/* File produced by Kranc */ #define KRANC_C #include #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 QAD(x) (SQR(SQR(x))) #define INV(x) ((1.0) / (x)) #define SQR(x) ((x) * (x)) #define CUB(x) ((x) * (x) * (x)) extern "C" void psis_calc_Nth_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 */, "WeylScal4::Psi4i_group","flat"); if (ierr < 0) CCTK_WARN(1, "Failed to register flat BC for WeylScal4::Psi4i_group."); ierr = Boundary_SelectGroupForBC(cctkGH, CCTK_ALL_FACES, GenericFD_GetBoundaryWidth(cctkGH), -1 /* no table */, "WeylScal4::Psi4r_group","flat"); if (ierr < 0) CCTK_WARN(1, "Failed to register flat BC for WeylScal4::Psi4r_group."); return; } static void psis_calc_Nth_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 psis_calc_Nth_Body"); } if (cctk_iteration % psis_calc_Nth_calc_every != psis_calc_Nth_calc_offset) { return; } const char *groups[] = {"admbase::curv","admbase::metric","grid::coordinates","WeylScal4::Psi4i_group","WeylScal4::Psi4r_group"}; GenericFD_AssertGroupStorage(cctkGH, "psis_calc_Nth", 5, groups); switch(fdOrder) { case 2: GenericFD_EnsureStencilFits(cctkGH, "psis_calc_Nth", 1, 1, 1); break; case 4: GenericFD_EnsureStencilFits(cctkGH, "psis_calc_Nth", 2, 2, 2); break; case 6: GenericFD_EnsureStencilFits(cctkGH, "psis_calc_Nth", 3, 3, 3); break; case 8: GenericFD_EnsureStencilFits(cctkGH, "psis_calc_Nth", 4, 4, 4); break; } /* Include user-supplied include files */ /* Initialise finite differencing variables */ ptrdiff_t const di = 1; ptrdiff_t const dj = CCTK_GFINDEX3D(cctkGH,0,1,0) - CCTK_GFINDEX3D(cctkGH,0,0,0); ptrdiff_t const dk = CCTK_GFINDEX3D(cctkGH,0,0,1) - CCTK_GFINDEX3D(cctkGH,0,0,0); ptrdiff_t const cdi = sizeof(CCTK_REAL) * di; ptrdiff_t const cdj = sizeof(CCTK_REAL) * dj; ptrdiff_t const cdk = sizeof(CCTK_REAL) * dk; CCTK_REAL const dx = ToReal(CCTK_DELTA_SPACE(0)); CCTK_REAL const dy = ToReal(CCTK_DELTA_SPACE(1)); CCTK_REAL const dz = ToReal(CCTK_DELTA_SPACE(2)); CCTK_REAL const dt = ToReal(CCTK_DELTA_TIME); CCTK_REAL const dxi = INV(dx); CCTK_REAL const dyi = INV(dy); CCTK_REAL const dzi = INV(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 p1o12dx = 0.0833333333333333333333333333333*INV(dx); CCTK_REAL const p1o12dy = 0.0833333333333333333333333333333*INV(dy); CCTK_REAL const p1o12dz = 0.0833333333333333333333333333333*INV(dz); CCTK_REAL const p1o144dxdy = 0.00694444444444444444444444444444*INV(dx)*INV(dy); CCTK_REAL const p1o144dxdz = 0.00694444444444444444444444444444*INV(dx)*INV(dz); CCTK_REAL const p1o144dydz = 0.00694444444444444444444444444444*INV(dy)*INV(dz); CCTK_REAL const p1o180dx2 = 0.00555555555555555555555555555556*INV(SQR(dx)); CCTK_REAL const p1o180dy2 = 0.00555555555555555555555555555556*INV(SQR(dy)); CCTK_REAL const p1o180dz2 = 0.00555555555555555555555555555556*INV(SQR(dz)); CCTK_REAL const p1o2dx = 0.5*INV(dx); CCTK_REAL const p1o2dy = 0.5*INV(dy); CCTK_REAL const p1o2dz = 0.5*INV(dz); CCTK_REAL const p1o3600dxdy = 0.000277777777777777777777777777778*INV(dx)*INV(dy); CCTK_REAL const p1o3600dxdz = 0.000277777777777777777777777777778*INV(dx)*INV(dz); CCTK_REAL const p1o3600dydz = 0.000277777777777777777777777777778*INV(dy)*INV(dz); CCTK_REAL const p1o4dxdy = 0.25*INV(dx)*INV(dy); CCTK_REAL const p1o4dxdz = 0.25*INV(dx)*INV(dz); CCTK_REAL const p1o4dydz = 0.25*INV(dy)*INV(dz); CCTK_REAL const p1o5040dx2 = 0.000198412698412698412698412698413*INV(SQR(dx)); CCTK_REAL const p1o5040dy2 = 0.000198412698412698412698412698413*INV(SQR(dy)); CCTK_REAL const p1o5040dz2 = 0.000198412698412698412698412698413*INV(SQR(dz)); CCTK_REAL const p1o60dx = 0.0166666666666666666666666666667*INV(dx); CCTK_REAL const p1o60dy = 0.0166666666666666666666666666667*INV(dy); CCTK_REAL const p1o60dz = 0.0166666666666666666666666666667*INV(dz); CCTK_REAL const p1o705600dxdy = 1.41723356009070294784580498866e-6*INV(dx)*INV(dy); CCTK_REAL const p1o705600dxdz = 1.41723356009070294784580498866e-6*INV(dx)*INV(dz); CCTK_REAL const p1o705600dydz = 1.41723356009070294784580498866e-6*INV(dy)*INV(dz); CCTK_REAL const p1o840dx = 0.00119047619047619047619047619048*INV(dx); CCTK_REAL const p1o840dy = 0.00119047619047619047619047619048*INV(dy); CCTK_REAL const p1o840dz = 0.00119047619047619047619047619048*INV(dz); CCTK_REAL const p1odx = INV(dx); CCTK_REAL const p1odx2 = INV(SQR(dx)); CCTK_REAL const p1odxdy = INV(dx)*INV(dy); CCTK_REAL const p1odxdz = INV(dx)*INV(dz); CCTK_REAL const p1ody = INV(dy); CCTK_REAL const p1ody2 = INV(SQR(dy)); CCTK_REAL const p1odydz = INV(dy)*INV(dz); CCTK_REAL const p1odz = INV(dz); CCTK_REAL const p1odz2 = INV(SQR(dz)); CCTK_REAL const pm1o12dx2 = -0.0833333333333333333333333333333*INV(SQR(dx)); CCTK_REAL const pm1o12dy2 = -0.0833333333333333333333333333333*INV(SQR(dy)); CCTK_REAL const pm1o12dz2 = -0.0833333333333333333333333333333*INV(SQR(dz)); CCTK_REAL const pm1o2dx = -0.5*INV(dx); CCTK_REAL const pm1o2dy = -0.5*INV(dy); CCTK_REAL const pm1o2dz = -0.5*INV(dz); /* Loop over the grid points */ #pragma omp parallel LC_LOOP3 (psis_calc_Nth, i,j,k, min[0],min[1],min[2], max[0],max[1],max[2], cctk_lsh[0],cctk_lsh[1],cctk_lsh[2]) { ptrdiff_t const index = di*i + dj*j + dk*k; /* Assign local copies of grid functions */ CCTK_REAL gxxL = gxx[index]; CCTK_REAL gxyL = gxy[index]; CCTK_REAL gxzL = gxz[index]; CCTK_REAL gyyL = gyy[index]; CCTK_REAL gyzL = gyz[index]; CCTK_REAL gzzL = gzz[index]; CCTK_REAL kxxL = kxx[index]; CCTK_REAL kxyL = kxy[index]; CCTK_REAL kxzL = kxz[index]; CCTK_REAL kyyL = kyy[index]; CCTK_REAL kyzL = kyz[index]; CCTK_REAL kzzL = kzz[index]; CCTK_REAL xL = x[index]; CCTK_REAL yL = y[index]; CCTK_REAL zL = z[index]; /* Include user supplied include files */ /* Precompute derivatives */ CCTK_REAL PDstandard1gxx; CCTK_REAL PDstandard2gxx; CCTK_REAL PDstandard3gxx; CCTK_REAL PDstandard22gxx; CCTK_REAL PDstandard33gxx; CCTK_REAL PDstandard23gxx; CCTK_REAL PDstandard1gxy; CCTK_REAL PDstandard2gxy; CCTK_REAL PDstandard3gxy; CCTK_REAL PDstandard33gxy; CCTK_REAL PDstandard12gxy; CCTK_REAL PDstandard13gxy; CCTK_REAL PDstandard23gxy; CCTK_REAL PDstandard1gxz; CCTK_REAL PDstandard2gxz; CCTK_REAL PDstandard3gxz; CCTK_REAL PDstandard22gxz; CCTK_REAL PDstandard12gxz; CCTK_REAL PDstandard13gxz; CCTK_REAL PDstandard23gxz; CCTK_REAL PDstandard1gyy; CCTK_REAL PDstandard2gyy; CCTK_REAL PDstandard3gyy; CCTK_REAL PDstandard11gyy; CCTK_REAL PDstandard33gyy; CCTK_REAL PDstandard13gyy; CCTK_REAL PDstandard1gyz; CCTK_REAL PDstandard2gyz; CCTK_REAL PDstandard3gyz; CCTK_REAL PDstandard11gyz; CCTK_REAL PDstandard12gyz; CCTK_REAL PDstandard13gyz; CCTK_REAL PDstandard23gyz; CCTK_REAL PDstandard1gzz; CCTK_REAL PDstandard2gzz; CCTK_REAL PDstandard3gzz; CCTK_REAL PDstandard11gzz; CCTK_REAL PDstandard22gzz; CCTK_REAL PDstandard12gzz; CCTK_REAL PDstandard2kxx; CCTK_REAL PDstandard3kxx; CCTK_REAL PDstandard1kxy; CCTK_REAL PDstandard2kxy; CCTK_REAL PDstandard3kxy; CCTK_REAL PDstandard1kxz; CCTK_REAL PDstandard2kxz; CCTK_REAL PDstandard3kxz; CCTK_REAL PDstandard1kyy; CCTK_REAL PDstandard3kyy; CCTK_REAL PDstandard1kyz; CCTK_REAL PDstandard2kyz; CCTK_REAL PDstandard3kyz; CCTK_REAL PDstandard1kzz; CCTK_REAL PDstandard2kzz; switch(fdOrder) { case 2: PDstandard1gxx = PDstandardfdOrder21(&gxx[index]); PDstandard2gxx = PDstandardfdOrder22(&gxx[index]); PDstandard3gxx = PDstandardfdOrder23(&gxx[index]); PDstandard22gxx = PDstandardfdOrder222(&gxx[index]); PDstandard33gxx = PDstandardfdOrder233(&gxx[index]); PDstandard23gxx = PDstandardfdOrder223(&gxx[index]); PDstandard1gxy = PDstandardfdOrder21(&gxy[index]); PDstandard2gxy = PDstandardfdOrder22(&gxy[index]); PDstandard3gxy = PDstandardfdOrder23(&gxy[index]); PDstandard33gxy = PDstandardfdOrder233(&gxy[index]); PDstandard12gxy = PDstandardfdOrder212(&gxy[index]); PDstandard13gxy = PDstandardfdOrder213(&gxy[index]); PDstandard23gxy = PDstandardfdOrder223(&gxy[index]); PDstandard1gxz = PDstandardfdOrder21(&gxz[index]); PDstandard2gxz = PDstandardfdOrder22(&gxz[index]); PDstandard3gxz = PDstandardfdOrder23(&gxz[index]); PDstandard22gxz = PDstandardfdOrder222(&gxz[index]); PDstandard12gxz = PDstandardfdOrder212(&gxz[index]); PDstandard13gxz = PDstandardfdOrder213(&gxz[index]); PDstandard23gxz = PDstandardfdOrder223(&gxz[index]); PDstandard1gyy = PDstandardfdOrder21(&gyy[index]); PDstandard2gyy = PDstandardfdOrder22(&gyy[index]); PDstandard3gyy = PDstandardfdOrder23(&gyy[index]); PDstandard11gyy = PDstandardfdOrder211(&gyy[index]); PDstandard33gyy = PDstandardfdOrder233(&gyy[index]); PDstandard13gyy = PDstandardfdOrder213(&gyy[index]); PDstandard1gyz = PDstandardfdOrder21(&gyz[index]); PDstandard2gyz = PDstandardfdOrder22(&gyz[index]); PDstandard3gyz = PDstandardfdOrder23(&gyz[index]); PDstandard11gyz = PDstandardfdOrder211(&gyz[index]); PDstandard12gyz = PDstandardfdOrder212(&gyz[index]); PDstandard13gyz = PDstandardfdOrder213(&gyz[index]); PDstandard23gyz = PDstandardfdOrder223(&gyz[index]); PDstandard1gzz = PDstandardfdOrder21(&gzz[index]); PDstandard2gzz = PDstandardfdOrder22(&gzz[index]); PDstandard3gzz = PDstandardfdOrder23(&gzz[index]); PDstandard11gzz = PDstandardfdOrder211(&gzz[index]); PDstandard22gzz = PDstandardfdOrder222(&gzz[index]); PDstandard12gzz = PDstandardfdOrder212(&gzz[index]); PDstandard2kxx = PDstandardfdOrder22(&kxx[index]); PDstandard3kxx = PDstandardfdOrder23(&kxx[index]); PDstandard1kxy = PDstandardfdOrder21(&kxy[index]); PDstandard2kxy = PDstandardfdOrder22(&kxy[index]); PDstandard3kxy = PDstandardfdOrder23(&kxy[index]); PDstandard1kxz = PDstandardfdOrder21(&kxz[index]); PDstandard2kxz = PDstandardfdOrder22(&kxz[index]); PDstandard3kxz = PDstandardfdOrder23(&kxz[index]); PDstandard1kyy = PDstandardfdOrder21(&kyy[index]); PDstandard3kyy = PDstandardfdOrder23(&kyy[index]); PDstandard1kyz = PDstandardfdOrder21(&kyz[index]); PDstandard2kyz = PDstandardfdOrder22(&kyz[index]); PDstandard3kyz = PDstandardfdOrder23(&kyz[index]); PDstandard1kzz = PDstandardfdOrder21(&kzz[index]); PDstandard2kzz = PDstandardfdOrder22(&kzz[index]); break; case 4: PDstandard1gxx = PDstandardfdOrder41(&gxx[index]); PDstandard2gxx = PDstandardfdOrder42(&gxx[index]); PDstandard3gxx = PDstandardfdOrder43(&gxx[index]); PDstandard22gxx = PDstandardfdOrder422(&gxx[index]); PDstandard33gxx = PDstandardfdOrder433(&gxx[index]); PDstandard23gxx = PDstandardfdOrder423(&gxx[index]); PDstandard1gxy = PDstandardfdOrder41(&gxy[index]); PDstandard2gxy = PDstandardfdOrder42(&gxy[index]); PDstandard3gxy = PDstandardfdOrder43(&gxy[index]); PDstandard33gxy = PDstandardfdOrder433(&gxy[index]); PDstandard12gxy = PDstandardfdOrder412(&gxy[index]); PDstandard13gxy = PDstandardfdOrder413(&gxy[index]); PDstandard23gxy = PDstandardfdOrder423(&gxy[index]); PDstandard1gxz = PDstandardfdOrder41(&gxz[index]); PDstandard2gxz = PDstandardfdOrder42(&gxz[index]); PDstandard3gxz = PDstandardfdOrder43(&gxz[index]); PDstandard22gxz = PDstandardfdOrder422(&gxz[index]); PDstandard12gxz = PDstandardfdOrder412(&gxz[index]); PDstandard13gxz = PDstandardfdOrder413(&gxz[index]); PDstandard23gxz = PDstandardfdOrder423(&gxz[index]); PDstandard1gyy = PDstandardfdOrder41(&gyy[index]); PDstandard2gyy = PDstandardfdOrder42(&gyy[index]); PDstandard3gyy = PDstandardfdOrder43(&gyy[index]); PDstandard11gyy = PDstandardfdOrder411(&gyy[index]); PDstandard33gyy = PDstandardfdOrder433(&gyy[index]); PDstandard13gyy = PDstandardfdOrder413(&gyy[index]); PDstandard1gyz = PDstandardfdOrder41(&gyz[index]); PDstandard2gyz = PDstandardfdOrder42(&gyz[index]); PDstandard3gyz = PDstandardfdOrder43(&gyz[index]); PDstandard11gyz = PDstandardfdOrder411(&gyz[index]); PDstandard12gyz = PDstandardfdOrder412(&gyz[index]); PDstandard13gyz = PDstandardfdOrder413(&gyz[index]); PDstandard23gyz = PDstandardfdOrder423(&gyz[index]); PDstandard1gzz = PDstandardfdOrder41(&gzz[index]); PDstandard2gzz = PDstandardfdOrder42(&gzz[index]); PDstandard3gzz = PDstandardfdOrder43(&gzz[index]); PDstandard11gzz = PDstandardfdOrder411(&gzz[index]); PDstandard22gzz = PDstandardfdOrder422(&gzz[index]); PDstandard12gzz = PDstandardfdOrder412(&gzz[index]); PDstandard2kxx = PDstandardfdOrder42(&kxx[index]); PDstandard3kxx = PDstandardfdOrder43(&kxx[index]); PDstandard1kxy = PDstandardfdOrder41(&kxy[index]); PDstandard2kxy = PDstandardfdOrder42(&kxy[index]); PDstandard3kxy = PDstandardfdOrder43(&kxy[index]); PDstandard1kxz = PDstandardfdOrder41(&kxz[index]); PDstandard2kxz = PDstandardfdOrder42(&kxz[index]); PDstandard3kxz = PDstandardfdOrder43(&kxz[index]); PDstandard1kyy = PDstandardfdOrder41(&kyy[index]); PDstandard3kyy = PDstandardfdOrder43(&kyy[index]); PDstandard1kyz = PDstandardfdOrder41(&kyz[index]); PDstandard2kyz = PDstandardfdOrder42(&kyz[index]); PDstandard3kyz = PDstandardfdOrder43(&kyz[index]); PDstandard1kzz = PDstandardfdOrder41(&kzz[index]); PDstandard2kzz = PDstandardfdOrder42(&kzz[index]); break; case 6: PDstandard1gxx = PDstandardfdOrder61(&gxx[index]); PDstandard2gxx = PDstandardfdOrder62(&gxx[index]); PDstandard3gxx = PDstandardfdOrder63(&gxx[index]); PDstandard22gxx = PDstandardfdOrder622(&gxx[index]); PDstandard33gxx = PDstandardfdOrder633(&gxx[index]); PDstandard23gxx = PDstandardfdOrder623(&gxx[index]); PDstandard1gxy = PDstandardfdOrder61(&gxy[index]); PDstandard2gxy = PDstandardfdOrder62(&gxy[index]); PDstandard3gxy = PDstandardfdOrder63(&gxy[index]); PDstandard33gxy = PDstandardfdOrder633(&gxy[index]); PDstandard12gxy = PDstandardfdOrder612(&gxy[index]); PDstandard13gxy = PDstandardfdOrder613(&gxy[index]); PDstandard23gxy = PDstandardfdOrder623(&gxy[index]); PDstandard1gxz = PDstandardfdOrder61(&gxz[index]); PDstandard2gxz = PDstandardfdOrder62(&gxz[index]); PDstandard3gxz = PDstandardfdOrder63(&gxz[index]); PDstandard22gxz = PDstandardfdOrder622(&gxz[index]); PDstandard12gxz = PDstandardfdOrder612(&gxz[index]); PDstandard13gxz = PDstandardfdOrder613(&gxz[index]); PDstandard23gxz = PDstandardfdOrder623(&gxz[index]); PDstandard1gyy = PDstandardfdOrder61(&gyy[index]); PDstandard2gyy = PDstandardfdOrder62(&gyy[index]); PDstandard3gyy = PDstandardfdOrder63(&gyy[index]); PDstandard11gyy = PDstandardfdOrder611(&gyy[index]); PDstandard33gyy = PDstandardfdOrder633(&gyy[index]); PDstandard13gyy = PDstandardfdOrder613(&gyy[index]); PDstandard1gyz = PDstandardfdOrder61(&gyz[index]); PDstandard2gyz = PDstandardfdOrder62(&gyz[index]); PDstandard3gyz = PDstandardfdOrder63(&gyz[index]); PDstandard11gyz = PDstandardfdOrder611(&gyz[index]); PDstandard12gyz = PDstandardfdOrder612(&gyz[index]); PDstandard13gyz = PDstandardfdOrder613(&gyz[index]); PDstandard23gyz = PDstandardfdOrder623(&gyz[index]); PDstandard1gzz = PDstandardfdOrder61(&gzz[index]); PDstandard2gzz = PDstandardfdOrder62(&gzz[index]); PDstandard3gzz = PDstandardfdOrder63(&gzz[index]); PDstandard11gzz = PDstandardfdOrder611(&gzz[index]); PDstandard22gzz = PDstandardfdOrder622(&gzz[index]); PDstandard12gzz = PDstandardfdOrder612(&gzz[index]); PDstandard2kxx = PDstandardfdOrder62(&kxx[index]); PDstandard3kxx = PDstandardfdOrder63(&kxx[index]); PDstandard1kxy = PDstandardfdOrder61(&kxy[index]); PDstandard2kxy = PDstandardfdOrder62(&kxy[index]); PDstandard3kxy = PDstandardfdOrder63(&kxy[index]); PDstandard1kxz = PDstandardfdOrder61(&kxz[index]); PDstandard2kxz = PDstandardfdOrder62(&kxz[index]); PDstandard3kxz = PDstandardfdOrder63(&kxz[index]); PDstandard1kyy = PDstandardfdOrder61(&kyy[index]); PDstandard3kyy = PDstandardfdOrder63(&kyy[index]); PDstandard1kyz = PDstandardfdOrder61(&kyz[index]); PDstandard2kyz = PDstandardfdOrder62(&kyz[index]); PDstandard3kyz = PDstandardfdOrder63(&kyz[index]); PDstandard1kzz = PDstandardfdOrder61(&kzz[index]); PDstandard2kzz = PDstandardfdOrder62(&kzz[index]); break; case 8: PDstandard1gxx = PDstandardfdOrder81(&gxx[index]); PDstandard2gxx = PDstandardfdOrder82(&gxx[index]); PDstandard3gxx = PDstandardfdOrder83(&gxx[index]); PDstandard22gxx = PDstandardfdOrder822(&gxx[index]); PDstandard33gxx = PDstandardfdOrder833(&gxx[index]); PDstandard23gxx = PDstandardfdOrder823(&gxx[index]); PDstandard1gxy = PDstandardfdOrder81(&gxy[index]); PDstandard2gxy = PDstandardfdOrder82(&gxy[index]); PDstandard3gxy = PDstandardfdOrder83(&gxy[index]); PDstandard33gxy = PDstandardfdOrder833(&gxy[index]); PDstandard12gxy = PDstandardfdOrder812(&gxy[index]); PDstandard13gxy = PDstandardfdOrder813(&gxy[index]); PDstandard23gxy = PDstandardfdOrder823(&gxy[index]); PDstandard1gxz = PDstandardfdOrder81(&gxz[index]); PDstandard2gxz = PDstandardfdOrder82(&gxz[index]); PDstandard3gxz = PDstandardfdOrder83(&gxz[index]); PDstandard22gxz = PDstandardfdOrder822(&gxz[index]); PDstandard12gxz = PDstandardfdOrder812(&gxz[index]); PDstandard13gxz = PDstandardfdOrder813(&gxz[index]); PDstandard23gxz = PDstandardfdOrder823(&gxz[index]); PDstandard1gyy = PDstandardfdOrder81(&gyy[index]); PDstandard2gyy = PDstandardfdOrder82(&gyy[index]); PDstandard3gyy = PDstandardfdOrder83(&gyy[index]); PDstandard11gyy = PDstandardfdOrder811(&gyy[index]); PDstandard33gyy = PDstandardfdOrder833(&gyy[index]); PDstandard13gyy = PDstandardfdOrder813(&gyy[index]); PDstandard1gyz = PDstandardfdOrder81(&gyz[index]); PDstandard2gyz = PDstandardfdOrder82(&gyz[index]); PDstandard3gyz = PDstandardfdOrder83(&gyz[index]); PDstandard11gyz = PDstandardfdOrder811(&gyz[index]); PDstandard12gyz = PDstandardfdOrder812(&gyz[index]); PDstandard13gyz = PDstandardfdOrder813(&gyz[index]); PDstandard23gyz = PDstandardfdOrder823(&gyz[index]); PDstandard1gzz = PDstandardfdOrder81(&gzz[index]); PDstandard2gzz = PDstandardfdOrder82(&gzz[index]); PDstandard3gzz = PDstandardfdOrder83(&gzz[index]); PDstandard11gzz = PDstandardfdOrder811(&gzz[index]); PDstandard22gzz = PDstandardfdOrder822(&gzz[index]); PDstandard12gzz = PDstandardfdOrder812(&gzz[index]); PDstandard2kxx = PDstandardfdOrder82(&kxx[index]); PDstandard3kxx = PDstandardfdOrder83(&kxx[index]); PDstandard1kxy = PDstandardfdOrder81(&kxy[index]); PDstandard2kxy = PDstandardfdOrder82(&kxy[index]); PDstandard3kxy = PDstandardfdOrder83(&kxy[index]); PDstandard1kxz = PDstandardfdOrder81(&kxz[index]); PDstandard2kxz = PDstandardfdOrder82(&kxz[index]); PDstandard3kxz = PDstandardfdOrder83(&kxz[index]); PDstandard1kyy = PDstandardfdOrder81(&kyy[index]); PDstandard3kyy = PDstandardfdOrder83(&kyy[index]); PDstandard1kyz = PDstandardfdOrder81(&kyz[index]); PDstandard2kyz = PDstandardfdOrder82(&kyz[index]); PDstandard3kyz = PDstandardfdOrder83(&kyz[index]); PDstandard1kzz = PDstandardfdOrder81(&kzz[index]); PDstandard2kzz = PDstandardfdOrder82(&kzz[index]); break; } /* Calculate temporaries and grid functions */ CCTK_REAL detg = 2*gxyL*gxzL*gyzL + gzzL*(gxxL*gyyL - SQR(gxyL)) - gyyL*SQR(gxzL) - gxxL*SQR(gyzL); CCTK_REAL invdetg = INV(detg); CCTK_REAL gInv11 = invdetg*(gyyL*gzzL - SQR(gyzL)); CCTK_REAL gInv12 = (gxzL*gyzL - gxyL*gzzL)*invdetg; CCTK_REAL gInv13 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; CCTK_REAL gInv21 = (gxzL*gyzL - gxyL*gzzL)*invdetg; CCTK_REAL gInv22 = invdetg*(gxxL*gzzL - SQR(gxzL)); CCTK_REAL gInv23 = (gxyL*gxzL - gxxL*gyzL)*invdetg; CCTK_REAL gInv31 = (-(gxzL*gyyL) + gxyL*gyzL)*invdetg; CCTK_REAL gInv32 = (gxyL*gxzL - gxxL*gyzL)*invdetg; CCTK_REAL gInv33 = invdetg*(gxxL*gyyL - SQR(gxyL)); CCTK_REAL gamma111 = 0.5*(gInv11*PDstandard1gxx + 2*(gInv12*PDstandard1gxy + gInv13*PDstandard1gxz) - gInv12*PDstandard2gxx - gInv13*PDstandard3gxx); CCTK_REAL gamma211 = 0.5*(gInv21*PDstandard1gxx + 2*(gInv22*PDstandard1gxy + gInv23*PDstandard1gxz) - gInv22*PDstandard2gxx - gInv23*PDstandard3gxx); CCTK_REAL gamma311 = 0.5*(gInv31*PDstandard1gxx + 2*(gInv32*PDstandard1gxy + gInv33*PDstandard1gxz) - gInv32*PDstandard2gxx - gInv33*PDstandard3gxx); CCTK_REAL gamma121 = 0.5*(gInv12*PDstandard1gyy + gInv11*PDstandard2gxx + gInv13*(PDstandard1gyz + PDstandard2gxz - PDstandard3gxy)); CCTK_REAL gamma221 = 0.5*(gInv22*PDstandard1gyy + gInv21*PDstandard2gxx + gInv23*(PDstandard1gyz + PDstandard2gxz - PDstandard3gxy)); CCTK_REAL gamma321 = 0.5*(gInv32*PDstandard1gyy + gInv31*PDstandard2gxx + gInv33*(PDstandard1gyz + PDstandard2gxz - PDstandard3gxy)); CCTK_REAL gamma131 = 0.5*(gInv13*PDstandard1gzz + gInv11*PDstandard3gxx + gInv12*(PDstandard1gyz - PDstandard2gxz + PDstandard3gxy)); CCTK_REAL gamma231 = 0.5*(gInv23*PDstandard1gzz + gInv21*PDstandard3gxx + gInv22*(PDstandard1gyz - PDstandard2gxz + PDstandard3gxy)); CCTK_REAL gamma331 = 0.5*(gInv33*PDstandard1gzz + gInv31*PDstandard3gxx + gInv32*(PDstandard1gyz - PDstandard2gxz + PDstandard3gxy)); CCTK_REAL gamma122 = 0.5*(gInv11*(-PDstandard1gyy + 2*PDstandard2gxy) + gInv12*PDstandard2gyy + gInv13*(2*PDstandard2gyz - PDstandard3gyy)); CCTK_REAL gamma222 = 0.5*(gInv21*(-PDstandard1gyy + 2*PDstandard2gxy) + gInv22*PDstandard2gyy + gInv23*(2*PDstandard2gyz - PDstandard3gyy)); CCTK_REAL gamma322 = 0.5*(gInv31*(-PDstandard1gyy + 2*PDstandard2gxy) + gInv32*PDstandard2gyy + gInv33*(2*PDstandard2gyz - PDstandard3gyy)); CCTK_REAL gamma132 = 0.5*(gInv13*PDstandard2gzz + gInv11*(-PDstandard1gyz + PDstandard2gxz + PDstandard3gxy) + gInv12*PDstandard3gyy); CCTK_REAL gamma232 = 0.5*(gInv23*PDstandard2gzz + gInv21*(-PDstandard1gyz + PDstandard2gxz + PDstandard3gxy) + gInv22*PDstandard3gyy); CCTK_REAL gamma332 = 0.5*(gInv33*PDstandard2gzz + gInv31*(-PDstandard1gyz + PDstandard2gxz + PDstandard3gxy) + gInv32*PDstandard3gyy); CCTK_REAL gamma133 = 0.5*(gInv11*(-PDstandard1gzz + 2*PDstandard3gxz) + gInv12*(-PDstandard2gzz + 2*PDstandard3gyz) + gInv13*PDstandard3gzz); CCTK_REAL gamma233 = 0.5*(gInv21*(-PDstandard1gzz + 2*PDstandard3gxz) + gInv22*(-PDstandard2gzz + 2*PDstandard3gyz) + gInv23*PDstandard3gzz); CCTK_REAL gamma333 = 0.5*(gInv31*(-PDstandard1gzz + 2*PDstandard3gxz) + gInv32*(-PDstandard2gzz + 2*PDstandard3gyz) + gInv33*PDstandard3gzz); CCTK_REAL xmoved = xL - ToReal(xorig); CCTK_REAL ymoved = yL - ToReal(yorig); CCTK_REAL zmoved = zL - ToReal(zorig); CCTK_REAL va1 = -ymoved; CCTK_REAL va2 = xmoved + ToReal(offset); CCTK_REAL va3 = 0; CCTK_REAL vb1 = xmoved + ToReal(offset); CCTK_REAL vb2 = ymoved; CCTK_REAL vb3 = zmoved; CCTK_REAL vc1 = ((-(gInv13*va2) + gInv12*va3)*vb1 + (gInv13*va1 - gInv11*va3)*vb2 + (-(gInv12*va1) + gInv11*va2)*vb3)*sqrt(detg); CCTK_REAL vc2 = ((-(gInv23*va2) + gInv22*va3)*vb1 + (gInv23*va1 - gInv21*va3)*vb2 + (-(gInv22*va1) + gInv21*va2)*vb3)*sqrt(detg); CCTK_REAL vc3 = ((-(gInv33*va2) + gInv32*va3)*vb1 + (gInv33*va1 - gInv31*va3)*vb2 + (-(gInv32*va1) + gInv31*va2)*vb3)*sqrt(detg); CCTK_REAL wa1 = va1; CCTK_REAL wa2 = va2; CCTK_REAL wa3 = va3; CCTK_REAL omega11 = 2*(gyzL*wa2*wa3 + wa1*(gxyL*wa2 + gxzL*wa3)) + gxxL*SQR(wa1) + gyyL*SQR(wa2) + gzzL*SQR(wa3); CCTK_REAL ea1 = wa1*INV(sqrt(omega11)); CCTK_REAL ea2 = wa2*INV(sqrt(omega11)); CCTK_REAL ea3 = wa3*INV(sqrt(omega11)); CCTK_REAL omega12 = ea1*(gxxL*vb1 + gxyL*vb2 + gxzL*vb3) + ea2*(gxyL*vb1 + gyyL*vb2 + gyzL*vb3) + ea3*(gxzL*vb1 + gyzL*vb2 + gzzL*vb3); CCTK_REAL wb1 = -(ea1*omega12) + vb1; CCTK_REAL wb2 = -(ea2*omega12) + vb2; CCTK_REAL wb3 = -(ea3*omega12) + vb3; CCTK_REAL omega22 = 2*(gyzL*wb2*wb3 + wb1*(gxyL*wb2 + gxzL*wb3)) + gxxL*SQR(wb1) + gyyL*SQR(wb2) + gzzL*SQR(wb3); CCTK_REAL eb1 = wb1*INV(sqrt(omega22)); CCTK_REAL eb2 = wb2*INV(sqrt(omega22)); CCTK_REAL eb3 = wb3*INV(sqrt(omega22)); CCTK_REAL omega13 = ea1*(gxxL*vc1 + gxyL*vc2 + gxzL*vc3) + ea2*(gxyL*vc1 + gyyL*vc2 + gyzL*vc3) + ea3*(gxzL*vc1 + gyzL*vc2 + gzzL*vc3); CCTK_REAL omega23 = eb1*(gxxL*vc1 + gxyL*vc2 + gxzL*vc3) + eb2*(gxyL*vc1 + gyyL*vc2 + gyzL*vc3) + eb3*(gxzL*vc1 + gyzL*vc2 + gzzL*vc3); CCTK_REAL wc1 = -(ea1*omega13) - eb1*omega23 + vc1; CCTK_REAL wc2 = -(ea2*omega13) - eb2*omega23 + vc2; CCTK_REAL wc3 = -(ea3*omega13) - eb3*omega23 + vc3; CCTK_REAL omega33 = 2*(gyzL*wc2*wc3 + wc1*(gxyL*wc2 + gxzL*wc3)) + gxxL*SQR(wc1) + gyyL*SQR(wc2) + gzzL*SQR(wc3); CCTK_REAL ec1 = wc1*INV(sqrt(omega33)); CCTK_REAL ec2 = wc2*INV(sqrt(omega33)); CCTK_REAL ec3 = wc3*INV(sqrt(omega33)); CCTK_REAL isqrt2 = 0.707106781186547524; CCTK_REAL n1 = -(eb1*isqrt2); CCTK_REAL n2 = -(eb2*isqrt2); CCTK_REAL n3 = -(eb3*isqrt2); CCTK_REAL rm1 = ec1*isqrt2; CCTK_REAL rm2 = ec2*isqrt2; CCTK_REAL rm3 = ec3*isqrt2; CCTK_REAL im1 = ea1*isqrt2; CCTK_REAL im2 = ea2*isqrt2; CCTK_REAL im3 = ea3*isqrt2; CCTK_REAL rmbar1 = ec1*isqrt2; CCTK_REAL rmbar2 = ec2*isqrt2; CCTK_REAL rmbar3 = ec3*isqrt2; CCTK_REAL imbar1 = -(ea1*isqrt2); CCTK_REAL imbar2 = -(ea2*isqrt2); CCTK_REAL imbar3 = -(ea3*isqrt2); CCTK_REAL nn = isqrt2; CCTK_REAL R1111 = 0; CCTK_REAL R1112 = 0; CCTK_REAL R1113 = 0; CCTK_REAL R1121 = 0; CCTK_REAL R1122 = 0; CCTK_REAL R1123 = 0; CCTK_REAL R1131 = 0; CCTK_REAL R1132 = 0; CCTK_REAL R1133 = 0; CCTK_REAL R1211 = 0; CCTK_REAL R1212 = 0.5*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard11gyy + 2*PDstandard12gxy - PDstandard22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); CCTK_REAL R1213 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - gamma311*gamma332)*gzzL + 0.5*(-PDstandard11gyz + PDstandard12gxz + PDstandard13gxy - PDstandard23gxx); CCTK_REAL R1221 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard12gxy + 0.5*(PDstandard11gyy + PDstandard22gxx) - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); CCTK_REAL R1222 = 0; CCTK_REAL R1223 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - gamma321*gamma332)*gzzL + 0.5*(-PDstandard12gyz + PDstandard13gyy + PDstandard22gxz - PDstandard23gxy); CCTK_REAL R1231 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + 0.5*(PDstandard11gyz - PDstandard12gxz - PDstandard13gxy + PDstandard23gxx); CCTK_REAL R1232 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + 0.5*(PDstandard12gyz - PDstandard13gyy - PDstandard22gxz + PDstandard23gxy); CCTK_REAL R1233 = 0; CCTK_REAL R1311 = 0; CCTK_REAL R1312 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - gamma311*gamma332)*gzzL + 0.5*(-PDstandard11gyz + PDstandard12gxz + PDstandard13gxy - PDstandard23gxx); CCTK_REAL R1313 = 0.5*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard11gzz + 2*PDstandard13gxz - PDstandard33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); CCTK_REAL R1321 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + 0.5*(PDstandard11gyz - PDstandard12gxz - PDstandard13gxy + PDstandard23gxx); CCTK_REAL R1322 = 0; CCTK_REAL R1323 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - gamma321*gamma333)*gzzL + 0.5*(-PDstandard12gzz + PDstandard13gyz + PDstandard23gxz - PDstandard33gxy); CCTK_REAL R1331 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard13gxz + 0.5*(PDstandard11gzz + PDstandard33gxx) - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); CCTK_REAL R1332 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + 0.5*(PDstandard12gzz - PDstandard13gyz - PDstandard23gxz + PDstandard33gxy); CCTK_REAL R1333 = 0; CCTK_REAL R2111 = 0; CCTK_REAL R2112 = (-2*gamma121*gamma221 + gamma111*gamma222)*gxyL + (-2*gamma121*gamma321 + gamma111*gamma322)*gxzL + gamma122*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma221*gamma321 + gamma211*gamma322)*gyzL + gamma222*(gamma211*gyyL + gamma311*gyzL) - PDstandard12gxy + 0.5*(PDstandard11gyy + PDstandard22gxx) - gxxL*SQR(gamma121) - gyyL*SQR(gamma221) + gzzL*(gamma311*gamma322 - SQR(gamma321)); CCTK_REAL R2113 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + 0.5*(PDstandard11gyz - PDstandard12gxz - PDstandard13gxy + PDstandard23gxx); CCTK_REAL R2121 = 0.5*((4*gamma121*gamma221 - 2*gamma111*gamma222)*gxyL + (4*gamma121*gamma321 - 2*gamma111*gamma322)*gxzL + (4*gamma221*gamma321 - 2*gamma211*gamma322)*gyzL - 2*(gamma111*gamma122*gxxL + gamma122*gamma211*gxyL + gamma122*gamma311*gxzL + gamma211*gamma222*gyyL + gamma222*gamma311*gyzL + gamma311*gamma322*gzzL) - PDstandard11gyy + 2*PDstandard12gxy - PDstandard22gxx + 2*gxxL*SQR(gamma121) + 2*gyyL*SQR(gamma221) + 2*gzzL*SQR(gamma321)); CCTK_REAL R2122 = 0; CCTK_REAL R2123 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + 0.5*(PDstandard12gyz - PDstandard13gyy - PDstandard22gxz + PDstandard23gxy); CCTK_REAL R2131 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - gamma311*gamma332)*gzzL + 0.5*(-PDstandard11gyz + PDstandard12gxz + PDstandard13gxy - PDstandard23gxx); CCTK_REAL R2132 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - gamma321*gamma332)*gzzL + 0.5*(-PDstandard12gyz + PDstandard13gyy + PDstandard22gxz - PDstandard23gxy); CCTK_REAL R2133 = 0; CCTK_REAL R2211 = 0; CCTK_REAL R2212 = 0; CCTK_REAL R2213 = 0; CCTK_REAL R2221 = 0; CCTK_REAL R2222 = 0; CCTK_REAL R2223 = 0; CCTK_REAL R2231 = 0; CCTK_REAL R2232 = 0; CCTK_REAL R2233 = 0; CCTK_REAL R2311 = 0; CCTK_REAL R2312 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - gamma321*gamma332)*gzzL + 0.5*(-PDstandard12gyz + PDstandard13gyy + PDstandard22gxz - PDstandard23gxy); CCTK_REAL R2313 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - gamma321*gamma333)*gzzL + 0.5*(-PDstandard12gzz + PDstandard13gyz + PDstandard23gxz - PDstandard33gxy); CCTK_REAL R2321 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + 0.5*(PDstandard12gyz - PDstandard13gyy - PDstandard22gxz + PDstandard23gxy); CCTK_REAL R2322 = 0; CCTK_REAL R2323 = 0.5*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard22gzz + 2*PDstandard23gyz - PDstandard33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); CCTK_REAL R2331 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + 0.5*(PDstandard12gzz - PDstandard13gyz - PDstandard23gxz + PDstandard33gxy); CCTK_REAL R2332 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard23gyz + 0.5*(PDstandard22gzz + PDstandard33gyy) - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); CCTK_REAL R2333 = 0; CCTK_REAL R3111 = 0; CCTK_REAL R3112 = (-(gamma121*gamma131) + gamma111*gamma132)*gxxL + (gamma132*gamma211 - gamma131*gamma221 - gamma121*gamma231 + gamma111*gamma232)*gxyL + (gamma132*gamma311 - gamma131*gamma321 - gamma121*gamma331 + gamma111*gamma332)*gxzL + (-(gamma221*gamma231) + gamma211*gamma232)*gyyL + (gamma232*gamma311 - gamma231*gamma321 - gamma221*gamma331 + gamma211*gamma332)*gyzL + (-(gamma321*gamma331) + gamma311*gamma332)*gzzL + 0.5*(PDstandard11gyz - PDstandard12gxz - PDstandard13gxy + PDstandard23gxx); CCTK_REAL R3113 = (-2*gamma131*gamma231 + gamma111*gamma233)*gxyL + (-2*gamma131*gamma331 + gamma111*gamma333)*gxzL + gamma133*(gamma111*gxxL + gamma211*gxyL + gamma311*gxzL) + (-2*gamma231*gamma331 + gamma211*gamma333)*gyzL + gamma233*(gamma211*gyyL + gamma311*gyzL) - PDstandard13gxz + 0.5*(PDstandard11gzz + PDstandard33gxx) - gxxL*SQR(gamma131) - gyyL*SQR(gamma231) + gzzL*(gamma311*gamma333 - SQR(gamma331)); CCTK_REAL R3121 = (gamma121*gamma131 - gamma111*gamma132)*gxxL + (-(gamma132*gamma211) + gamma131*gamma221 + gamma121*gamma231 - gamma111*gamma232)*gxyL + (-(gamma132*gamma311) + gamma131*gamma321 + gamma121*gamma331 - gamma111*gamma332)*gxzL + (gamma221*gamma231 - gamma211*gamma232)*gyyL + (-(gamma232*gamma311) + gamma231*gamma321 + gamma221*gamma331 - gamma211*gamma332)*gyzL + (gamma321*gamma331 - gamma311*gamma332)*gzzL + 0.5*(-PDstandard11gyz + PDstandard12gxz + PDstandard13gxy - PDstandard23gxx); CCTK_REAL R3122 = 0; CCTK_REAL R3123 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + 0.5*(PDstandard12gzz - PDstandard13gyz - PDstandard23gxz + PDstandard33gxy); CCTK_REAL R3131 = 0.5*((4*gamma131*gamma231 - 2*gamma111*gamma233)*gxyL + (4*gamma131*gamma331 - 2*gamma111*gamma333)*gxzL + (4*gamma231*gamma331 - 2*gamma211*gamma333)*gyzL - 2*(gamma111*gamma133*gxxL + gamma133*gamma211*gxyL + gamma133*gamma311*gxzL + gamma211*gamma233*gyyL + gamma233*gamma311*gyzL + gamma311*gamma333*gzzL) - PDstandard11gzz + 2*PDstandard13gxz - PDstandard33gxx + 2*gxxL*SQR(gamma131) + 2*gyyL*SQR(gamma231) + 2*gzzL*SQR(gamma331)); CCTK_REAL R3132 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - gamma321*gamma333)*gzzL + 0.5*(-PDstandard12gzz + PDstandard13gyz + PDstandard23gxz - PDstandard33gxy); CCTK_REAL R3133 = 0; CCTK_REAL R3211 = 0; CCTK_REAL R3212 = (-(gamma122*gamma131) + gamma121*gamma132)*gxxL + (gamma132*gamma221 - gamma131*gamma222 - gamma122*gamma231 + gamma121*gamma232)*gxyL + (gamma132*gamma321 - gamma131*gamma322 - gamma122*gamma331 + gamma121*gamma332)*gxzL + (-(gamma222*gamma231) + gamma221*gamma232)*gyyL + (gamma232*gamma321 - gamma231*gamma322 - gamma222*gamma331 + gamma221*gamma332)*gyzL + (-(gamma322*gamma331) + gamma321*gamma332)*gzzL + 0.5*(PDstandard12gyz - PDstandard13gyy - PDstandard22gxz + PDstandard23gxy); CCTK_REAL R3213 = (-(gamma131*gamma132) + gamma121*gamma133)*gxxL + (gamma133*gamma221 - gamma132*gamma231 - gamma131*gamma232 + gamma121*gamma233)*gxyL + (gamma133*gamma321 - gamma132*gamma331 - gamma131*gamma332 + gamma121*gamma333)*gxzL + (-(gamma231*gamma232) + gamma221*gamma233)*gyyL + (gamma233*gamma321 - gamma232*gamma331 - gamma231*gamma332 + gamma221*gamma333)*gyzL + (-(gamma331*gamma332) + gamma321*gamma333)*gzzL + 0.5*(PDstandard12gzz - PDstandard13gyz - PDstandard23gxz + PDstandard33gxy); CCTK_REAL R3221 = (gamma122*gamma131 - gamma121*gamma132)*gxxL + (-(gamma132*gamma221) + gamma131*gamma222 + gamma122*gamma231 - gamma121*gamma232)*gxyL + (-(gamma132*gamma321) + gamma131*gamma322 + gamma122*gamma331 - gamma121*gamma332)*gxzL + (gamma222*gamma231 - gamma221*gamma232)*gyyL + (-(gamma232*gamma321) + gamma231*gamma322 + gamma222*gamma331 - gamma221*gamma332)*gyzL + (gamma322*gamma331 - gamma321*gamma332)*gzzL + 0.5*(-PDstandard12gyz + PDstandard13gyy + PDstandard22gxz - PDstandard23gxy); CCTK_REAL R3222 = 0; CCTK_REAL R3223 = (-2*gamma132*gamma232 + gamma122*gamma233)*gxyL + (-2*gamma132*gamma332 + gamma122*gamma333)*gxzL + gamma133*(gamma122*gxxL + gamma222*gxyL + gamma322*gxzL) + (-2*gamma232*gamma332 + gamma222*gamma333)*gyzL + gamma233*(gamma222*gyyL + gamma322*gyzL) - PDstandard23gyz + 0.5*(PDstandard22gzz + PDstandard33gyy) - gxxL*SQR(gamma132) - gyyL*SQR(gamma232) + gzzL*(gamma322*gamma333 - SQR(gamma332)); CCTK_REAL R3231 = (gamma131*gamma132 - gamma121*gamma133)*gxxL + (-(gamma133*gamma221) + gamma132*gamma231 + gamma131*gamma232 - gamma121*gamma233)*gxyL + (-(gamma133*gamma321) + gamma132*gamma331 + gamma131*gamma332 - gamma121*gamma333)*gxzL + (gamma231*gamma232 - gamma221*gamma233)*gyyL + (-(gamma233*gamma321) + gamma232*gamma331 + gamma231*gamma332 - gamma221*gamma333)*gyzL + (gamma331*gamma332 - gamma321*gamma333)*gzzL + 0.5*(-PDstandard12gzz + PDstandard13gyz + PDstandard23gxz - PDstandard33gxy); CCTK_REAL R3232 = 0.5*((4*gamma132*gamma232 - 2*gamma122*gamma233)*gxyL + (4*gamma132*gamma332 - 2*gamma122*gamma333)*gxzL + (4*gamma232*gamma332 - 2*gamma222*gamma333)*gyzL - 2*(gamma122*gamma133*gxxL + gamma133*gamma222*gxyL + gamma133*gamma322*gxzL + gamma222*gamma233*gyyL + gamma233*gamma322*gyzL + gamma322*gamma333*gzzL) - PDstandard22gzz + 2*PDstandard23gyz - PDstandard33gyy + 2*gxxL*SQR(gamma132) + 2*gyyL*SQR(gamma232) + 2*gzzL*SQR(gamma332)); CCTK_REAL R3233 = 0; CCTK_REAL R3311 = 0; CCTK_REAL R3312 = 0; CCTK_REAL R3313 = 0; CCTK_REAL R3321 = 0; CCTK_REAL R3322 = 0; CCTK_REAL R3323 = 0; CCTK_REAL R3331 = 0; CCTK_REAL R3332 = 0; CCTK_REAL R3333 = 0; CCTK_REAL R4p1111 = R1111; CCTK_REAL R4p1112 = R1112; CCTK_REAL R4p1113 = R1113; CCTK_REAL R4p1121 = R1121; CCTK_REAL R4p1122 = R1122; CCTK_REAL R4p1123 = R1123; CCTK_REAL R4p1131 = R1131; CCTK_REAL R4p1132 = R1132; CCTK_REAL R4p1133 = R1133; CCTK_REAL R4p1211 = R1211; CCTK_REAL R4p1212 = kxxL*kyyL + R1212 - SQR(kxyL); CCTK_REAL R4p1213 = -(kxyL*kxzL) + kxxL*kyzL + R1213; CCTK_REAL R4p1221 = -(kxxL*kyyL) + R1221 + SQR(kxyL); CCTK_REAL R4p1222 = R1222; CCTK_REAL R4p1223 = -(kxzL*kyyL) + kxyL*kyzL + R1223; CCTK_REAL R4p1231 = kxyL*kxzL - kxxL*kyzL + R1231; CCTK_REAL R4p1232 = kxzL*kyyL - kxyL*kyzL + R1232; CCTK_REAL R4p1233 = R1233; CCTK_REAL R4p1311 = R1311; CCTK_REAL R4p1312 = -(kxyL*kxzL) + kxxL*kyzL + R1312; CCTK_REAL R4p1313 = kxxL*kzzL + R1313 - SQR(kxzL); CCTK_REAL R4p1321 = kxyL*kxzL - kxxL*kyzL + R1321; CCTK_REAL R4p1322 = R1322; CCTK_REAL R4p1323 = -(kxzL*kyzL) + kxyL*kzzL + R1323; CCTK_REAL R4p1331 = -(kxxL*kzzL) + R1331 + SQR(kxzL); CCTK_REAL R4p1332 = kxzL*kyzL - kxyL*kzzL + R1332; CCTK_REAL R4p1333 = R1333; CCTK_REAL R4p2111 = R2111; CCTK_REAL R4p2112 = -(kxxL*kyyL) + R2112 + SQR(kxyL); CCTK_REAL R4p2113 = kxyL*kxzL - kxxL*kyzL + R2113; CCTK_REAL R4p2121 = kxxL*kyyL + R2121 - SQR(kxyL); CCTK_REAL R4p2122 = R2122; CCTK_REAL R4p2123 = kxzL*kyyL - kxyL*kyzL + R2123; CCTK_REAL R4p2131 = -(kxyL*kxzL) + kxxL*kyzL + R2131; CCTK_REAL R4p2132 = -(kxzL*kyyL) + kxyL*kyzL + R2132; CCTK_REAL R4p2133 = R2133; CCTK_REAL R4p2211 = R2211; CCTK_REAL R4p2212 = R2212; CCTK_REAL R4p2213 = R2213; CCTK_REAL R4p2221 = R2221; CCTK_REAL R4p2222 = R2222; CCTK_REAL R4p2223 = R2223; CCTK_REAL R4p2231 = R2231; CCTK_REAL R4p2232 = R2232; CCTK_REAL R4p2233 = R2233; CCTK_REAL R4p2311 = R2311; CCTK_REAL R4p2312 = -(kxzL*kyyL) + kxyL*kyzL + R2312; CCTK_REAL R4p2313 = -(kxzL*kyzL) + kxyL*kzzL + R2313; CCTK_REAL R4p2321 = kxzL*kyyL - kxyL*kyzL + R2321; CCTK_REAL R4p2322 = R2322; CCTK_REAL R4p2323 = kyyL*kzzL + R2323 - SQR(kyzL); CCTK_REAL R4p2331 = kxzL*kyzL - kxyL*kzzL + R2331; CCTK_REAL R4p2332 = -(kyyL*kzzL) + R2332 + SQR(kyzL); CCTK_REAL R4p2333 = R2333; CCTK_REAL R4p3111 = R3111; CCTK_REAL R4p3112 = kxyL*kxzL - kxxL*kyzL + R3112; CCTK_REAL R4p3113 = -(kxxL*kzzL) + R3113 + SQR(kxzL); CCTK_REAL R4p3121 = -(kxyL*kxzL) + kxxL*kyzL + R3121; CCTK_REAL R4p3122 = R3122; CCTK_REAL R4p3123 = kxzL*kyzL - kxyL*kzzL + R3123; CCTK_REAL R4p3131 = kxxL*kzzL + R3131 - SQR(kxzL); CCTK_REAL R4p3132 = -(kxzL*kyzL) + kxyL*kzzL + R3132; CCTK_REAL R4p3133 = R3133; CCTK_REAL R4p3211 = R3211; CCTK_REAL R4p3212 = kxzL*kyyL - kxyL*kyzL + R3212; CCTK_REAL R4p3213 = kxzL*kyzL - kxyL*kzzL + R3213; CCTK_REAL R4p3221 = -(kxzL*kyyL) + kxyL*kyzL + R3221; CCTK_REAL R4p3222 = R3222; CCTK_REAL R4p3223 = -(kyyL*kzzL) + R3223 + SQR(kyzL); CCTK_REAL R4p3231 = -(kxzL*kyzL) + kxyL*kzzL + R3231; CCTK_REAL R4p3232 = kyyL*kzzL + R3232 - SQR(kyzL); CCTK_REAL R4p3233 = R3233; CCTK_REAL R4p3311 = R3311; CCTK_REAL R4p3312 = R3312; CCTK_REAL R4p3313 = R3313; CCTK_REAL R4p3321 = R3321; CCTK_REAL R4p3322 = R3322; CCTK_REAL R4p3323 = R3323; CCTK_REAL R4p3331 = R3331; CCTK_REAL R4p3332 = R3332; CCTK_REAL R4p3333 = R3333; CCTK_REAL Ro111 = 0; CCTK_REAL Ro112 = gamma121*kxxL + (-gamma111 + gamma221)*kxyL + gamma321*kxzL - gamma211*kyyL - gamma311*kyzL + PDstandard1kxy - PDstandard2kxx; CCTK_REAL Ro113 = gamma131*kxxL + gamma231*kxyL + (-gamma111 + gamma331)*kxzL - gamma211*kyzL - gamma311*kzzL + PDstandard1kxz - PDstandard3kxx; CCTK_REAL Ro121 = -(gamma121*kxxL) + (gamma111 - gamma221)*kxyL - gamma321*kxzL + gamma211*kyyL + gamma311*kyzL - PDstandard1kxy + PDstandard2kxx; CCTK_REAL Ro122 = 0; CCTK_REAL Ro123 = gamma131*kxyL - gamma121*kxzL + gamma231*kyyL + (-gamma221 + gamma331)*kyzL - gamma321*kzzL + PDstandard2kxz - PDstandard3kxy; CCTK_REAL Ro131 = -(gamma131*kxxL) - gamma231*kxyL + (gamma111 - gamma331)*kxzL + gamma211*kyzL + gamma311*kzzL - PDstandard1kxz + PDstandard3kxx; CCTK_REAL Ro132 = -(gamma131*kxyL) + gamma121*kxzL - gamma231*kyyL + (gamma221 - gamma331)*kyzL + gamma321*kzzL - PDstandard2kxz + PDstandard3kxy; CCTK_REAL Ro133 = 0; CCTK_REAL Ro211 = 0; CCTK_REAL Ro212 = gamma122*kxxL + (-gamma121 + gamma222)*kxyL + gamma322*kxzL - gamma221*kyyL - gamma321*kyzL + PDstandard1kyy - PDstandard2kxy; CCTK_REAL Ro213 = gamma132*kxxL + gamma232*kxyL + (-gamma121 + gamma332)*kxzL - gamma221*kyzL - gamma321*kzzL + PDstandard1kyz - PDstandard3kxy; CCTK_REAL Ro221 = -(gamma122*kxxL) + (gamma121 - gamma222)*kxyL - gamma322*kxzL + gamma221*kyyL + gamma321*kyzL - PDstandard1kyy + PDstandard2kxy; CCTK_REAL Ro222 = 0; CCTK_REAL Ro223 = gamma132*kxyL - gamma122*kxzL + gamma232*kyyL + (-gamma222 + gamma332)*kyzL - gamma322*kzzL + PDstandard2kyz - PDstandard3kyy; CCTK_REAL Ro231 = -(gamma132*kxxL) - gamma232*kxyL + (gamma121 - gamma332)*kxzL + gamma221*kyzL + gamma321*kzzL - PDstandard1kyz + PDstandard3kxy; CCTK_REAL Ro232 = -(gamma132*kxyL) + gamma122*kxzL - gamma232*kyyL + (gamma222 - gamma332)*kyzL + gamma322*kzzL - PDstandard2kyz + PDstandard3kyy; CCTK_REAL Ro233 = 0; CCTK_REAL Ro311 = 0; CCTK_REAL Ro312 = gamma132*kxxL + (-gamma131 + gamma232)*kxyL + gamma332*kxzL - gamma231*kyyL - gamma331*kyzL + PDstandard1kyz - PDstandard2kxz; CCTK_REAL Ro313 = gamma133*kxxL + gamma233*kxyL + (-gamma131 + gamma333)*kxzL - gamma231*kyzL - gamma331*kzzL + PDstandard1kzz - PDstandard3kxz; CCTK_REAL Ro321 = -(gamma132*kxxL) + (gamma131 - gamma232)*kxyL - gamma332*kxzL + gamma231*kyyL + gamma331*kyzL - PDstandard1kyz + PDstandard2kxz; CCTK_REAL Ro322 = 0; CCTK_REAL Ro323 = gamma133*kxyL - gamma132*kxzL + gamma233*kyyL + (-gamma232 + gamma333)*kyzL - gamma332*kzzL + PDstandard2kzz - PDstandard3kyz; CCTK_REAL Ro331 = -(gamma133*kxxL) - gamma233*kxyL + (gamma131 - gamma333)*kxzL + gamma231*kyzL + gamma331*kzzL - PDstandard1kzz + PDstandard3kxz; CCTK_REAL Ro332 = -(gamma133*kxyL) + gamma132*kxzL - gamma233*kyyL + (gamma232 - gamma333)*kyzL + gamma332*kzzL - PDstandard2kzz + PDstandard3kyz; CCTK_REAL Ro333 = 0; CCTK_REAL Rojo11 = gInv11*R1111 + gInv12*R1112 + gInv13*R1113 + gInv21*R1211 + gInv23*(-(kxyL*kxzL) + kxxL*kyzL + R1213) + gInv31*R1311 + gInv32*(-(kxyL*kxzL) + kxxL*kyzL + R1312) + gInv22*(kxxL*kyyL + R1212 - SQR(kxyL)) + gInv33*(kxxL*kzzL + R1313 - SQR(kxzL)); CCTK_REAL Rojo12 = gInv11*R1121 + gInv13*(kxyL*kxzL - kxxL*kyzL + R1123) + gInv21*R1221 + gInv22*R1222 + gInv23*R1223 + gInv31*R1321 + gInv32*(-(kxzL*kyyL) + kxyL*kyzL + R1322) + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R1323) + gInv12*(-(kxxL*kyyL) + R1122 + SQR(kxyL)); CCTK_REAL Rojo13 = gInv11*R1131 + gInv12*(kxyL*kxzL - kxxL*kyzL + R1132) + gInv21*R1231 + gInv22*(kxzL*kyyL - kxyL*kyzL + R1232) + gInv23*(kxzL*kyzL - kxyL*kzzL + R1233) + gInv31*R1331 + gInv32*R1332 + gInv33*R1333 + gInv13*(-(kxxL*kzzL) + R1133 + SQR(kxzL)); CCTK_REAL Rojo21 = gInv11*R2111 + gInv12*R2112 + gInv13*R2113 + gInv22*R2212 + gInv23*(-(kxzL*kyyL) + kxyL*kyzL + R2213) + gInv31*(kxyL*kxzL - kxxL*kyzL + R2311) + gInv32*R2312 + gInv33*(-(kxzL*kyzL) + kxyL*kzzL + R2313) + gInv21*(-(kxxL*kyyL) + R2211 + SQR(kxyL)); CCTK_REAL Rojo22 = gInv12*R2122 + gInv13*(kxzL*kyyL - kxyL*kyzL + R2123) + gInv21*R2221 + gInv22*R2222 + gInv23*R2223 + gInv31*(kxzL*kyyL - kxyL*kyzL + R2321) + gInv32*R2322 + gInv11*(kxxL*kyyL + R2121 - SQR(kxyL)) + gInv33*(kyyL*kzzL + R2323 - SQR(kyzL)); CCTK_REAL Rojo23 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R2131) + gInv12*R2132 + gInv13*(kxzL*kyzL - kxyL*kzzL + R2133) + gInv21*(-(kxzL*kyyL) + kxyL*kyzL + R2231) + gInv22*R2232 + gInv31*R2331 + gInv32*R2332 + gInv33*R2333 + gInv23*(-(kyyL*kzzL) + R2233 + SQR(kyzL)); CCTK_REAL Rojo31 = gInv11*R3111 + gInv12*R3112 + gInv13*R3113 + gInv21*(kxyL*kxzL - kxxL*kyzL + R3211) + gInv22*(kxzL*kyyL - kxyL*kyzL + R3212) + gInv23*R3213 + gInv32*(kxzL*kyzL - kxyL*kzzL + R3312) + gInv33*R3313 + gInv31*(-(kxxL*kzzL) + R3311 + SQR(kxzL)); CCTK_REAL Rojo32 = gInv11*(-(kxyL*kxzL) + kxxL*kyzL + R3121) + gInv12*(-(kxzL*kyyL) + kxyL*kyzL + R3122) + gInv13*R3123 + gInv21*R3221 + gInv22*R3222 + gInv23*R3223 + gInv31*(kxzL*kyzL - kxyL*kzzL + R3321) + gInv33*R3323 + gInv32*(-(kyyL*kzzL) + R3322 + SQR(kyzL)); CCTK_REAL Rojo33 = gInv12*(-(kxzL*kyzL) + kxyL*kzzL + R3132) + gInv13*R3133 + gInv21*(-(kxzL*kyzL) + kxyL*kzzL + R3231) + gInv23*R3233 + gInv31*R3331 + gInv32*R3332 + gInv33*R3333 + gInv11*(kxxL*kzzL + R3131 - SQR(kxzL)) + gInv22*(kyyL*kzzL + R3232 - SQR(kyzL)); CCTK_REAL Psi4rL = n3*(-(n2*R4p2333) - n1*R4p3313)*SQR(imbar3) + n1*(n3*R4p1132*rmbar1*rmbar2 + n2*R4p1221*rmbar1*rmbar2 + n3*R4p1231*rmbar1*rmbar2 + n2*R4p1123*rmbar1*rmbar3 + n3*R4p1331*rmbar1*rmbar3 + n2*R4p2113*rmbar1*rmbar3 + n3*R4p1233*rmbar2*rmbar3 + n2*R4p1322*rmbar2*rmbar3 + n3*R4p1332*rmbar2*rmbar3 + n2*R4p2213*rmbar2*rmbar3 + 2*nn*rmbar1*rmbar2*Ro112 + 2*nn*rmbar1*rmbar3*Ro113 + 2*nn*rmbar1*rmbar2*Ro211 + 2*nn*rmbar2*rmbar3*Ro213 + 2*nn*rmbar1*rmbar3*Ro311 + 2*nn*rmbar2*rmbar3*Ro312 + n2*(R4p1122*rmbar1*rmbar2 - R4p1323*SQR(imbar3))) + n3*(n2*R4p3122*rmbar1*rmbar2 + n1*R4p3211*rmbar1*rmbar2 + n2*R4p3221*rmbar1*rmbar2 + n1*R4p1133*rmbar1*rmbar3 + n2*R4p2331*rmbar1*rmbar3 + n1*R4p3113*rmbar1*rmbar3 + n2*R4p3123*rmbar1*rmbar3 + n1*R4p3311*rmbar1*rmbar3 + n2*R4p2332*rmbar2*rmbar3 + n1*R4p3213*rmbar2*rmbar3 + n2*R4p3223*rmbar2*rmbar3 + n1*R4p3312*rmbar2*rmbar3 + n2*R4p3322*rmbar2*rmbar3 + 2*nn*rmbar1*rmbar2*Ro132 + 2*nn*rmbar1*rmbar3*Ro133 + 2*nn*rmbar1*rmbar2*Ro231 + 2*nn*rmbar2*rmbar3*Ro233 + 2*nn*rmbar1*rmbar3*Ro331 + 2*nn*rmbar2*rmbar3*Ro332 + n1*(R4p3112*rmbar1*rmbar2 - R4p1333*SQR(imbar3))) + n2*(n3*R4p2132*rmbar1*rmbar2 + n1*R4p2211*rmbar1*rmbar2 + n3*R4p2231*rmbar1*rmbar2 + n1*R4p1321*rmbar1*rmbar3 + n3*R4p2133*rmbar1*rmbar3 + n1*R4p2311*rmbar1*rmbar3 + n3*R4p3321*rmbar1*rmbar3 + n1*R4p1223*rmbar2*rmbar3 + n3*R4p2233*rmbar2*rmbar3 + n1*R4p2312*rmbar2*rmbar3 + 2*nn*rmbar1*rmbar2*Ro122 + 2*nn*rmbar1*rmbar3*Ro123 + 2*nn*rmbar1*rmbar2*Ro221 + 2*nn*rmbar2*rmbar3*Ro223 + 2*nn*rmbar1*rmbar3*Ro321 + 2*nn*rmbar2*rmbar3*Ro322 + n1*(R4p2112*rmbar1*rmbar2 - R4p2313*SQR(imbar3))) + R4p1112*rmbar1*rmbar2*SQR(n1) + R4p1211*rmbar1*rmbar2*SQR(n1) + R4p1113*rmbar1*rmbar3*SQR(n1) + R4p1311*rmbar1*rmbar3*SQR(n1) + R4p1213*rmbar2*rmbar3*SQR(n1) + R4p1312*rmbar2*rmbar3*SQR(n1) + R4p2122*rmbar1*rmbar2*SQR(n2) + R4p2221*rmbar1*rmbar2*SQR(n2) + R4p2123*rmbar1*rmbar3*SQR(n2) + R4p2321*rmbar1*rmbar3*SQR(n2) + R4p2223*rmbar2*rmbar3*SQR(n2) + R4p2322*rmbar2*rmbar3*SQR(n2) + SQR(imbar3)*(-2*n2*nn*Ro323 - R4p2323*SQR(n2)) + R4p3132*rmbar1*rmbar2*SQR(n3) + R4p3231*rmbar1*rmbar2*SQR(n3) + R4p3133*rmbar1*rmbar3*SQR(n3) + R4p3331*rmbar1*rmbar3*SQR(n3) + R4p3233*rmbar2*rmbar3*SQR(n3) + R4p3332*rmbar2*rmbar3*SQR(n3) + SQR(imbar3)*(-2*n3*nn*Ro333 - R4p3333*SQR(n3)) + rmbar1*rmbar2*Rojo12*SQR(nn) + rmbar1*rmbar3*Rojo13*SQR(nn) + rmbar1*rmbar2*Rojo21*SQR(nn) + rmbar2*rmbar3*Rojo23*SQR(nn) + rmbar1*rmbar3*Rojo31*SQR(nn) + rmbar2*rmbar3*Rojo32*SQR(nn) - SQR(imbar1)*(n2*n3*R4p2131 + n2*n3*R4p3121 + n1*(n2*(R4p1121 + R4p2111) + n3*(R4p1131 + R4p3111) + 2*nn*Ro111) + 2*n2*nn*Ro121 + 2*n3*nn*Ro131 + R4p1111*SQR(n1) + R4p2121*SQR(n2) + R4p3131*SQR(n3) + Rojo11*SQR(nn)) - SQR(imbar2)*(n2*n3*R4p2232 + n2*n3*R4p3222 + n1*(n2*(R4p1222 + R4p2212) + n3*(R4p1232 + R4p3212) + 2*nn*Ro212) + 2*n2*nn*Ro222 + 2*n3*nn*Ro232 + R4p1212*SQR(n1) + R4p2222*SQR(n2) + R4p3232*SQR(n3) + Rojo22*SQR(nn)) - imbar2*imbar3*(2*n3*nn*Ro233 + n1*(n2*(R4p1223 + R4p1322 + R4p2213 + R4p2312) + n3*(R4p1233 + R4p1332 + R4p3213 + R4p3312) + 2*nn*(Ro213 + Ro312)) + n2*(n3*(R4p2233 + R4p2332 + R4p3223 + R4p3322) + 2*nn*(Ro223 + Ro322)) + 2*n3*nn*Ro332 + (R4p1213 + R4p1312)*SQR(n1) + (R4p2223 + R4p2322)*SQR(n2) + R4p3233*SQR(n3) + R4p3332*SQR(n3) + Rojo23*SQR(nn) + Rojo32*SQR(nn)) + SQR(imbar3)*(-(n2*n3*R4p3323) - 2*n1*nn*Ro313 - R4p1313*SQR(n1) - Rojo33*SQR(nn)) - imbar1*(imbar2*(2*n3*nn*Ro132 + n1*(n2*(R4p1122 + R4p1221 + R4p2112 + R4p2211) + n3*(R4p1132 + R4p1231 + R4p3112 + R4p3211) + 2*nn*(Ro112 + Ro211)) + n2*(n3*(R4p2132 + R4p2231 + R4p3122 + R4p3221) + 2*nn*(Ro122 + Ro221)) + 2*n3*nn*Ro231 + (R4p1112 + R4p1211)*SQR(n1) + (R4p2122 + R4p2221)*SQR(n2) + R4p3132*SQR(n3) + R4p3231*SQR(n3) + Rojo12*SQR(nn) + Rojo21*SQR(nn)) + imbar3*(2*n3*nn*Ro133 + n1*(n2*(R4p1123 + R4p1321 + R4p2113 + R4p2311) + n3*(R4p1133 + R4p1331 + R4p3113 + R4p3311) + 2*nn*(Ro113 + Ro311)) + n2*(n3*(R4p2133 + R4p2331 + R4p3123 + R4p3321) + 2*nn*(Ro123 + Ro321)) + 2*n3*nn*Ro331 + (R4p1113 + R4p1311)*SQR(n1) + (R4p2123 + R4p2321)*SQR(n2) + R4p3133*SQR(n3) + R4p3331*SQR(n3) + Rojo13*SQR(nn) + Rojo31*SQR(nn))) + n1*n2*R4p1121*SQR(rmbar1) + n1*n3*R4p1131*SQR(rmbar1) + n1*n2*R4p2111*SQR(rmbar1) + n2*n3*R4p2131*SQR(rmbar1) + n1*n3*R4p3111*SQR(rmbar1) + n2*n3*R4p3121*SQR(rmbar1) + 2*n1*nn*Ro111*SQR(rmbar1) + 2*n2*nn*Ro121*SQR(rmbar1) + 2*n3*nn*Ro131*SQR(rmbar1) + R4p1111*SQR(n1)*SQR(rmbar1) + R4p2121*SQR(n2)*SQR(rmbar1) + R4p3131*SQR(n3)*SQR(rmbar1) + Rojo11*SQR(nn)*SQR(rmbar1) + n1*n2*R4p1222*SQR(rmbar2) + n1*n3*R4p1232*SQR(rmbar2) + n1*n2*R4p2212*SQR(rmbar2) + n2*n3*R4p2232*SQR(rmbar2) + n1*n3*R4p3212*SQR(rmbar2) + n2*n3*R4p3222*SQR(rmbar2) + 2*n1*nn*Ro212*SQR(rmbar2) + 2*n2*nn*Ro222*SQR(rmbar2) + 2*n3*nn*Ro232*SQR(rmbar2) + R4p1212*SQR(n1)*SQR(rmbar2) + R4p2222*SQR(n2)*SQR(rmbar2) + R4p3232*SQR(n3)*SQR(rmbar2) + Rojo22*SQR(nn)*SQR(rmbar2) + n1*n2*R4p1323*SQR(rmbar3) + n1*n3*R4p1333*SQR(rmbar3) + n1*n2*R4p2313*SQR(rmbar3) + n2*n3*R4p2333*SQR(rmbar3) + n1*n3*R4p3313*SQR(rmbar3) + n2*n3*R4p3323*SQR(rmbar3) + 2*n1*nn*Ro313*SQR(rmbar3) + 2*n2*nn*Ro323*SQR(rmbar3) + 2*n3*nn*Ro333*SQR(rmbar3) + R4p1313*SQR(n1)*SQR(rmbar3) + R4p2323*SQR(n2)*SQR(rmbar3) + R4p3333*SQR(n3)*SQR(rmbar3) + Rojo33*SQR(nn)*SQR(rmbar3); CCTK_REAL Psi4iL = -(im1*(4*n3*nn*rm1*Ro131 + 2*n3*nn*rm2*Ro132 + 2*n3*nn*rm3*Ro133 + 2*n3*nn*rm2*Ro231 + n1*(n2*(2*R4p1121*rm1 + 2*R4p2111*rm1 + R4p1122*rm2 + R4p1221*rm2 + R4p2112*rm2 + R4p2211*rm2 + R4p1123*rm3 + R4p1321*rm3 + R4p2113*rm3 + R4p2311*rm3) + n3*(2*R4p1131*rm1 + 2*R4p3111*rm1 + R4p1132*rm2 + R4p1231*rm2 + R4p3112*rm2 + R4p3211*rm2 + R4p1133*rm3 + R4p1331*rm3 + R4p3113*rm3 + R4p3311*rm3) + 2*nn*(2*rm1*Ro111 + rm2*(Ro112 + Ro211) + rm3*(Ro113 + Ro311))) + n2*(n3*(2*R4p2131*rm1 + 2*R4p3121*rm1 + R4p2132*rm2 + R4p2231*rm2 + R4p3122*rm2 + R4p3221*rm2 + R4p2133*rm3 + R4p2331*rm3 + R4p3123*rm3 + R4p3321*rm3) + 2*nn*(2*rm1*Ro121 + rm2*(Ro122 + Ro221) + rm3*(Ro123 + Ro321))) + 2*n3*nn*rm3*Ro331 + (2*R4p1111*rm1 + R4p1112*rm2 + R4p1211*rm2 + R4p1113*rm3 + R4p1311*rm3)*SQR(n1) + (2*R4p2121*rm1 + R4p2122*rm2 + R4p2221*rm2 + R4p2123*rm3 + R4p2321*rm3)*SQR(n2) + 2*R4p3131*rm1*SQR(n3) + R4p3132*rm2*SQR(n3) + R4p3231*rm2*SQR(n3) + R4p3133*rm3*SQR(n3) + R4p3331*rm3*SQR(n3) + 2*rm1*Rojo11*SQR(nn) + rm2*Rojo12*SQR(nn) + rm3*Rojo13*SQR(nn) + rm2*Rojo21*SQR(nn) + rm3*Rojo31*SQR(nn))) - im2*(2*n3*nn*rm1*Ro132 + 2*n3*nn*rm1*Ro231 + 4*n3*nn*rm2*Ro232 + 2*n3*nn*rm3*Ro233 + n1*(n2*(R4p1122*rm1 + R4p1221*rm1 + R4p2112*rm1 + R4p2211*rm1 + 2*R4p1222*rm2 + 2*R4p2212*rm2 + R4p1223*rm3 + R4p1322*rm3 + R4p2213*rm3 + R4p2312*rm3) + n3*(R4p1132*rm1 + R4p1231*rm1 + R4p3112*rm1 + R4p3211*rm1 + 2*R4p1232*rm2 + 2*R4p3212*rm2 + R4p1233*rm3 + R4p1332*rm3 + R4p3213*rm3 + R4p3312*rm3) + 2*nn*(rm1*(Ro112 + Ro211) + 2*rm2*Ro212 + rm3*(Ro213 + Ro312))) + n2*(n3*(R4p2132*rm1 + R4p2231*rm1 + R4p3122*rm1 + R4p3221*rm1 + 2*R4p2232*rm2 + 2*R4p3222*rm2 + R4p2233*rm3 + R4p2332*rm3 + R4p3223*rm3 + R4p3322*rm3) + 2*nn*(rm1*(Ro122 + Ro221) + 2*rm2*Ro222 + rm3*(Ro223 + Ro322))) + 2*n3*nn*rm3*Ro332 + (R4p1112*rm1 + R4p1211*rm1 + 2*R4p1212*rm2 + R4p1213*rm3 + R4p1312*rm3)*SQR(n1) + (R4p2122*rm1 + R4p2221*rm1 + 2*R4p2222*rm2 + R4p2223*rm3 + R4p2322*rm3)*SQR(n2) + R4p3132*rm1*SQR(n3) + R4p3231*rm1*SQR(n3) + 2*R4p3232*rm2*SQR(n3) + R4p3233*rm3*SQR(n3) + R4p3332*rm3*SQR(n3) + rm1*Rojo12*SQR(nn) + rm1*Rojo21*SQR(nn) + 2*rm2*Rojo22*SQR(nn) + rm3*Rojo23*SQR(nn) + rm3*Rojo32*SQR(nn)) - im3*(2*n3*nn*rm1*Ro133 + 2*n3*nn*rm2*Ro233 + n1*(n2*(R4p1123*rm1 + R4p1321*rm1 + R4p2113*rm1 + R4p2311*rm1 + R4p1223*rm2 + R4p1322*rm2 + R4p2213*rm2 + R4p2312*rm2 + 2*R4p1323*rm3 + 2*R4p2313*rm3) + n3*(R4p1133*rm1 + R4p1331*rm1 + R4p3113*rm1 + R4p3311*rm1 + R4p1233*rm2 + R4p1332*rm2 + R4p3213*rm2 + R4p3312*rm2 + 2*R4p1333*rm3 + 2*R4p3313*rm3) + 2*nn*(rm1*(Ro113 + Ro311) + rm2*(Ro213 + Ro312) + 2*rm3*Ro313)) + n2*(n3*(R4p2133*rm1 + R4p2331*rm1 + R4p3123*rm1 + R4p3321*rm1 + R4p2233*rm2 + R4p2332*rm2 + R4p3223*rm2 + R4p3322*rm2 + 2*R4p2333*rm3 + 2*R4p3323*rm3) + 2*nn*(rm1*(Ro123 + Ro321) + rm2*(Ro223 + Ro322) + 2*rm3*Ro323)) + 2*n3*nn*rm1*Ro331 + 2*n3*nn*rm2*Ro332 + 4*n3*nn*rm3*Ro333 + (R4p1113*rm1 + R4p1311*rm1 + R4p1213*rm2 + R4p1312*rm2 + 2*R4p1313*rm3)*SQR(n1) + (R4p2123*rm1 + R4p2321*rm1 + R4p2223*rm2 + R4p2322*rm2 + 2*R4p2323*rm3)*SQR(n2) + R4p3133*rm1*SQR(n3) + R4p3331*rm1*SQR(n3) + R4p3233*rm2*SQR(n3) + R4p3332*rm2*SQR(n3) + 2*R4p3333*rm3*SQR(n3) + rm1*Rojo13*SQR(nn) + rm2*Rojo23*SQR(nn) + rm1*Rojo31*SQR(nn) + rm2*Rojo32*SQR(nn) + 2*rm3*Rojo33*SQR(nn)); /* Copy local copies back to grid functions */ Psi4i[index] = Psi4iL; Psi4r[index] = Psi4rL; } LC_ENDLOOP3 (psis_calc_Nth); } extern "C" void psis_calc_Nth(CCTK_ARGUMENTS) { DECLARE_CCTK_ARGUMENTS; DECLARE_CCTK_PARAMETERS; GenericFD_LoopOverInterior(cctkGH, &psis_calc_Nth_Body); }