gtu33*(cdphi233 + 2*SQR(cdphi3)))); CCTK_REAL Rphi33 = -2*(cdphi233 + gt33L*((4*cdphi1*cdphi2 + 2*cdphi212)*gtu12 + 4*cdphi3*(cdphi1*gtu13 + cdphi2*gtu23) + 2*(cdphi213*gtu13 + cdphi223*gtu23) + cdphi233*gtu33 + gtu11*(cdphi211 + 2*SQR(cdphi1)) + gtu22*(cdphi222 + 2*SQR(cdphi2))) + 2*(-1 + gt33L*gtu33)*SQR(cdphi3)); CCTK_REAL e4phi = IfThen(conformalMethod,pow(phiL,-2),exp(4*phiL)); CCTK_REAL em4phi = INV(e4phi); CCTK_REAL gu11 = em4phi*gtu11; CCTK_REAL gu12 = em4phi*gtu12; CCTK_REAL gu13 = em4phi*gtu13; CCTK_REAL gu22 = em4phi*gtu22; CCTK_REAL gu23 = em4phi*gtu23; CCTK_REAL gu33 = em4phi*gtu33; CCTK_REAL R11 = Rphi11 + Rt11; CCTK_REAL R12 = Rphi12 + Rt12; CCTK_REAL R13 = Rphi13 + Rt13; CCTK_REAL R22 = Rphi22 + Rt22; CCTK_REAL R23 = Rphi23 + Rt23; CCTK_REAL R33 = Rphi33 + Rt33; CCTK_REAL trR = gu11*R11 + gu22*R22 + 2*(gu12*R12 + gu13*R13 + gu23*R23) + gu33*R33; CCTK_REAL Atm11 = At11L*gtu11 + At12L*gtu12 + At13L*gtu13; CCTK_REAL Atm21 = At11L*gtu12 + At12L*gtu22 + At13L*gtu23; CCTK_REAL Atm31 = At11L*gtu13 + At12L*gtu23 + At13L*gtu33; CCTK_REAL Atm12 = At12L*gtu11 + At22L*gtu12 + At23L*gtu13; CCTK_REAL Atm22 = At12L*gtu12 + At22L*gtu22 + At23L*gtu23; CCTK_REAL Atm32 = At12L*gtu13 + At22L*gtu23 + At23L*gtu33; CCTK_REAL Atm13 = At13L*gtu11 + At23L*gtu12 + At33L*gtu13; CCTK_REAL Atm23 = At13L*gtu12 + At23L*gtu22 + At33L*gtu23; CCTK_REAL Atm33 = At13L*gtu13 + At23L*gtu23 + At33L*gtu33; CCTK_REAL rho = pow(alphaL,-2)*(eTttL - 2*(beta2L*eTtyL + beta3L*eTtzL) + 2*(beta1L*(-eTtxL + beta2L*eTxyL + beta3L*eTxzL) + beta2L*beta3L*eTyzL) + eTxxL*SQR(beta1L) + eTyyL*SQR(beta2L) + eTzzL*SQR(beta3L)); CCTK_REAL HL = -2.*(Atm12*Atm21 + Atm13*Atm31 + Atm23*Atm32) - 50.26548245743669181540229413247204614715*rho + trR - 1.*(SQR(Atm11) + SQR(Atm22) + SQR(Atm33)) + 0.6666666666666666666666666666666666666667*SQR(trKL); /* Copy local copies back to grid functions */ H[index] = HL; } LC_ENDLOOP3 (ML_BSSN_MP_O8_constraints1); } void ML_BSSN_MP_O8_constraints1(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; GenericFD_LoopOverInterior(cctkGH, &ML_BSSN_MP_O8_constraints1_Body); }