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cjy-goldst
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chb-parall
| Author | SHA1 | Date | |
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9c44d1c885
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4b9de28feb
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4eb5dc4ddb
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@@ -5253,10 +5253,10 @@ void Parallel::PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry)
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delete[] transfer_src;
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delete[] transfer_dst;
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}
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double Parallel::L2Norm(Patch *Pat, var *vf)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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double Parallel::L2Norm(Patch *Pat, var *vf)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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double tvf, dtvf = 0;
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int BDW = ghost_width;
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@@ -5281,48 +5281,13 @@ double Parallel::L2Norm(Patch *Pat, var *vf)
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MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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tvf = sqrt(tvf);
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return tvf;
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}
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void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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double tvf[7], dtvf[7];
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int BDW = ghost_width;
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for (int i = 0; i < 7; i++)
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dtvf[i] = 0;
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MyList<Block> *BP = Pat->blb;
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while (BP)
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{
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Block *cg = BP->data;
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if (myrank == cg->rank)
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{
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f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
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Pat->bbox[0], Pat->bbox[1], Pat->bbox[2],
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Pat->bbox[3], Pat->bbox[4], Pat->bbox[5],
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cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
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cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
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cg->fgfs[vf[6]->sgfn], tvf, BDW);
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for (int i = 0; i < 7; i++)
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dtvf[i] += tvf[i];
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}
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if (BP == Pat->ble)
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break;
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BP = BP->next;
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}
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MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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for (int i = 0; i < 7; i++)
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norms[i] = sqrt(tvf[i]);
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}
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double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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return tvf;
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}
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double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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double tvf, dtvf = 0;
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int BDW = ghost_width;
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@@ -5347,47 +5312,12 @@ double Parallel::L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here)
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MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, Comm_here);
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tvf = sqrt(tvf);
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return tvf;
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}
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void Parallel::L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here)
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{
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int myrank;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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double tvf[7], dtvf[7];
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int BDW = ghost_width;
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for (int i = 0; i < 7; i++)
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dtvf[i] = 0;
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MyList<Block> *BP = Pat->blb;
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while (BP)
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{
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Block *cg = BP->data;
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if (myrank == cg->rank)
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{
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f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
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Pat->bbox[0], Pat->bbox[1], Pat->bbox[2],
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Pat->bbox[3], Pat->bbox[4], Pat->bbox[5],
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cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
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cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
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cg->fgfs[vf[6]->sgfn], tvf, BDW);
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for (int i = 0; i < 7; i++)
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dtvf[i] += tvf[i];
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}
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if (BP == Pat->ble)
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break;
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BP = BP->next;
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}
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MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, Comm_here);
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for (int i = 0; i < 7; i++)
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norms[i] = sqrt(tvf[i]);
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}
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void Parallel::checkgsl(MyList<Parallel::gridseg> *pp, bool first_only)
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{
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int myrank = 0;
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return tvf;
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}
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void Parallel::checkgsl(MyList<Parallel::gridseg> *pp, bool first_only)
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{
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int myrank = 0;
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MPI_Comm_rank(MPI_COMM_WORLD, &myrank);
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if (myrank == 0)
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{
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@@ -179,13 +179,12 @@ namespace Parallel
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MyList<Parallel::gridseg> *clone_gsl(MyList<Parallel::gridseg> *p, bool first_only);
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MyList<Parallel::gridseg> *build_bulk_gsl(Patch *Pat); // similar to build_owned_gsl0 but does not care rank issue
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MyList<Parallel::gridseg> *build_bulk_gsl(Block *bp, Patch *Pat);
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void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
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MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
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void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
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double L2Norm(Patch *Pat, var *vf);
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void L2Norm7(Patch *Pat, var **vf, double *norms);
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void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
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void checkvarl(MyList<var> *pp, bool first_only);
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void build_PhysBD_gstl(Patch *Pat, MyList<Parallel::gridseg> *srci, MyList<Parallel::gridseg> *dsti,
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MyList<Parallel::gridseg> **out_src, MyList<Parallel::gridseg> **out_dst);
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void PeriodicBD(Patch *Pat, MyList<var> *VarList, int Symmetry);
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double L2Norm(Patch *Pat, var *vf);
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void checkgsl(MyList<Parallel::gridseg> *pp, bool first_only);
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void checkvarl(MyList<var> *pp, bool first_only);
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MyList<Parallel::gridseg> *divide_gsl(MyList<Parallel::gridseg> *p, Patch *Pat);
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MyList<Parallel::gridseg> *divide_gs(MyList<Parallel::gridseg> *p, Patch *Pat);
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void prepare_inter_time_level(Patch *Pat,
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@@ -217,12 +216,11 @@ namespace Parallel
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void aligncheck(double *bbox0, double *bboxl, int lev, double *DH0, int *shape);
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bool point_locat_gsl(double *pox, MyList<Parallel::gridseg> *gsl);
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void checkpatchlist(MyList<Patch> *PatL, bool buflog);
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double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
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void L2Norm7(Patch *Pat, var **vf, double *norms, MPI_Comm Comm_here);
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bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
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int NN, double **XX,
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double *Shellf, int Symmetry, MPI_Comm Comm_here);
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double L2Norm(Patch *Pat, var *vf, MPI_Comm Comm_here);
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bool PatList_Interp_Points(MyList<Patch> *PatL, MyList<var> *VarList,
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int NN, double **XX,
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double *Shellf, int Symmetry, MPI_Comm Comm_here);
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#if (PSTR == 1 || PSTR == 2 || PSTR == 3)
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MyList<Block> *distribute(MyList<Patch> *PatchLIST, int cpusize, int ingfsi, int fngfsi,
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bool periodic, int start_rank, int end_rank, int nodes = 0);
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@@ -3439,10 +3439,10 @@ void ShellPatch::write_Pablo_file_ss(int *ext, double xmin, double xmax, double
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delete[] Z;
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}
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double ShellPatch::L2Norm(var *vf)
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{
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double tvf, dtvf = 0;
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int BDW = overghost;
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double ShellPatch::L2Norm(var *vf)
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{
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double tvf, dtvf = 0;
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int BDW = overghost;
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MyList<ss_patch> *sPp = PatL;
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while (sPp)
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@@ -3469,50 +3469,13 @@ double ShellPatch::L2Norm(var *vf)
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MPI_Allreduce(&dtvf, &tvf, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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tvf = sqrt(tvf);
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return tvf;
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}
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void ShellPatch::L2Norm7(var **vf, double *norms)
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{
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double tvf[7], dtvf[7];
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int BDW = overghost;
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for (int i = 0; i < 7; i++)
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dtvf[i] = 0;
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MyList<ss_patch> *sPp = PatL;
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while (sPp)
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{
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MyList<Block> *Bp = sPp->data->blb;
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while (Bp)
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{
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Block *cg = Bp->data;
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if (myrank == cg->rank)
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{
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f_l2normhelper7(cg->shape, cg->X[0], cg->X[1], cg->X[2],
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sPp->data->bbox[0], sPp->data->bbox[1], sPp->data->bbox[2],
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sPp->data->bbox[3], sPp->data->bbox[4], sPp->data->bbox[5],
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cg->fgfs[vf[0]->sgfn], cg->fgfs[vf[1]->sgfn], cg->fgfs[vf[2]->sgfn],
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cg->fgfs[vf[3]->sgfn], cg->fgfs[vf[4]->sgfn], cg->fgfs[vf[5]->sgfn],
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cg->fgfs[vf[6]->sgfn], tvf, BDW);
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for (int i = 0; i < 7; i++)
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dtvf[i] += tvf[i];
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}
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if (Bp == sPp->data->ble)
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break;
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Bp = Bp->next;
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}
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sPp = sPp->next;
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}
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MPI_Allreduce(dtvf, tvf, 7, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
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for (int i = 0; i < 7; i++)
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norms[i] = sqrt(tvf[i]);
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}
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// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
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void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
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double *Shellf)
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return tvf;
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}
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// find maximum of abstract value, XX store position for maximum, Shellf store maximum themselvs
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void ShellPatch::Find_Maximum(MyList<var> *VarList, double *XX,
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double *Shellf)
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{
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MyList<var> *varl;
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int num_var = 0;
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@@ -195,11 +195,10 @@ public:
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bool Interp_One_Point(MyList<var> *VarList,
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double *XX, /*input global Cartesian coordinate*/
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double *Shellf, int Symmetry);
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void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
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char *filename, int sst);
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double L2Norm(var *vf);
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void L2Norm7(var **vf, double *norms);
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void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
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};
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void write_Pablo_file_ss(int *ext, double xmin, double xmax, double ymin, double ymax, double zmin, double zmax,
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char *filename, int sst);
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double L2Norm(var *vf);
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void Find_Maximum(MyList<var> *VarList, double *XX, double *Shellf);
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};
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#endif /* SHELLPATCH_H */
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File diff suppressed because it is too large
Load Diff
@@ -45,11 +45,10 @@ public:
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int checkrun;
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char checkfilename[50];
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int Steps;
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double StartTime, TotalTime;
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double AnasTime, DumpTime, d2DumpTime, CheckTime;
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double LastAnas, LastConsOut;
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int *ConstraintRefreshLevels;
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double Courant;
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double StartTime, TotalTime;
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double AnasTime, DumpTime, d2DumpTime, CheckTime;
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double LastAnas, LastConsOut;
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double Courant;
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double numepss, numepsb, numepsh;
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int Symmetry;
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int maxl, decn;
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@@ -134,9 +133,9 @@ public:
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Parallel::SyncCache *sync_cache_restrict; // cached Restrict in RestrictProlong
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Parallel::SyncCache *sync_cache_outbd; // cached OutBdLow2Hi in RestrictProlong
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monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
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monitor *ConVMonitor, *TimingMonitor;
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surface_integral *Waveshell;
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monitor *ErrorMonitor, *Psi4Monitor, *BHMonitor, *MAPMonitor;
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monitor *ConVMonitor;
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surface_integral *Waveshell;
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checkpoint *CheckPoint;
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public:
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@@ -59,10 +59,9 @@
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real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
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real*8,intent(in) :: eps
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real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: ham_Res, movx_Res, movy_Res, movz_Res
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real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
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! gont = 0: success; gont = 1: something wrong
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integer::gont
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integer :: i,j,k
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real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
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! gont = 0: success; gont = 1: something wrong
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integer::gont
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!~~~~~~> Other variables:
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@@ -84,18 +83,11 @@
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
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real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
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real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
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real*8 :: dX, dY, dZ, PI
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real*8 :: divb_loc,det_loc
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real*8 :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
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real*8 :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
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real*8 :: fxx_loc,fxy_loc,fxz_loc
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real*8 :: Gamxa_loc,Gamya_loc,Gamza_loc
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real*8 :: f_loc,chin_loc
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real*8 :: l_fxx,l_fxy,l_fxz,l_fyy,l_fyz,l_fzz,S_loc
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real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
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real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
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real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
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real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
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real*8 :: dX, dY, dZ, PI
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real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
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real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
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real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
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double precision,parameter::FF = 0.75d0,eta=2.d0
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real*8, parameter :: F1o3 = 1.D0/3.D0, F2o3 = 2.D0/3.D0,F3o2=1.5d0, F1o6 = 1.D0/6.D0
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real*8, parameter :: F16=1.6d1,F8=8.d0
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@@ -104,11 +96,11 @@
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real*8, dimension(ex(1),ex(2),ex(3)) :: reta
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#endif
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#if (GAUGE == 6 || GAUGE == 7)
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integer :: BHN
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real*8, dimension(9) :: Porg
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real*8, dimension(3) :: Mass
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real*8 :: r1,r2,M,A,w1,w2,C1,C2
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#if (GAUGE == 6 || GAUGE == 7)
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integer :: BHN,i,j,k
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real*8, dimension(9) :: Porg
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real*8, dimension(3) :: Mass
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real*8 :: r1,r2,M,A,w1,w2,C1,C2
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real*8, dimension(ex(1),ex(2),ex(3)) :: reta
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call getpbh(BHN,Porg,Mass)
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@@ -153,204 +145,174 @@
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dY = Y(2) - Y(1)
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dZ = Z(2) - Z(1)
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do k=1,ex(3)
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do j=1,ex(2)
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do i=1,ex(1)
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alpn1(i,j,k) = Lap(i,j,k) + ONE
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chin1(i,j,k) = chi(i,j,k) + ONE
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gxx(i,j,k) = dxx(i,j,k) + ONE
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gyy(i,j,k) = dyy(i,j,k) + ONE
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gzz(i,j,k) = dzz(i,j,k) + ONE
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enddo
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enddo
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enddo
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alpn1 = Lap + ONE
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chin1 = chi + ONE
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gxx = dxx + ONE
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gyy = dyy + ONE
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gzz = dzz + ONE
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call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
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call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
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call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
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call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
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div_beta = betaxx + betayy + betazz
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call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
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|
||||
call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
|
||||
call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
|
||||
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
|
||||
div_beta(i,j,k) = divb_loc
|
||||
|
||||
chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
|
||||
|
||||
gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
|
||||
TWO * ( gxx(i,j,k) * betaxx(i,j,k) + gxy(i,j,k) * betayx(i,j,k) + gxz(i,j,k) * betazx(i,j,k) )
|
||||
|
||||
gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
|
||||
TWO * ( gxy(i,j,k) * betaxy(i,j,k) + gyy(i,j,k) * betayy(i,j,k) + gyz(i,j,k) * betazy(i,j,k) )
|
||||
|
||||
gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
|
||||
TWO * ( gxz(i,j,k) * betaxz(i,j,k) + gyz(i,j,k) * betayz(i,j,k) + gzz(i,j,k) * betazz(i,j,k) )
|
||||
|
||||
gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
|
||||
gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
|
||||
gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
|
||||
|
||||
gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
|
||||
gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
|
||||
gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
|
||||
|
||||
gxz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axz(i,j,k) + F1o3 * gxz(i,j,k) * divb_loc + &
|
||||
gxx(i,j,k) * betaxz(i,j,k) + gxy(i,j,k) * betayz(i,j,k) + gyz(i,j,k) * betayx(i,j,k) + &
|
||||
gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
|
||||
|
||||
det_loc = gxx(i,j,k) * gyy(i,j,k) * gzz(i,j,k) + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) + &
|
||||
gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
|
||||
gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
|
||||
gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
|
||||
gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
|
||||
gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
|
||||
gupyy_loc = ( gxx(i,j,k) * gzz(i,j,k) - gxz(i,j,k) * gxz(i,j,k) ) / det_loc
|
||||
gupyz_loc = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / det_loc
|
||||
gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
|
||||
gupxx(i,j,k) = gupxx_loc
|
||||
gupxy(i,j,k) = gupxy_loc
|
||||
gupxz(i,j,k) = gupxz_loc
|
||||
gupyy(i,j,k) = gupyy_loc
|
||||
gupyz(i,j,k) = gupyz_loc
|
||||
gupzz(i,j,k) = gupzz_loc
|
||||
|
||||
if(co == 0)then
|
||||
Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
|
||||
gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
|
||||
gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
|
||||
gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
|
||||
gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
|
||||
gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
|
||||
gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
|
||||
gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
||||
gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
||||
gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
||||
Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
|
||||
gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
|
||||
gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
|
||||
gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
|
||||
gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
|
||||
gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
|
||||
gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
|
||||
gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
||||
gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
||||
gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
||||
Gmz_Res(i,j,k) = Gamz(i,j,k) - ( &
|
||||
gupxx_loc*(gupxz_loc*gxxx(i,j,k)+gupyz_loc*gxyx(i,j,k)+gupzz_loc*gxzx(i,j,k)) + &
|
||||
gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
|
||||
gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
|
||||
gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
|
||||
gupyy_loc*(gupxz_loc*gxyy(i,j,k)+gupyz_loc*gyyy(i,j,k)+gupzz_loc*gyzy(i,j,k)) + &
|
||||
gupyz_loc*(gupxz_loc*gxzy(i,j,k)+gupyz_loc*gyzy(i,j,k)+gupzz_loc*gzzy(i,j,k)) + &
|
||||
gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
||||
gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
||||
gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
||||
endif
|
||||
|
||||
Gamxxx(i,j,k)=HALF*( gupxx_loc*gxxx(i,j,k) + gupxy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupxz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
|
||||
Gamyxx(i,j,k)=HALF*( gupxy_loc*gxxx(i,j,k) + gupyy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupyz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
|
||||
Gamzxx(i,j,k)=HALF*( gupxz_loc*gxxx(i,j,k) + gupyz_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupzz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
|
||||
|
||||
Gamxyy(i,j,k)=HALF*( gupxx_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupxy_loc*gyyy(i,j,k) + gupxz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
|
||||
Gamyyy(i,j,k)=HALF*( gupxy_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyy_loc*gyyy(i,j,k) + gupyz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
|
||||
Gamzyy(i,j,k)=HALF*( gupxz_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyz_loc*gyyy(i,j,k) + gupzz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
|
||||
|
||||
Gamxzz(i,j,k)=HALF*( gupxx_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupxy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupxz_loc*gzzz(i,j,k))
|
||||
Gamyzz(i,j,k)=HALF*( gupxy_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupyz_loc*gzzz(i,j,k))
|
||||
Gamzzz(i,j,k)=HALF*( gupxz_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyz_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupzz_loc*gzzz(i,j,k))
|
||||
|
||||
Gamxxy(i,j,k)=HALF*( gupxx_loc*gxxy(i,j,k) + gupxy_loc*gyyx(i,j,k) + gupxz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
|
||||
Gamyxy(i,j,k)=HALF*( gupxy_loc*gxxy(i,j,k) + gupyy_loc*gyyx(i,j,k) + gupyz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
|
||||
Gamzxy(i,j,k)=HALF*( gupxz_loc*gxxy(i,j,k) + gupyz_loc*gyyx(i,j,k) + gupzz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
|
||||
|
||||
Gamxxz(i,j,k)=HALF*( gupxx_loc*gxxz(i,j,k) + gupxy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupxz_loc*gzzx(i,j,k) )
|
||||
Gamyxz(i,j,k)=HALF*( gupxy_loc*gxxz(i,j,k) + gupyy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupyz_loc*gzzx(i,j,k) )
|
||||
Gamzxz(i,j,k)=HALF*( gupxz_loc*gxxz(i,j,k) + gupyz_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupzz_loc*gzzx(i,j,k) )
|
||||
|
||||
Gamxyz(i,j,k)=HALF*( gupxx_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupxy_loc*gyyz(i,j,k) + gupxz_loc*gzzy(i,j,k) )
|
||||
Gamyyz(i,j,k)=HALF*( gupxy_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyy_loc*gyyz(i,j,k) + gupyz_loc*gzzy(i,j,k) )
|
||||
Gamzyz(i,j,k)=HALF*( gupxz_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyz_loc*gyyz(i,j,k) + gupzz_loc*gzzy(i,j,k) )
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
! Raise indices of \tilde A_{ij} and store in R_ij
|
||||
|
||||
! Right hand side for Gam^i without shift terms...
|
||||
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
gupxx_loc = gupxx(i,j,k)
|
||||
gupxy_loc = gupxy(i,j,k)
|
||||
gupxz_loc = gupxz(i,j,k)
|
||||
gupyy_loc = gupyy(i,j,k)
|
||||
gupyz_loc = gupyz(i,j,k)
|
||||
gupzz_loc = gupzz(i,j,k)
|
||||
|
||||
Rxx_loc = gupxx_loc * gupxx_loc * Axx(i,j,k) + gupxy_loc * gupxy_loc * Ayy(i,j,k) + gupxz_loc * gupxz_loc * Azz(i,j,k) + &
|
||||
TWO * (gupxx_loc * gupxy_loc * Axy(i,j,k) + gupxx_loc * gupxz_loc * Axz(i,j,k) + gupxy_loc * gupxz_loc * Ayz(i,j,k))
|
||||
Ryy_loc = gupxy_loc * gupxy_loc * Axx(i,j,k) + gupyy_loc * gupyy_loc * Ayy(i,j,k) + gupyz_loc * gupyz_loc * Azz(i,j,k) + &
|
||||
TWO * (gupxy_loc * gupyy_loc * Axy(i,j,k) + gupxy_loc * gupyz_loc * Axz(i,j,k) + gupyy_loc * gupyz_loc * Ayz(i,j,k))
|
||||
Rzz_loc = gupxz_loc * gupxz_loc * Axx(i,j,k) + gupyz_loc * gupyz_loc * Ayy(i,j,k) + gupzz_loc * gupzz_loc * Azz(i,j,k) + &
|
||||
TWO * (gupxz_loc * gupyz_loc * Axy(i,j,k) + gupxz_loc * gupzz_loc * Axz(i,j,k) + gupyz_loc * gupzz_loc * Ayz(i,j,k))
|
||||
Rxy_loc = gupxx_loc * gupxy_loc * Axx(i,j,k) + gupxy_loc * gupyy_loc * Ayy(i,j,k) + gupxz_loc * gupyz_loc * Azz(i,j,k) + &
|
||||
(gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
|
||||
(gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
|
||||
(gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
|
||||
Rxz_loc = gupxx_loc * gupxz_loc * Axx(i,j,k) + gupxy_loc * gupyz_loc * Ayy(i,j,k) + gupxz_loc * gupzz_loc * Azz(i,j,k) + &
|
||||
(gupxx_loc * gupyz_loc + gupxy_loc * gupxz_loc) * Axy(i,j,k) + &
|
||||
(gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
|
||||
(gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
|
||||
Ryz_loc = gupxy_loc * gupxz_loc * Axx(i,j,k) + gupyy_loc * gupyz_loc * Ayy(i,j,k) + gupyz_loc * gupzz_loc * Azz(i,j,k) + &
|
||||
(gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
|
||||
(gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
|
||||
(gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
|
||||
Rxx(i,j,k) = Rxx_loc
|
||||
Ryy(i,j,k) = Ryy_loc
|
||||
Rzz(i,j,k) = Rzz_loc
|
||||
Rxy(i,j,k) = Rxy_loc
|
||||
Rxz(i,j,k) = Rxz_loc
|
||||
Ryz(i,j,k) = Ryz_loc
|
||||
|
||||
Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
|
||||
TWO * alpn1(i,j,k) * ( &
|
||||
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
|
||||
gupxx_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
|
||||
gupxy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
|
||||
gupxz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
|
||||
Gamxxx(i,j,k) * Rxx_loc + Gamxyy(i,j,k) * Ryy_loc + Gamxzz(i,j,k) * Rzz_loc + &
|
||||
TWO * (Gamxxy(i,j,k) * Rxy_loc + Gamxxz(i,j,k) * Rxz_loc + Gamxyz(i,j,k) * Ryz_loc))
|
||||
|
||||
Gamy_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxy_loc + Lapy(i,j,k) * Ryy_loc + Lapz(i,j,k) * Ryz_loc) + &
|
||||
TWO * alpn1(i,j,k) * ( &
|
||||
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxy_loc + chiy(i,j,k) * Ryy_loc + chiz(i,j,k) * Ryz_loc) - &
|
||||
gupxy_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
|
||||
gupyy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
|
||||
gupyz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
|
||||
Gamyxx(i,j,k) * Rxx_loc + Gamyyy(i,j,k) * Ryy_loc + Gamyzz(i,j,k) * Rzz_loc + &
|
||||
TWO * (Gamyxy(i,j,k) * Rxy_loc + Gamyxz(i,j,k) * Rxz_loc + Gamyyz(i,j,k) * Ryz_loc))
|
||||
|
||||
Gamz_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxz_loc + Lapy(i,j,k) * Ryz_loc + Lapz(i,j,k) * Rzz_loc) + &
|
||||
TWO * alpn1(i,j,k) * ( &
|
||||
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxz_loc + chiy(i,j,k) * Ryz_loc + chiz(i,j,k) * Rzz_loc) - &
|
||||
gupxz_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
|
||||
gupyz_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
|
||||
gupzz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
|
||||
Gamzxx(i,j,k) * Rxx_loc + Gamzyy(i,j,k) * Ryy_loc + Gamzzz(i,j,k) * Rzz_loc + &
|
||||
TWO * (Gamzxy(i,j,k) * Rxy_loc + Gamzxz(i,j,k) * Rxz_loc + Gamzyz(i,j,k) * Ryz_loc))
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
|
||||
|
||||
call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
|
||||
call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
|
||||
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||
|
||||
gxx_rhs = - TWO * alpn1 * Axx - F2o3 * gxx * div_beta + &
|
||||
TWO *( gxx * betaxx + gxy * betayx + gxz * betazx)
|
||||
|
||||
gyy_rhs = - TWO * alpn1 * Ayy - F2o3 * gyy * div_beta + &
|
||||
TWO *( gxy * betaxy + gyy * betayy + gyz * betazy)
|
||||
|
||||
gzz_rhs = - TWO * alpn1 * Azz - F2o3 * gzz * div_beta + &
|
||||
TWO *( gxz * betaxz + gyz * betayz + gzz * betazz)
|
||||
|
||||
gxy_rhs = - TWO * alpn1 * Axy + F1o3 * gxy * div_beta + &
|
||||
gxx * betaxy + gxz * betazy + &
|
||||
gyy * betayx + gyz * betazx &
|
||||
- gxy * betazz
|
||||
|
||||
gyz_rhs = - TWO * alpn1 * Ayz + F1o3 * gyz * div_beta + &
|
||||
gxy * betaxz + gyy * betayz + &
|
||||
gxz * betaxy + gzz * betazy &
|
||||
- gyz * betaxx
|
||||
|
||||
gxz_rhs = - TWO * alpn1 * Axz + F1o3 * gxz * div_beta + &
|
||||
gxx * betaxz + gxy * betayz + &
|
||||
gyz * betayx + gzz * betazx &
|
||||
- gxz * betayy !rhs for gij
|
||||
|
||||
! invert tilted metric
|
||||
gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
|
||||
gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
|
||||
gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
|
||||
gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
|
||||
gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
|
||||
gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
|
||||
gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
|
||||
gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
|
||||
|
||||
if(co == 0)then
|
||||
! Gam^i_Res = Gam^i + gup^ij_,j
|
||||
Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
|
||||
+gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
|
||||
+gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
|
||||
+gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
|
||||
+gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
|
||||
+gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
|
||||
+gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||
+gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||
+gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||
Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
|
||||
+gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
|
||||
+gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
|
||||
+gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
|
||||
+gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
|
||||
+gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
|
||||
+gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||
+gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||
+gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||
Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
|
||||
+gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
|
||||
+gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
|
||||
+gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
|
||||
+gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
|
||||
+gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
|
||||
+gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||
+gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||
+gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||
endif
|
||||
|
||||
! second kind of connection
|
||||
Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
|
||||
Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
|
||||
Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
|
||||
|
||||
Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
|
||||
Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
|
||||
Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
|
||||
|
||||
Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
|
||||
Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
|
||||
Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
|
||||
|
||||
Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
|
||||
Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
|
||||
Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
|
||||
|
||||
Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
|
||||
Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
|
||||
Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
|
||||
|
||||
Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
|
||||
Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
|
||||
Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
|
||||
! Raise indices of \tilde A_{ij} and store in R_ij
|
||||
|
||||
Rxx = gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
|
||||
TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
|
||||
|
||||
Ryy = gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
|
||||
TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
|
||||
|
||||
Rzz = gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
|
||||
TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
|
||||
|
||||
Rxy = gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
|
||||
(gupxx * gupyy + gupxy * gupxy)* Axy + &
|
||||
(gupxx * gupyz + gupxz * gupxy)* Axz + &
|
||||
(gupxy * gupyz + gupxz * gupyy)* Ayz
|
||||
|
||||
Rxz = gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
|
||||
(gupxx * gupyz + gupxy * gupxz)* Axy + &
|
||||
(gupxx * gupzz + gupxz * gupxz)* Axz + &
|
||||
(gupxy * gupzz + gupxz * gupyz)* Ayz
|
||||
|
||||
Ryz = gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
|
||||
(gupxy * gupyz + gupyy * gupxz)* Axy + &
|
||||
(gupxy * gupzz + gupyz * gupxz)* Axz + &
|
||||
(gupyy * gupzz + gupyz * gupyz)* Ayz
|
||||
|
||||
! Right hand side for Gam^i without shift terms...
|
||||
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
|
||||
|
||||
Gamx_rhs = - TWO * ( Lapx * Rxx + Lapy * Rxy + Lapz * Rxz ) + &
|
||||
TWO * alpn1 * ( &
|
||||
-F3o2/chin1 * ( chix * Rxx + chiy * Rxy + chiz * Rxz ) - &
|
||||
gupxx * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||
gupxy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||
gupxz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||
Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz + &
|
||||
TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
|
||||
|
||||
Gamy_rhs = - TWO * ( Lapx * Rxy + Lapy * Ryy + Lapz * Ryz ) + &
|
||||
TWO * alpn1 * ( &
|
||||
-F3o2/chin1 * ( chix * Rxy + chiy * Ryy + chiz * Ryz ) - &
|
||||
gupxy * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||
gupyy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||
gupyz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||
Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz + &
|
||||
TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
|
||||
|
||||
Gamz_rhs = - TWO * ( Lapx * Rxz + Lapy * Ryz + Lapz * Rzz ) + &
|
||||
TWO * alpn1 * ( &
|
||||
-F3o2/chin1 * ( chix * Rxz + chiy * Ryz + chiz * Rzz ) - &
|
||||
gupxz * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||
gupyz * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||
gupzz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||
Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz + &
|
||||
TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
|
||||
|
||||
call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
|
||||
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
|
||||
@@ -359,54 +321,38 @@
|
||||
call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
|
||||
X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
|
||||
|
||||
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
divb_loc = div_beta(i,j,k)
|
||||
fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
|
||||
fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
|
||||
fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
|
||||
|
||||
gupxx_loc = gupxx(i,j,k)
|
||||
gupxy_loc = gupxy(i,j,k)
|
||||
gupxz_loc = gupxz(i,j,k)
|
||||
gupyy_loc = gupyy(i,j,k)
|
||||
gupyz_loc = gupyz(i,j,k)
|
||||
gupzz_loc = gupzz(i,j,k)
|
||||
|
||||
Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
|
||||
TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
|
||||
Gamya_loc = gupxx_loc * Gamyxx(i,j,k) + gupyy_loc * Gamyyy(i,j,k) + gupzz_loc * Gamyzz(i,j,k) + &
|
||||
TWO * (gupxy_loc * Gamyxy(i,j,k) + gupxz_loc * Gamyxz(i,j,k) + gupyz_loc * Gamyyz(i,j,k))
|
||||
Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
|
||||
TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
|
||||
Gamxa(i,j,k) = Gamxa_loc
|
||||
Gamya(i,j,k) = Gamya_loc
|
||||
Gamza(i,j,k) = Gamza_loc
|
||||
|
||||
Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
|
||||
Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
|
||||
F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
|
||||
gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
|
||||
TWO * (gupxy_loc * gxyx(i,j,k) + gupxz_loc * gxzx(i,j,k) + gupyz_loc * gyzx(i,j,k))
|
||||
|
||||
Gamy_rhs(i,j,k) = Gamy_rhs(i,j,k) + F2o3 * Gamya_loc * divb_loc - &
|
||||
Gamxa_loc * betayx(i,j,k) - Gamya_loc * betayy(i,j,k) - Gamza_loc * betayz(i,j,k) + &
|
||||
F1o3 * (gupxy_loc * fxx_loc + gupyy_loc * fxy_loc + gupyz_loc * fxz_loc) + &
|
||||
gupxx_loc * gxxy(i,j,k) + gupyy_loc * gyyy(i,j,k) + gupzz_loc * gzzy(i,j,k) + &
|
||||
TWO * (gupxy_loc * gxyy(i,j,k) + gupxz_loc * gxzy(i,j,k) + gupyz_loc * gyzy(i,j,k))
|
||||
|
||||
Gamz_rhs(i,j,k) = Gamz_rhs(i,j,k) + F2o3 * Gamza_loc * divb_loc - &
|
||||
Gamxa_loc * betazx(i,j,k) - Gamya_loc * betazy(i,j,k) - Gamza_loc * betazz(i,j,k) + &
|
||||
F1o3 * (gupxz_loc * fxx_loc + gupyz_loc * fxy_loc + gupzz_loc * fxz_loc) + &
|
||||
gupxx_loc * gxxz(i,j,k) + gupyy_loc * gyyz(i,j,k) + gupzz_loc * gzzz(i,j,k) + &
|
||||
TWO * (gupxy_loc * gxyz(i,j,k) + gupxz_loc * gxzz(i,j,k) + gupyz_loc * gyzz(i,j,k))
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
fxx = gxxx + gxyy + gxzz
|
||||
fxy = gxyx + gyyy + gyzz
|
||||
fxz = gxzx + gyzy + gzzz
|
||||
|
||||
Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
|
||||
TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
|
||||
Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
|
||||
TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
|
||||
Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
|
||||
TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
|
||||
|
||||
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
|
||||
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
|
||||
|
||||
Gamx_rhs = Gamx_rhs + F2o3 * Gamxa * div_beta - &
|
||||
Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz + &
|
||||
F1o3 * (gupxx * fxx + gupxy * fxy + gupxz * fxz ) + &
|
||||
gupxx * gxxx + gupyy * gyyx + gupzz * gzzx + &
|
||||
TWO * (gupxy * gxyx + gupxz * gxzx + gupyz * gyzx )
|
||||
|
||||
Gamy_rhs = Gamy_rhs + F2o3 * Gamya * div_beta - &
|
||||
Gamxa * betayx - Gamya * betayy - Gamza * betayz + &
|
||||
F1o3 * (gupxy * fxx + gupyy * fxy + gupyz * fxz ) + &
|
||||
gupxx * gxxy + gupyy * gyyy + gupzz * gzzy + &
|
||||
TWO * (gupxy * gxyy + gupxz * gxzy + gupyz * gyzy )
|
||||
|
||||
Gamz_rhs = Gamz_rhs + F2o3 * Gamza * div_beta - &
|
||||
Gamxa * betazx - Gamya * betazy - Gamza * betazz + &
|
||||
F1o3 * (gupxz * fxx + gupyz * fxy + gupzz * fxz ) + &
|
||||
gupxx * gxxz + gupyy * gyyz + gupzz * gzzz + &
|
||||
TWO * (gupxy * gxyz + gupxz * gxzz + gupyz * gyzz ) !rhs for Gam^i
|
||||
|
||||
!first kind of connection stored in gij,k
|
||||
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
|
||||
@@ -655,190 +601,192 @@
|
||||
Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz + &
|
||||
Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy + &
|
||||
Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
|
||||
!covariant second derivative of chi respect to tilted metric
|
||||
call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k) * chix(i,j,k) - Gamyxx(i,j,k) * chiy(i,j,k) - Gamzxx(i,j,k) * chiz(i,j,k)
|
||||
fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k) * chix(i,j,k) - Gamyxy(i,j,k) * chiy(i,j,k) - Gamzxy(i,j,k) * chiz(i,j,k)
|
||||
fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k) * chix(i,j,k) - Gamyxz(i,j,k) * chiy(i,j,k) - Gamzxz(i,j,k) * chiz(i,j,k)
|
||||
fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k) * chix(i,j,k) - Gamyyy(i,j,k) * chiy(i,j,k) - Gamzyy(i,j,k) * chiz(i,j,k)
|
||||
fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k) * chix(i,j,k) - Gamyyz(i,j,k) * chiy(i,j,k) - Gamzyz(i,j,k) * chiz(i,j,k)
|
||||
fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k) * chix(i,j,k) - Gamyzz(i,j,k) * chiy(i,j,k) - Gamzzz(i,j,k) * chiz(i,j,k)
|
||||
|
||||
chin_loc = chin1(i,j,k)
|
||||
f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
|
||||
gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
|
||||
gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
|
||||
TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
|
||||
TWO * gupxz(i,j,k) * (fxz(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiz(i,j,k)) + &
|
||||
TWO * gupyz(i,j,k) * (fyz(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiz(i,j,k))
|
||||
f(i,j,k) = f_loc
|
||||
|
||||
Rxx(i,j,k) = Rxx(i,j,k) + (fxx(i,j,k) - chix(i,j,k)*chix(i,j,k)/chin_loc/TWO + gxx(i,j,k) * f_loc)/chin_loc/TWO
|
||||
Ryy(i,j,k) = Ryy(i,j,k) + (fyy(i,j,k) - chiy(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gyy(i,j,k) * f_loc)/chin_loc/TWO
|
||||
Rzz(i,j,k) = Rzz(i,j,k) + (fzz(i,j,k) - chiz(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gzz(i,j,k) * f_loc)/chin_loc/TWO
|
||||
Rxy(i,j,k) = Rxy(i,j,k) + (fxy(i,j,k) - chix(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gxy(i,j,k) * f_loc)/chin_loc/TWO
|
||||
Rxz(i,j,k) = Rxz(i,j,k) + (fxz(i,j,k) - chix(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gxz(i,j,k) * f_loc)/chin_loc/TWO
|
||||
Ryz(i,j,k) = Ryz(i,j,k) + (fyz(i,j,k) - chiy(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gyz(i,j,k) * f_loc)/chin_loc/TWO
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
! covariant second derivatives of the lapse respect to physical metric
|
||||
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
|
||||
SYM,SYM,SYM,symmetry,Lev)
|
||||
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
chin_loc = chin1(i,j,k)
|
||||
gxxx(i,j,k) = (gupxx(i,j,k) * chix(i,j,k) + gupxy(i,j,k) * chiy(i,j,k) + gupxz(i,j,k) * chiz(i,j,k)) / chin_loc
|
||||
gxxy(i,j,k) = (gupxy(i,j,k) * chix(i,j,k) + gupyy(i,j,k) * chiy(i,j,k) + gupyz(i,j,k) * chiz(i,j,k)) / chin_loc
|
||||
gxxz(i,j,k) = (gupxz(i,j,k) * chix(i,j,k) + gupyz(i,j,k) * chiy(i,j,k) + gupzz(i,j,k) * chiz(i,j,k)) / chin_loc
|
||||
|
||||
Gamxxx(i,j,k) = Gamxxx(i,j,k) - ( (chix(i,j,k) + chix(i,j,k))/chin_loc - gxx(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyxx(i,j,k) = Gamyxx(i,j,k) - ( - gxx(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzxx(i,j,k) = Gamzxx(i,j,k) - ( - gxx(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
Gamxyy(i,j,k) = Gamxyy(i,j,k) - ( - gyy(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyyy(i,j,k) = Gamyyy(i,j,k) - ( (chiy(i,j,k) + chiy(i,j,k))/chin_loc - gyy(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzyy(i,j,k) = Gamzyy(i,j,k) - ( - gyy(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
Gamxzz(i,j,k) = Gamxzz(i,j,k) - ( - gzz(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyzz(i,j,k) = Gamyzz(i,j,k) - ( - gzz(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzzz(i,j,k) = Gamzzz(i,j,k) - ( (chiz(i,j,k) + chiz(i,j,k))/chin_loc - gzz(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
Gamxxy(i,j,k) = Gamxxy(i,j,k) - ( chiy(i,j,k) /chin_loc - gxy(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzxy(i,j,k) = Gamzxy(i,j,k) - ( - gxy(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyxz(i,j,k) = Gamyxz(i,j,k) - ( - gxz(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzxz(i,j,k) = Gamzxz(i,j,k) - ( chix(i,j,k) /chin_loc - gxz(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
Gamxyz(i,j,k) = Gamxyz(i,j,k) - ( - gyz(i,j,k) * gxxx(i,j,k) )*HALF
|
||||
Gamyyz(i,j,k) = Gamyyz(i,j,k) - ( chiz(i,j,k) /chin_loc - gyz(i,j,k) * gxxy(i,j,k) )*HALF
|
||||
Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
|
||||
|
||||
fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k)*Lapx(i,j,k) - Gamyxx(i,j,k)*Lapy(i,j,k) - Gamzxx(i,j,k)*Lapz(i,j,k)
|
||||
fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k)*Lapx(i,j,k) - Gamyyy(i,j,k)*Lapy(i,j,k) - Gamzyy(i,j,k)*Lapz(i,j,k)
|
||||
fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k)*Lapx(i,j,k) - Gamyzz(i,j,k)*Lapy(i,j,k) - Gamzzz(i,j,k)*Lapz(i,j,k)
|
||||
fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k)*Lapx(i,j,k) - Gamyxy(i,j,k)*Lapy(i,j,k) - Gamzxy(i,j,k)*Lapz(i,j,k)
|
||||
fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k)*Lapx(i,j,k) - Gamyxz(i,j,k)*Lapy(i,j,k) - Gamzxz(i,j,k)*Lapz(i,j,k)
|
||||
fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k)*Lapx(i,j,k) - Gamyyz(i,j,k)*Lapy(i,j,k) - Gamzyz(i,j,k)*Lapz(i,j,k)
|
||||
|
||||
trK_rhs(i,j,k) = gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k))
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
do k=1,ex(3)
|
||||
do j=1,ex(2)
|
||||
do i=1,ex(1)
|
||||
divb_loc = div_beta(i,j,k)
|
||||
chin_loc = chin1(i,j,k)
|
||||
|
||||
S_loc = chin_loc * ( gupxx(i,j,k) * Sxx(i,j,k) + gupyy(i,j,k) * Syy(i,j,k) + gupzz(i,j,k) * Szz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * Sxy(i,j,k) + gupxz(i,j,k) * Sxz(i,j,k) + gupyz(i,j,k) * Syz(i,j,k)) )
|
||||
S(i,j,k) = S_loc
|
||||
|
||||
f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
|
||||
gupxx(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + &
|
||||
gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
|
||||
gupyy(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
|
||||
gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
|
||||
gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
|
||||
gupzz(i,j,k) * ( gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
|
||||
gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
|
||||
TWO * ( gupxy(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
|
||||
gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k)) ) + &
|
||||
gupxz(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
|
||||
gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k)) ) + &
|
||||
gupyz(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + &
|
||||
gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k)) ) ) ) - &
|
||||
F16 * PI * rho(i,j,k) + EIGHT * PI * S_loc
|
||||
|
||||
f_loc = -F1o3 * ( gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
|
||||
alpn1(i,j,k)/chin_loc * f_loc )
|
||||
f(i,j,k) = f_loc
|
||||
|
||||
l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
|
||||
l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
|
||||
l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
|
||||
l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
|
||||
l_fyz = alpn1(i,j,k) * (Ryz(i,j,k) - EIGHT * PI * Syz(i,j,k)) - fyz(i,j,k)
|
||||
l_fzz = alpn1(i,j,k) * (Rzz(i,j,k) - EIGHT * PI * Szz(i,j,k)) - fzz(i,j,k)
|
||||
|
||||
Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
|
||||
Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
|
||||
Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
|
||||
Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
|
||||
Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
|
||||
Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
|
||||
|
||||
fxx(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + &
|
||||
gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
|
||||
fyy(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
|
||||
gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
|
||||
gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
|
||||
fzz(i,j,k) = gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
|
||||
gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k))
|
||||
fxy(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k))
|
||||
fxz(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k))
|
||||
fyz(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
|
||||
gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
|
||||
gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
|
||||
gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k))
|
||||
|
||||
trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
|
||||
|
||||
Axx_rhs(i,j,k) = chin_loc * Axx_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axx(i,j,k) - TWO * fxx(i,j,k)) + &
|
||||
TWO * (Axx(i,j,k) * betaxx(i,j,k) + Axy(i,j,k) * betayx(i,j,k) + Axz(i,j,k) * betazx(i,j,k)) - &
|
||||
F2o3 * Axx(i,j,k) * divb_loc
|
||||
Ayy_rhs(i,j,k) = chin_loc * Ayy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayy(i,j,k) - TWO * fyy(i,j,k)) + &
|
||||
TWO * (Axy(i,j,k) * betaxy(i,j,k) + Ayy(i,j,k) * betayy(i,j,k) + Ayz(i,j,k) * betazy(i,j,k)) - &
|
||||
F2o3 * Ayy(i,j,k) * divb_loc
|
||||
Azz_rhs(i,j,k) = chin_loc * Azz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Azz(i,j,k) - TWO * fzz(i,j,k)) + &
|
||||
TWO * (Axz(i,j,k) * betaxz(i,j,k) + Ayz(i,j,k) * betayz(i,j,k) + Azz(i,j,k) * betazz(i,j,k)) - &
|
||||
F2o3 * Azz(i,j,k) * divb_loc
|
||||
Axy_rhs(i,j,k) = chin_loc * Axy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axy(i,j,k) - TWO * fxy(i,j,k)) + &
|
||||
Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
|
||||
Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
|
||||
Ayz_rhs(i,j,k) = chin_loc * Ayz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayz(i,j,k) - TWO * fyz(i,j,k)) + &
|
||||
Axy(i,j,k) * betaxz(i,j,k) + Ayy(i,j,k) * betayz(i,j,k) + Axz(i,j,k) * betaxy(i,j,k) + &
|
||||
Azz(i,j,k) * betazy(i,j,k) + F1o3 * Ayz(i,j,k) * divb_loc - Ayz(i,j,k) * betaxx(i,j,k)
|
||||
Axz_rhs(i,j,k) = chin_loc * Axz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axz(i,j,k) - TWO * fxz(i,j,k)) + &
|
||||
Axx(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
|
||||
Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
|
||||
|
||||
trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(i,j,k) + &
|
||||
gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
|
||||
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
|
||||
FOUR * PI * (rho(i,j,k) + S_loc) )
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
!covariant second derivative of chi respect to tilted metric
|
||||
call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||
|
||||
fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
|
||||
fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
|
||||
fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * chiz
|
||||
fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * chiz
|
||||
fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * chiz
|
||||
fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
|
||||
! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
|
||||
|
||||
f = gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
|
||||
gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
|
||||
gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
|
||||
TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
|
||||
TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
|
||||
TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz )
|
||||
! Add chi part to Ricci tensor:
|
||||
|
||||
Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
|
||||
Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
|
||||
Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
|
||||
Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
|
||||
Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
|
||||
Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO
|
||||
|
||||
! covariant second derivatives of the lapse respect to physical metric
|
||||
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
|
||||
SYM,SYM,SYM,symmetry,Lev)
|
||||
|
||||
gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
|
||||
gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
|
||||
gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
|
||||
! now get physical second kind of connection
|
||||
Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
|
||||
Gamyxx = Gamyxx - ( - gxx * gxxy )*HALF
|
||||
Gamzxx = Gamzxx - ( - gxx * gxxz )*HALF
|
||||
Gamxyy = Gamxyy - ( - gyy * gxxx )*HALF
|
||||
Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
|
||||
Gamzyy = Gamzyy - ( - gyy * gxxz )*HALF
|
||||
Gamxzz = Gamxzz - ( - gzz * gxxx )*HALF
|
||||
Gamyzz = Gamyzz - ( - gzz * gxxy )*HALF
|
||||
Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
|
||||
Gamxxy = Gamxxy - ( chiy /chin1 - gxy * gxxx )*HALF
|
||||
Gamyxy = Gamyxy - ( chix /chin1 - gxy * gxxy )*HALF
|
||||
Gamzxy = Gamzxy - ( - gxy * gxxz )*HALF
|
||||
Gamxxz = Gamxxz - ( chiz /chin1 - gxz * gxxx )*HALF
|
||||
Gamyxz = Gamyxz - ( - gxz * gxxy )*HALF
|
||||
Gamzxz = Gamzxz - ( chix /chin1 - gxz * gxxz )*HALF
|
||||
Gamxyz = Gamxyz - ( - gyz * gxxx )*HALF
|
||||
Gamyyz = Gamyyz - ( chiz /chin1 - gyz * gxxy )*HALF
|
||||
Gamzyz = Gamzyz - ( chiy /chin1 - gyz * gxxz )*HALF
|
||||
|
||||
fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
|
||||
fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
|
||||
fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
|
||||
fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
|
||||
fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
|
||||
fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz
|
||||
|
||||
! store D^i D_i Lap in trK_rhs upto chi
|
||||
trK_rhs = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz )
|
||||
#if 1
|
||||
!! follow bam code
|
||||
S = chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
|
||||
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
|
||||
f = F2o3 * trK * trK -(&
|
||||
gupxx * ( &
|
||||
gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
|
||||
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
|
||||
gupyy * ( &
|
||||
gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
|
||||
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
|
||||
gupzz * ( &
|
||||
gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
|
||||
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
|
||||
TWO * ( &
|
||||
gupxy * ( &
|
||||
gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
|
||||
gupxy * (Axx * Ayy + Axy * Axy) + &
|
||||
gupxz * (Axx * Ayz + Axz * Axy) + &
|
||||
gupyz * (Axy * Ayz + Axz * Ayy) ) + &
|
||||
gupxz * ( &
|
||||
gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
|
||||
gupxy * (Axx * Ayz + Axy * Axz) + &
|
||||
gupxz * (Axx * Azz + Axz * Axz) + &
|
||||
gupyz * (Axy * Azz + Axz * Ayz) ) + &
|
||||
gupyz * ( &
|
||||
gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
|
||||
gupxy * (Axy * Ayz + Ayy * Axz) + &
|
||||
gupxz * (Axy * Azz + Ayz * Axz) + &
|
||||
gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
|
||||
f = - F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
|
||||
|
||||
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
|
||||
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
|
||||
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
|
||||
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
|
||||
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
|
||||
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
|
||||
#else
|
||||
! Add lapse and S_ij parts to Ricci tensor:
|
||||
|
||||
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
|
||||
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
|
||||
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
|
||||
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
|
||||
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
|
||||
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
|
||||
|
||||
! Compute trace-free part (note: chi^-1 and chi cancel!):
|
||||
|
||||
f = F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) )
|
||||
#endif
|
||||
|
||||
Axx_rhs = fxx - gxx * f
|
||||
Ayy_rhs = fyy - gyy * f
|
||||
Azz_rhs = fzz - gzz * f
|
||||
Axy_rhs = fxy - gxy * f
|
||||
Axz_rhs = fxz - gxz * f
|
||||
Ayz_rhs = fyz - gyz * f
|
||||
|
||||
! Now: store A_il A^l_j into fij:
|
||||
|
||||
fxx = gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
|
||||
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
|
||||
fyy = gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
|
||||
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
|
||||
fzz = gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
|
||||
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
|
||||
fxy = gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
|
||||
gupxy *(Axx * Ayy + Axy * Axy) + &
|
||||
gupxz *(Axx * Ayz + Axz * Axy) + &
|
||||
gupyz *(Axy * Ayz + Axz * Ayy)
|
||||
fxz = gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
|
||||
gupxy *(Axx * Ayz + Axy * Axz) + &
|
||||
gupxz *(Axx * Azz + Axz * Axz) + &
|
||||
gupyz *(Axy * Azz + Axz * Ayz)
|
||||
fyz = gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
|
||||
gupxy *(Axy * Ayz + Ayy * Axz) + &
|
||||
gupxz *(Axy * Azz + Ayz * Axz) + &
|
||||
gupyz *(Ayy * Azz + Ayz * Ayz)
|
||||
|
||||
f = chin1
|
||||
! store D^i D_i Lap in trK_rhs
|
||||
trK_rhs = f*trK_rhs
|
||||
|
||||
Axx_rhs = f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx) + &
|
||||
TWO * ( Axx * betaxx + Axy * betayx + Axz * betazx )- &
|
||||
F2o3 * Axx * div_beta
|
||||
|
||||
Ayy_rhs = f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy) + &
|
||||
TWO * ( Axy * betaxy + Ayy * betayy + Ayz * betazy )- &
|
||||
F2o3 * Ayy * div_beta
|
||||
|
||||
Azz_rhs = f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz) + &
|
||||
TWO * ( Axz * betaxz + Ayz * betayz + Azz * betazz )- &
|
||||
F2o3 * Azz * div_beta
|
||||
|
||||
Axy_rhs = f * Axy_rhs+ alpn1 *( trK * Axy - TWO * fxy )+ &
|
||||
Axx * betaxy + Axz * betazy + &
|
||||
Ayy * betayx + Ayz * betazx + &
|
||||
F1o3 * Axy * div_beta - Axy * betazz
|
||||
|
||||
Ayz_rhs = f * Ayz_rhs+ alpn1 *( trK * Ayz - TWO * fyz )+ &
|
||||
Axy * betaxz + Ayy * betayz + &
|
||||
Axz * betaxy + Azz * betazy + &
|
||||
F1o3 * Ayz * div_beta - Ayz * betaxx
|
||||
|
||||
Axz_rhs = f * Axz_rhs+ alpn1 *( trK * Axz - TWO * fxz )+ &
|
||||
Axx * betaxz + Axy * betayz + &
|
||||
Ayz * betayx + Azz * betazx + &
|
||||
F1o3 * Axz * div_beta - Axz * betayy !rhs for Aij
|
||||
|
||||
! Compute trace of S_ij
|
||||
|
||||
S = f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
|
||||
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
|
||||
|
||||
trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK + &
|
||||
gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||
TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
|
||||
FOUR * PI * ( rho + S )) !rhs for trK
|
||||
|
||||
!!!! gauge variable part
|
||||
|
||||
@@ -1000,15 +948,15 @@
|
||||
!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
|
||||
! lopsided_kodis shares the symmetry_bd buffer between advection and
|
||||
! dissipation, eliminating redundant full-grid copies. For metric variables
|
||||
! gxx/gyy/gzz (=dxx/dyy/dzz+1): stencil coefficients sum to zero,
|
||||
! so the constant offset has no effect on dissipation.
|
||||
|
||||
call lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
|
||||
! so the constant offset has no effect on dissipation.
|
||||
|
||||
call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
|
||||
call lopsided_kodis(ex,X,Y,Z,Axx,Axx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
|
||||
call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
|
||||
|
||||
@@ -22,32 +22,19 @@
|
||||
#define f_compute_rhs_Z4c_ss COMPUTE_RHS_Z4C_SS
|
||||
#define f_compute_constraint_fr COMPUTE_CONSTRAINT_FR
|
||||
#endif
|
||||
#ifdef fortran3
|
||||
#define f_compute_rhs_bssn compute_rhs_bssn_
|
||||
#ifdef fortran3
|
||||
#define f_compute_rhs_bssn compute_rhs_bssn_
|
||||
#define f_compute_rhs_bssn_ss compute_rhs_bssn_ss_
|
||||
#define f_compute_rhs_bssn_escalar compute_rhs_bssn_escalar_
|
||||
#define f_compute_rhs_bssn_escalar_ss compute_rhs_bssn_escalar_ss_
|
||||
#define f_compute_rhs_Z4c compute_rhs_z4c_
|
||||
#define f_compute_rhs_Z4cnot compute_rhs_z4cnot_
|
||||
#define f_compute_rhs_Z4c_ss compute_rhs_z4c_ss_
|
||||
#define f_compute_constraint_fr compute_constraint_fr_
|
||||
#endif
|
||||
|
||||
#ifdef __cplusplus
|
||||
extern "C"
|
||||
{
|
||||
#endif
|
||||
void f_bssn_rhs_kernel_timing_reset();
|
||||
int f_bssn_rhs_kernel_timing_bucket_count();
|
||||
const double *f_bssn_rhs_kernel_timing_local_seconds();
|
||||
const char *f_bssn_rhs_kernel_timing_label(int);
|
||||
#ifdef __cplusplus
|
||||
}
|
||||
#endif
|
||||
|
||||
extern "C"
|
||||
{
|
||||
int f_compute_rhs_bssn(int *, double &, double *, double *, double *, // ex,T,X,Y,Z
|
||||
#define f_compute_constraint_fr compute_constraint_fr_
|
||||
#endif
|
||||
extern "C"
|
||||
{
|
||||
int f_compute_rhs_bssn(int *, double &, double *, double *, double *, // ex,T,X,Y,Z
|
||||
double *, double *, // chi, trK
|
||||
double *, double *, double *, double *, double *, double *, // gij
|
||||
double *, double *, double *, double *, double *, double *, // Aij
|
||||
|
||||
@@ -2,88 +2,12 @@
|
||||
#include "bssn_rhs.h"
|
||||
#include "share_func.h"
|
||||
#include "tool.h"
|
||||
#include <time.h>
|
||||
// 0-based i,j,k
|
||||
// #define IDX_F(i,j,k,nx,ny) ((i) + (j)*(nx) + (k)*(nx)*(ny))
|
||||
// ex(1)=nx, ex(2)=ny, ex(3)=nz
|
||||
|
||||
// 用法：a[ IDX_F(i,j,k,nx,ny) ]
|
||||
|
||||
#ifndef BSSN_KERNEL_FINE_TIMING
|
||||
#define BSSN_KERNEL_FINE_TIMING 0
|
||||
#endif
|
||||
|
||||
#if BSSN_KERNEL_FINE_TIMING
|
||||
namespace rhs_kernel_timing
|
||||
{
|
||||
enum Bucket
|
||||
{
|
||||
KB_SETUP_DERIVS = 0,
|
||||
KB_GEOM_GAMMA,
|
||||
KB_RICCI_METRIC,
|
||||
KB_CHI_LAPSE,
|
||||
KB_AIJ_TRK_GAUGE,
|
||||
KB_KO_CONSTRAINT,
|
||||
KB_COUNT
|
||||
};
|
||||
|
||||
static double local_bucket_seconds[KB_COUNT];
|
||||
|
||||
static const char *bucket_labels[KB_COUNT] =
|
||||
{
|
||||
"setup_derivs",
|
||||
"geom_gamma",
|
||||
"ricci_metric",
|
||||
"chi_lapse",
|
||||
"aij_trk_gauge",
|
||||
"ko_constraint"
|
||||
};
|
||||
|
||||
static inline double now_seconds()
|
||||
{
|
||||
struct timespec ts;
|
||||
clock_gettime(CLOCK_MONOTONIC, &ts);
|
||||
return double(ts.tv_sec) + 1.0e-9 * double(ts.tv_nsec);
|
||||
}
|
||||
}
|
||||
|
||||
extern "C" void f_bssn_rhs_kernel_timing_reset()
|
||||
{
|
||||
for (int i = 0; i < rhs_kernel_timing::KB_COUNT; ++i)
|
||||
rhs_kernel_timing::local_bucket_seconds[i] = 0.0;
|
||||
}
|
||||
|
||||
extern "C" int f_bssn_rhs_kernel_timing_bucket_count()
|
||||
{
|
||||
return rhs_kernel_timing::KB_COUNT;
|
||||
}
|
||||
|
||||
extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds()
|
||||
{
|
||||
return rhs_kernel_timing::local_bucket_seconds;
|
||||
}
|
||||
|
||||
extern "C" const char *f_bssn_rhs_kernel_timing_label(int bucket_index)
|
||||
{
|
||||
if (bucket_index < 0 || bucket_index >= rhs_kernel_timing::KB_COUNT)
|
||||
return "unknown";
|
||||
return rhs_kernel_timing::bucket_labels[bucket_index];
|
||||
}
|
||||
|
||||
#define RHS_KERNEL_TIMER_DECL(var_name) const double var_name = rhs_kernel_timing::now_seconds()
|
||||
#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name) \
|
||||
rhs_kernel_timing::local_bucket_seconds[int(rhs_kernel_timing::bucket_name)] += \
|
||||
rhs_kernel_timing::now_seconds() - (var_name)
|
||||
#else
|
||||
extern "C" void f_bssn_rhs_kernel_timing_reset() {}
|
||||
extern "C" int f_bssn_rhs_kernel_timing_bucket_count() { return 0; }
|
||||
extern "C" const double *f_bssn_rhs_kernel_timing_local_seconds() { return 0; }
|
||||
extern "C" const char *f_bssn_rhs_kernel_timing_label(int) { return "disabled"; }
|
||||
|
||||
#define RHS_KERNEL_TIMER_DECL(var_name)
|
||||
#define RHS_KERNEL_TIMER_ADD(bucket_name, var_name)
|
||||
#endif
|
||||
|
||||
// C function that calculates the right-hand side for BSSN equations
|
||||
int f_compute_rhs_bssn(int *ex, double &T,
|
||||
double *X, double *Y, double *Z,
|
||||
@@ -178,7 +102,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
dY = Y[1] - Y[0];
|
||||
dZ = Z[1] - Z[0];
|
||||
|
||||
RHS_KERNEL_TIMER_DECL(timer_setup_derivs);
|
||||
// 1ms //
|
||||
for(int i=0;i<all;i+=1){
|
||||
alpn1[i] = Lap[i] + 1.0;
|
||||
@@ -218,8 +141,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
(dxx[i] + ONE) * betaxz[i] + gxy[i] * betayz[i] + gyz[i] * betayx[i]
|
||||
+ (dzz[i] + ONE) * betazx[i] - gxz[i] * betayy[i];
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_SETUP_DERIVS, timer_setup_derivs);
|
||||
RHS_KERNEL_TIMER_DECL(timer_geom_gamma);
|
||||
// Fused: inverse metric + Gamma constraint + Christoffel (3 loops -> 1)
|
||||
for(int i=0;i<all;i+=1){
|
||||
double det = (dxx[i] + ONE) * (dyy[i] + ONE) * (dzz[i] + ONE) + gxy[i] * gyz[i] * gxz[i] + gxz[i] * gxy[i] * gyz[i] -
|
||||
@@ -362,6 +283,9 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
+ ( gupxy[i]*gupyz[i] + gupyy[i]*gupxz[i] ) * Axy[i]
|
||||
+ ( gupxy[i]*gupzz[i] + gupyz[i]*gupxz[i] ) * Axz[i]
|
||||
+ ( gupyy[i]*gupzz[i] + gupyz[i]*gupyz[i] ) * Ayz[i];
|
||||
Rxx[i] = axx; Ryy[i] = ayy; Rzz[i] = azz;
|
||||
Rxy[i] = axy; Rxz[i] = axz; Ryz[i] = ayz;
|
||||
|
||||
Gamx_rhs[i] = - TWO * ( Lapx[i]*axx + Lapy[i]*axy + Lapz[i]*axz ) +
|
||||
TWO * alpn1[i] * (
|
||||
-F3o2/chin1[i] * ( chix[i]*axx + chiy[i]*axy + chiz[i]*axz ) -
|
||||
@@ -391,8 +315,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
+ TWO * ( Gamzxy[i]*axy + Gamzxz[i]*axz + Gamzyz[i]*ayz )
|
||||
);
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_GEOM_GAMMA, timer_geom_gamma);
|
||||
RHS_KERNEL_TIMER_DECL(timer_ricci_metric);
|
||||
// 22.3ms //
|
||||
fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,
|
||||
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev);
|
||||
@@ -410,6 +332,7 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
double lfxx = gxxx[i] + gxyy[i] + gxzz[i];
|
||||
double lfxy = gxyx[i] + gyyy[i] + gyzz[i];
|
||||
double lfxz = gxzx[i] + gyzy[i] + gzzz[i];
|
||||
fxx[i] = lfxx; fxy[i] = lfxy; fxz[i] = lfxz;
|
||||
|
||||
double gxa = gupxx[i]*Gamxxx[i] + gupyy[i]*Gamxyy[i] + gupzz[i]*Gamxzz[i]
|
||||
+ TWO * ( gupxy[i]*Gamxxy[i] + gupxz[i]*Gamxxz[i] + gupyz[i]*Gamxyz[i] );
|
||||
@@ -763,38 +686,32 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
+ Gamxyz[i] * gzzx[i] + Gamyyz[i] * gzzy[i] + Gamzyz[i] * gzzz[i]
|
||||
);
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_RICCI_METRIC, timer_ricci_metric);
|
||||
|
||||
RHS_KERNEL_TIMER_DECL(timer_chi_lapse);
|
||||
// 22.3ms //
|
||||
fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
|
||||
|
||||
// 7ms //
|
||||
for (int i=0;i<all;i+=1) {
|
||||
const double inv_chin1 = ONE / chin1[i];
|
||||
const double half_inv_chin1 = HALF * inv_chin1;
|
||||
const double scaled_inv = F3o2 * inv_chin1;
|
||||
const double cxx = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
|
||||
const double cxy = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
|
||||
const double cxz = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
|
||||
const double cyy = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
|
||||
const double cyz = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
|
||||
const double czz = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
|
||||
const double ricci_chi =
|
||||
gupxx[i] * (cxx - scaled_inv * chix[i] * chix[i])
|
||||
+ gupyy[i] * (cyy - scaled_inv * chiy[i] * chiy[i])
|
||||
+ gupzz[i] * (czz - scaled_inv * chiz[i] * chiz[i])
|
||||
+ TWO * gupxy[i] * (cxy - scaled_inv * chix[i] * chiy[i])
|
||||
+ TWO * gupxz[i] * (cxz - scaled_inv * chix[i] * chiz[i])
|
||||
+ TWO * gupyz[i] * (cyz - scaled_inv * chiy[i] * chiz[i]);
|
||||
f[i] = ricci_chi;
|
||||
Rxx[i] = Rxx[i] + ( cxx - half_inv_chin1 * chix[i] * chix[i] + (dxx[i] + ONE) * ricci_chi ) * half_inv_chin1;
|
||||
Ryy[i] = Ryy[i] + ( cyy - half_inv_chin1 * chiy[i] * chiy[i] + (dyy[i] + ONE) * ricci_chi ) * half_inv_chin1;
|
||||
Rzz[i] = Rzz[i] + ( czz - half_inv_chin1 * chiz[i] * chiz[i] + (dzz[i] + ONE) * ricci_chi ) * half_inv_chin1;
|
||||
fxx[i] = fxx[i] - Gamxxx[i] * chix[i] - Gamyxx[i] * chiy[i] - Gamzxx[i] * chiz[i];
|
||||
fxy[i] = fxy[i] - Gamxxy[i] * chix[i] - Gamyxy[i] * chiy[i] - Gamzxy[i] * chiz[i];
|
||||
fxz[i] = fxz[i] - Gamxxz[i] * chix[i] - Gamyxz[i] * chiy[i] - Gamzxz[i] * chiz[i];
|
||||
fyy[i] = fyy[i] - Gamxyy[i] * chix[i] - Gamyyy[i] * chiy[i] - Gamzyy[i] * chiz[i];
|
||||
fyz[i] = fyz[i] - Gamxyz[i] * chix[i] - Gamyyz[i] * chiy[i] - Gamzyz[i] * chiz[i];
|
||||
fzz[i] = fzz[i] - Gamxzz[i] * chix[i] - Gamyzz[i] * chiy[i] - Gamzzz[i] * chiz[i];
|
||||
f[i] =
|
||||
gupxx[i] * (fxx[i] - (F3o2 / chin1[i]) * chix[i] * chix[i])
|
||||
+ gupyy[i] * (fyy[i] - (F3o2 / chin1[i]) * chiy[i] * chiy[i])
|
||||
+ gupzz[i] * (fzz[i] - (F3o2 / chin1[i]) * chiz[i] * chiz[i])
|
||||
+ TWO * gupxy[i] * (fxy[i] - (F3o2 / chin1[i]) * chix[i] * chiy[i])
|
||||
+ TWO * gupxz[i] * (fxz[i] - (F3o2 / chin1[i]) * chix[i] * chiz[i])
|
||||
+ TWO * gupyz[i] * (fyz[i] - (F3o2 / chin1[i]) * chiy[i] * chiz[i]);
|
||||
Rxx[i] = Rxx[i] + ( fxx[i] - (chix[i] * chix[i]) / (chin1[i] * TWO) + (dxx[i] + ONE) * f[i] ) / (chin1[i] * TWO);
|
||||
Ryy[i] = Ryy[i] + ( fyy[i] - (chiy[i] * chiy[i]) / (chin1[i] * TWO) + (dyy[i] + ONE) * f[i] ) / (chin1[i] * TWO);
|
||||
Rzz[i] = Rzz[i] + ( fzz[i] - (chiz[i] * chiz[i]) / (chin1[i] * TWO) + (dzz[i] + ONE) * f[i] ) / (chin1[i] * TWO);
|
||||
|
||||
Rxy[i] = Rxy[i] + ( cxy - half_inv_chin1 * chix[i] * chiy[i] + gxy[i] * ricci_chi ) * half_inv_chin1;
|
||||
Rxz[i] = Rxz[i] + ( cxz - half_inv_chin1 * chix[i] * chiz[i] + gxz[i] * ricci_chi ) * half_inv_chin1;
|
||||
Ryz[i] = Ryz[i] + ( cyz - half_inv_chin1 * chiy[i] * chiz[i] + gyz[i] * ricci_chi ) * half_inv_chin1;
|
||||
Rxy[i] = Rxy[i] + ( fxy[i] - (chix[i] * chiy[i]) / (chin1[i] * TWO) + gxy[i] * f[i] ) / (chin1[i] * TWO);
|
||||
Rxz[i] = Rxz[i] + ( fxz[i] - (chix[i] * chiz[i]) / (chin1[i] * TWO) + gxz[i] * f[i] ) / (chin1[i] * TWO);
|
||||
Ryz[i] = Ryz[i] + ( fyz[i] - (chiy[i] * chiz[i]) / (chin1[i] * TWO) + gyz[i] * f[i] ) / (chin1[i] * TWO);
|
||||
}
|
||||
|
||||
// 24ms //
|
||||
@@ -802,35 +719,35 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
|
||||
// 6ms //
|
||||
for (int i=0;i<all;i+=1) {
|
||||
const double inv_chin1 = ONE / chin1[i];
|
||||
const double gchi_x = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) * inv_chin1;
|
||||
const double gchi_y = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) * inv_chin1;
|
||||
const double gchi_z = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) * inv_chin1;
|
||||
/* gxxx,gxxy,gxxz (这里是“升指标后的chi导数/chi”那类量，你沿用原变量名即可) */
|
||||
gxxx[i] = (gupxx[i] * chix[i] + gupxy[i] * chiy[i] + gupxz[i] * chiz[i]) / chin1[i];
|
||||
gxxy[i] = (gupxy[i] * chix[i] + gupyy[i] * chiy[i] + gupyz[i] * chiz[i]) / chin1[i];
|
||||
gxxz[i] = (gupxz[i] * chix[i] + gupyz[i] * chiy[i] + gupzz[i] * chiz[i]) / chin1[i];
|
||||
|
||||
/* Christoffel 修正项 */
|
||||
Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) * inv_chin1) - (dxx[i] + ONE) * gchi_x ) * HALF;
|
||||
Gamyxx[i] = Gamyxx[i] - ( 0.0 - (dxx[i] + ONE) * gchi_y ) * HALF; /* 原式只有 -gxx*gxxy */
|
||||
Gamzxx[i] = Gamzxx[i] - ( 0.0 - (dxx[i] + ONE) * gchi_z ) * HALF;
|
||||
Gamxxx[i] = Gamxxx[i] - ( ((chix[i] + chix[i]) / chin1[i]) - (dxx[i] + ONE) * gxxx[i] ) * HALF;
|
||||
Gamyxx[i] = Gamyxx[i] - ( 0.0 - (dxx[i] + ONE) * gxxy[i] ) * HALF; /* 原式只有 -gxx*gxxy */
|
||||
Gamzxx[i] = Gamzxx[i] - ( 0.0 - (dxx[i] + ONE) * gxxz[i] ) * HALF;
|
||||
|
||||
Gamxyy[i] = Gamxyy[i] - ( 0.0 - (dyy[i] + ONE) * gchi_x ) * HALF;
|
||||
Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) * inv_chin1) - (dyy[i] + ONE) * gchi_y ) * HALF;
|
||||
Gamzyy[i] = Gamzyy[i] - ( 0.0 - (dyy[i] + ONE) * gchi_z ) * HALF;
|
||||
Gamxyy[i] = Gamxyy[i] - ( 0.0 - (dyy[i] + ONE) * gxxx[i] ) * HALF;
|
||||
Gamyyy[i] = Gamyyy[i] - ( ((chiy[i] + chiy[i]) / chin1[i]) - (dyy[i] + ONE) * gxxy[i] ) * HALF;
|
||||
Gamzyy[i] = Gamzyy[i] - ( 0.0 - (dyy[i] + ONE) * gxxz[i] ) * HALF;
|
||||
|
||||
Gamxzz[i] = Gamxzz[i] - ( 0.0 - (dzz[i] + ONE) * gchi_x ) * HALF;
|
||||
Gamyzz[i] = Gamyzz[i] - ( 0.0 - (dzz[i] + ONE) * gchi_y ) * HALF;
|
||||
Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) * inv_chin1) - (dzz[i] + ONE) * gchi_z ) * HALF;
|
||||
Gamxzz[i] = Gamxzz[i] - ( 0.0 - (dzz[i] + ONE) * gxxx[i] ) * HALF;
|
||||
Gamyzz[i] = Gamyzz[i] - ( 0.0 - (dzz[i] + ONE) * gxxy[i] ) * HALF;
|
||||
Gamzzz[i] = Gamzzz[i] - ( ((chiz[i] + chiz[i]) / chin1[i]) - (dzz[i] + ONE) * gxxz[i] ) * HALF;
|
||||
|
||||
Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] * inv_chin1) - gxy[i] * gchi_x ) * HALF;
|
||||
Gamyxy[i] = Gamyxy[i] - ( ( chix[i] * inv_chin1) - gxy[i] * gchi_y ) * HALF;
|
||||
Gamzxy[i] = Gamzxy[i] - ( 0.0 - gxy[i] * gchi_z ) * HALF;
|
||||
Gamxxy[i] = Gamxxy[i] - ( ( chiy[i] / chin1[i]) - gxy[i] * gxxx[i] ) * HALF;
|
||||
Gamyxy[i] = Gamyxy[i] - ( ( chix[i] / chin1[i]) - gxy[i] * gxxy[i] ) * HALF;
|
||||
Gamzxy[i] = Gamzxy[i] - ( 0.0 - gxy[i] * gxxz[i] ) * HALF;
|
||||
|
||||
Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] * inv_chin1) - gxz[i] * gchi_x ) * HALF;
|
||||
Gamyxz[i] = Gamyxz[i] - ( 0.0 - gxz[i] * gchi_y ) * HALF;
|
||||
Gamzxz[i] = Gamzxz[i] - ( ( chix[i] * inv_chin1) - gxz[i] * gchi_z ) * HALF;
|
||||
Gamxxz[i] = Gamxxz[i] - ( ( chiz[i] / chin1[i]) - gxz[i] * gxxx[i] ) * HALF;
|
||||
Gamyxz[i] = Gamyxz[i] - ( 0.0 - gxz[i] * gxxy[i] ) * HALF;
|
||||
Gamzxz[i] = Gamzxz[i] - ( ( chix[i] / chin1[i]) - gxz[i] * gxxz[i] ) * HALF;
|
||||
|
||||
Gamxyz[i] = Gamxyz[i] - ( 0.0 - gyz[i] * gchi_x ) * HALF;
|
||||
Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] * inv_chin1) - gyz[i] * gchi_y ) * HALF;
|
||||
Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] * inv_chin1) - gyz[i] * gchi_z ) * HALF;
|
||||
Gamxyz[i] = Gamxyz[i] - ( 0.0 - gyz[i] * gxxx[i] ) * HALF;
|
||||
Gamyyz[i] = Gamyyz[i] - ( ( chiz[i] / chin1[i]) - gyz[i] * gxxy[i] ) * HALF;
|
||||
Gamzyz[i] = Gamzyz[i] - ( ( chiy[i] / chin1[i]) - gyz[i] * gxxz[i] ) * HALF;
|
||||
|
||||
/* fxx..fyz 修正：减去 Γ * ∂Lap */
|
||||
fxx[i] = fxx[i] - Gamxxx[i] * Lapx[i] - Gamyxx[i] * Lapy[i] - Gamzxx[i] * Lapz[i];
|
||||
@@ -844,8 +761,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
trK_rhs[i] = gupxx[i] * fxx[i] + gupyy[i] * fyy[i] + gupzz[i] * fzz[i]
|
||||
+ TWO * ( gupxy[i] * fxy[i] + gupxz[i] * fxz[i] + gupyz[i] * fyz[i] );
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_CHI_LAPSE, timer_chi_lapse);
|
||||
RHS_KERNEL_TIMER_DECL(timer_aij_trk_gauge);
|
||||
// 2.5ms //
|
||||
for (int i=0;i<all;i+=1) {
|
||||
const double divb = betaxx[i] + betayy[i] + betazz[i];
|
||||
@@ -1098,12 +1013,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
betaz_rhs[i] = FF * dtSfz[i];
|
||||
|
||||
reta[i] =
|
||||
gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
|
||||
+ gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
|
||||
+ gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
|
||||
+ TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
|
||||
+ gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
|
||||
+ gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
|
||||
gupxx[i] * chix[i] * chix[i]
|
||||
+ gupyy[i] * chiy[i] * chiy[i]
|
||||
+ gupzz[i] * chiz[i] * chiz[i]
|
||||
+ TWO * ( gupxy[i] * chix[i] * chiy[i]
|
||||
+ gupxz[i] * chix[i] * chiz[i]
|
||||
+ gupyz[i] * chiy[i] * chiz[i] );
|
||||
|
||||
#if (GAUGE == 2)
|
||||
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
||||
@@ -1116,12 +1031,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
|
||||
#elif (GAUGE == 4 || GAUGE == 5)
|
||||
reta[i] =
|
||||
gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
|
||||
+ gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
|
||||
+ gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
|
||||
+ TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
|
||||
+ gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
|
||||
+ gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
|
||||
gupxx[i] * chix[i] * chix[i]
|
||||
+ gupyy[i] * chiy[i] * chiy[i]
|
||||
+ gupzz[i] * chiz[i] * chiz[i]
|
||||
+ TWO * ( gupxy[i] * chix[i] * chiy[i]
|
||||
+ gupxz[i] * chix[i] * chiz[i]
|
||||
+ gupyz[i] * chiy[i] * chiz[i] );
|
||||
|
||||
#if (GAUGE == 4)
|
||||
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
||||
@@ -1146,8 +1061,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
|
||||
#endif
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_AIJ_TRK_GAUGE, timer_aij_trk_gauge);
|
||||
RHS_KERNEL_TIMER_DECL(timer_ko_constraint);
|
||||
// advection + KO dissipation with shared symmetry buffer
|
||||
lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps);
|
||||
lopsided_kodis(ex,X,Y,Z,Gamz,Gamz_rhs,betax,betay,betaz,Symmetry,SSA,eps);
|
||||
@@ -1279,7 +1192,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
||||
movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
|
||||
}
|
||||
}
|
||||
RHS_KERNEL_TIMER_ADD(KB_KO_CONSTRAINT, timer_ko_constraint);
|
||||
|
||||
|
||||
|
||||
|
||||
@@ -1511,88 +1511,13 @@ deallocate(f_flat)
|
||||
|
||||
f_out = f_out*dX*dY*dZ
|
||||
|
||||
return
|
||||
|
||||
end subroutine l2normhelper
|
||||
!--------------------------------------------------------------------------------------
|
||||
subroutine l2normhelper7(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
|
||||
f1,f2,f3,f4,f5,f6,f7,f_out,gw)
|
||||
|
||||
implicit none
|
||||
!~~~~~~> Input parameters:
|
||||
integer,intent(in ):: ex(1:3)
|
||||
real*8, intent(in ):: X(1:ex(1)),Y(1:ex(2)),Z(1:ex(3)),xmin,ymin,zmin,xmax,ymax,zmax
|
||||
integer,intent(in)::gw
|
||||
real*8, dimension(ex(1),ex(2),ex(3)),intent(in) :: f1,f2,f3,f4,f5,f6,f7
|
||||
real*8, intent(out) :: f_out(7)
|
||||
!~~~~~~> Other variables:
|
||||
|
||||
real*8 :: dX, dY, dZ
|
||||
integer::imin,jmin,kmin
|
||||
integer::imax,jmax,kmax
|
||||
integer::i,j,k
|
||||
real*8 :: s1,s2,s3,s4,s5,s6,s7
|
||||
|
||||
dX = X(2) - X(1)
|
||||
dY = Y(2) - Y(1)
|
||||
dZ = Z(2) - Z(1)
|
||||
|
||||
! for ghost zone
|
||||
imin = gw+1
|
||||
jmin = gw+1
|
||||
kmin = gw+1
|
||||
|
||||
imax = ex(1) - gw
|
||||
jmax = ex(2) - gw
|
||||
kmax = ex(3) - gw
|
||||
|
||||
!for patch boundary (i.e., not ghost boundary)
|
||||
|
||||
if(dabs(X(ex(1))-xmax) < dX) imax = ex(1)
|
||||
if(dabs(Y(ex(2))-ymax) < dY) jmax = ex(2)
|
||||
if(dabs(Z(ex(3))-zmax) < dZ) kmax = ex(3)
|
||||
if(dabs(X(1)-xmin) < dX) imin = 1
|
||||
if(dabs(Y(1)-ymin) < dY) jmin = 1
|
||||
if(dabs(Z(1)-zmin) < dZ) kmin = 1
|
||||
|
||||
s1 = 0.d0
|
||||
s2 = 0.d0
|
||||
s3 = 0.d0
|
||||
s4 = 0.d0
|
||||
s5 = 0.d0
|
||||
s6 = 0.d0
|
||||
s7 = 0.d0
|
||||
|
||||
do k=kmin,kmax
|
||||
do j=jmin,jmax
|
||||
!DIR$ SIMD REDUCTION(+:s1,s2,s3,s4,s5,s6,s7)
|
||||
do i=imin,imax
|
||||
s1 = s1 + f1(i,j,k)*f1(i,j,k)
|
||||
s2 = s2 + f2(i,j,k)*f2(i,j,k)
|
||||
s3 = s3 + f3(i,j,k)*f3(i,j,k)
|
||||
s4 = s4 + f4(i,j,k)*f4(i,j,k)
|
||||
s5 = s5 + f5(i,j,k)*f5(i,j,k)
|
||||
s6 = s6 + f6(i,j,k)*f6(i,j,k)
|
||||
s7 = s7 + f7(i,j,k)*f7(i,j,k)
|
||||
enddo
|
||||
enddo
|
||||
enddo
|
||||
|
||||
f_out(1) = s1*dX*dY*dZ
|
||||
f_out(2) = s2*dX*dY*dZ
|
||||
f_out(3) = s3*dX*dY*dZ
|
||||
f_out(4) = s4*dX*dY*dZ
|
||||
f_out(5) = s5*dX*dY*dZ
|
||||
f_out(6) = s6*dX*dY*dZ
|
||||
f_out(7) = s7*dX*dY*dZ
|
||||
|
||||
return
|
||||
|
||||
end subroutine l2normhelper7
|
||||
!--------------------------------------------------------------------------------------
|
||||
! calculate L2norm especially for shell Blocks
|
||||
subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
|
||||
f,f_out,gw,ogw,Symmetry)
|
||||
return
|
||||
|
||||
end subroutine l2normhelper
|
||||
!--------------------------------------------------------------------------------------
|
||||
! calculate L2norm especially for shell Blocks
|
||||
subroutine l2normhelper_sh(ex, X, Y, Z,xmin,ymin,zmin,xmax,ymax,zmax,&
|
||||
f,f_out,gw,ogw,Symmetry)
|
||||
|
||||
implicit none
|
||||
!~~~~~~> Input parameters:
|
||||
|
||||
@@ -12,10 +12,9 @@
|
||||
#define f_global_interpind global_interpind
|
||||
#define f_global_interpind2d global_interpind2d
|
||||
#define f_global_interpind1d global_interpind1d
|
||||
#define f_l2normhelper l2normhelper
|
||||
#define f_l2normhelper7 l2normhelper7
|
||||
#define f_l2normhelper_sh l2normhelper_sh
|
||||
#define f_l2normhelper_sh_rms l2normhelper_sh_rms
|
||||
#define f_l2normhelper l2normhelper
|
||||
#define f_l2normhelper_sh l2normhelper_sh
|
||||
#define f_l2normhelper_sh_rms l2normhelper_sh_rms
|
||||
#define f_average average
|
||||
#define f_average3 average3
|
||||
#define f_average2 average2
|
||||
@@ -42,10 +41,9 @@
|
||||
#define f_global_interpind GLOBAL_INTERPIND
|
||||
#define f_global_interpind2d GLOBAL_INTERPIND2D
|
||||
#define f_global_interpind1d GLOBAL_INTERPIND1D
|
||||
#define f_l2normhelper L2NORMHELPER
|
||||
#define f_l2normhelper7 L2NORMHELPER7
|
||||
#define f_l2normhelper_sh L2NORMHELPER_SH
|
||||
#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
|
||||
#define f_l2normhelper L2NORMHELPER
|
||||
#define f_l2normhelper_sh L2NORMHELPER_SH
|
||||
#define f_l2normhelper_sh_rms L2NORMHELPER_SH_RMS
|
||||
#define f_average AVERAGE
|
||||
#define f_average3 AVERAGE3
|
||||
#define f_average2 AVERAGE2
|
||||
@@ -72,10 +70,9 @@
|
||||
#define f_global_interpind global_interpind_
|
||||
#define f_global_interpind2d global_interpind2d_
|
||||
#define f_global_interpind1d global_interpind1d_
|
||||
#define f_l2normhelper l2normhelper_
|
||||
#define f_l2normhelper7 l2normhelper7_
|
||||
#define f_l2normhelper_sh l2normhelper_sh_
|
||||
#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
|
||||
#define f_l2normhelper l2normhelper_
|
||||
#define f_l2normhelper_sh l2normhelper_sh_
|
||||
#define f_l2normhelper_sh_rms l2normhelper_sh_rms_
|
||||
#define f_average average_
|
||||
#define f_average3 average3_
|
||||
#define f_average2 average2_
|
||||
@@ -159,29 +156,20 @@ extern "C"
|
||||
int *, double *, int &, int &);
|
||||
}
|
||||
|
||||
extern "C"
|
||||
{
|
||||
void f_l2normhelper(int *, double *, double *, double *,
|
||||
double &, double &, double &,
|
||||
double &, double &, double &,
|
||||
double *, double &, int &);
|
||||
}
|
||||
|
||||
extern "C"
|
||||
{
|
||||
void f_l2normhelper7(int *, double *, double *, double *,
|
||||
double &, double &, double &,
|
||||
double &, double &, double &,
|
||||
double *, double *, double *, double *,
|
||||
double *, double *, double *, double *, int &);
|
||||
}
|
||||
|
||||
extern "C"
|
||||
{
|
||||
void f_l2normhelper_sh(int *, double *, double *, double *,
|
||||
double &, double &, double &,
|
||||
double &, double &, double &,
|
||||
double *, double &, int &, int &, int &);
|
||||
extern "C"
|
||||
{
|
||||
void f_l2normhelper(int *, double *, double *, double *,
|
||||
double &, double &, double &,
|
||||
double &, double &, double &,
|
||||
double *, double &, int &);
|
||||
}
|
||||
|
||||
extern "C"
|
||||
{
|
||||
void f_l2normhelper_sh(int *, double *, double *, double *,
|
||||
double &, double &, double &,
|
||||
double &, double &, double &,
|
||||
double *, double &, int &, int &, int &);
|
||||
}
|
||||
|
||||
extern "C"
|
||||
|
||||
@@ -29,16 +29,6 @@
|
||||
|
||||
#define REGLEV 0
|
||||
|
||||
#define BSSN_FINE_TIMING 0
|
||||
|
||||
#define BSSN_FINE_TIMING_EVERY 1
|
||||
|
||||
#define BSSN_FINE_TIMING_TOPN 8
|
||||
|
||||
#define BSSN_KERNEL_FINE_TIMING 0
|
||||
|
||||
#define BSSN_ENABLE_STDIN_ABORT_POLL 0
|
||||
|
||||
//#define USE_GPU
|
||||
|
||||
//#define CHECKDETAIL
|
||||
@@ -98,21 +88,6 @@
|
||||
// 0: for every level;
|
||||
// 1: for all
|
||||
//
|
||||
// define BSSN_FINE_TIMING
|
||||
// enable fine-grained per-timestep timing monitor
|
||||
//
|
||||
// define BSSN_FINE_TIMING_EVERY
|
||||
// report timing every N coarse timesteps
|
||||
//
|
||||
// define BSSN_FINE_TIMING_TOPN
|
||||
// number of hottest timing buckets shown in stdout
|
||||
//
|
||||
// define BSSN_KERNEL_FINE_TIMING
|
||||
// enable split timing inside compute_rhs_bssn
|
||||
//
|
||||
// define BSSN_ENABLE_STDIN_ABORT_POLL
|
||||
// poll stdin and broadcast abort flag every coarse step
|
||||
//
|
||||
// define USE_GPU
|
||||
// use gpu or not
|
||||
//
|
||||
@@ -167,3 +142,4 @@
|
||||
#define TINY 1e-10
|
||||
|
||||
#endif /* MICRODEF_H */
|
||||
|
||||
|
||||
@@ -64,8 +64,8 @@ lopsided_c.o: lopsided_c.C
|
||||
lopsided_kodis_c.o: lopsided_kodis_c.C
|
||||
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
||||
|
||||
#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
|
||||
# ${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
||||
interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
|
||||
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
||||
|
||||
## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
|
||||
TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
@@ -27,24 +27,19 @@ using namespace std;
|
||||
class surface_integral
|
||||
{
|
||||
|
||||
private:
|
||||
int Symmetry, factor;
|
||||
int N_theta, N_phi; // Number of points in Theta & Phi directions
|
||||
double dphi, dcostheta;
|
||||
double *arcostheta, *wtcostheta;
|
||||
int n_tot; // size of arrays
|
||||
|
||||
double *nx_g, *ny_g, *nz_g; // global list of unit normals
|
||||
int myrank, cpusize;
|
||||
int wave_cache_spinw, wave_cache_maxl, wave_cache_modes;
|
||||
double *wave_theta_pos, *wave_theta_neg;
|
||||
double *wave_phi_cos, *wave_phi_sin;
|
||||
void clear_wave_cache();
|
||||
void build_wave_cache(int spinw, int maxl);
|
||||
|
||||
public:
|
||||
surface_integral(int iSymmetry);
|
||||
~surface_integral();
|
||||
private:
|
||||
int Symmetry, factor;
|
||||
int N_theta, N_phi; // Number of points in Theta & Phi directions
|
||||
double dphi, dcostheta;
|
||||
double *arcostheta, *wtcostheta;
|
||||
int n_tot; // size of arrays
|
||||
|
||||
double *nx_g, *ny_g, *nz_g; // global list of unit normals
|
||||
int myrank, cpusize;
|
||||
|
||||
public:
|
||||
surface_integral(int iSymmetry);
|
||||
~surface_integral();
|
||||
|
||||
void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
|
||||
int spinw, int maxl, int NN, double *RP, double *IP,
|
||||
@@ -82,37 +77,21 @@ public:
|
||||
double &, double &, double &, double &, double &, double &, double &,
|
||||
double &, double &, double &, double &, double &, double &,
|
||||
double &, double &)); // NN is the length of RP and IP
|
||||
void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
|
||||
void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
|
||||
void surf_WaveMassPAng(double rex, int lev, cgh *GH,
|
||||
var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
|
||||
var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
|
||||
void surf_WaveMassPAng(double rex, int lev, ShellPatch *GH,
|
||||
var *Rpsi4, var *Ipsi4, int spinw, int maxl, int NN, double *RP, double *IP,
|
||||
var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor, bool refresh_mass_fields = true);
|
||||
void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
|
||||
var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor);
|
||||
void surf_MassPAng(double rex, int lev, ShellPatch *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs,
|
||||
double *Rout, monitor *Monitor);
|
||||
void surf_Wave(double rex, cgh *GH, ShellPatch *SH,
|
||||
var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *chix, var *chiy, var *chiz,
|
||||
var *trKx, var *trKy, var *trKz,
|
||||
@@ -131,12 +110,12 @@ public:
|
||||
bool SR_Interp_Points(MyList<var> *VarList, cgh *GH, ShellPatch *SH,
|
||||
int NN, double **XX, double *Shellf);
|
||||
|
||||
void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
|
||||
double *Rout, monitor *Monitor, MPI_Comm Comm_here, bool refresh_mass_fields = true);
|
||||
void surf_MassPAng(double rex, int lev, cgh *GH, var *chi, var *trK,
|
||||
var *gxx, var *gxy, var *gxz, var *gyy, var *gyz, var *gzz,
|
||||
var *Axx, var *Axy, var *Axz, var *Ayy, var *Ayz, var *Azz,
|
||||
var *Gmx, var *Gmy, var *Gmz,
|
||||
var *Sfx_rhs, var *Sfy_rhs, var *Sfz_rhs, // temparay memory for mass^i
|
||||
double *Rout, monitor *Monitor, MPI_Comm Comm_here);
|
||||
void surf_Wave(double rex, int lev, cgh *GH, var *Rpsi4, var *Ipsi4,
|
||||
int spinw, int maxl, int NN, double *RP, double *IP,
|
||||
monitor *Monitor, MPI_Comm Comm_here);
|
||||
|
||||
@@ -144,62 +144,6 @@ def generate_macrodef_h():
|
||||
print( "#define REGLEV 0", file=file1 )
|
||||
print( file=file1 )
|
||||
|
||||
# Define fine-grained timing/debug macros.
|
||||
# All of them default to OFF so production builds do not pay profiling overhead.
|
||||
|
||||
fine_timing = getattr(input_data, "Fine_Timing",
|
||||
getattr(input_data, "Finegrained_Timing", "no"))
|
||||
kernel_fine_timing = getattr(input_data, "Kernel_Fine_Timing",
|
||||
getattr(input_data, "BSSN_Kernel_Fine_Timing", "no"))
|
||||
stdin_abort_poll = getattr(input_data, "Enable_Stdin_Abort_Poll",
|
||||
getattr(input_data, "Stdin_Abort_Poll", "no"))
|
||||
timing_report_every = max(1, int(getattr(
|
||||
input_data, "Timing_Every_Steps",
|
||||
getattr(input_data, "Timing_Report_Every", 1))))
|
||||
timing_top_hotspots = max(1, int(getattr(
|
||||
input_data, "Timing_Top_Hotspots", 8)))
|
||||
|
||||
if ( fine_timing == "yes" ):
|
||||
print( "#define BSSN_FINE_TIMING 1", file=file1 )
|
||||
print( file=file1 )
|
||||
elif ( fine_timing == "no" ):
|
||||
print( "#define BSSN_FINE_TIMING 0", file=file1 )
|
||||
print( file=file1 )
|
||||
else:
|
||||
print( "Fine_Timing setting error!!!" )
|
||||
print()
|
||||
print( "# Fine_Timing setting error!!!", file=file1 )
|
||||
print( file=file1 )
|
||||
|
||||
print( f"#define BSSN_FINE_TIMING_EVERY {timing_report_every}", file=file1 )
|
||||
print( file=file1 )
|
||||
print( f"#define BSSN_FINE_TIMING_TOPN {timing_top_hotspots}", file=file1 )
|
||||
print( file=file1 )
|
||||
|
||||
if ( kernel_fine_timing == "yes" ):
|
||||
print( "#define BSSN_KERNEL_FINE_TIMING 1", file=file1 )
|
||||
print( file=file1 )
|
||||
elif ( kernel_fine_timing == "no" ):
|
||||
print( "#define BSSN_KERNEL_FINE_TIMING 0", file=file1 )
|
||||
print( file=file1 )
|
||||
else:
|
||||
print( "Kernel_Fine_Timing setting error!!!" )
|
||||
print()
|
||||
print( "# Kernel_Fine_Timing setting error!!!", file=file1 )
|
||||
print( file=file1 )
|
||||
|
||||
if ( stdin_abort_poll == "yes" ):
|
||||
print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 1", file=file1 )
|
||||
print( file=file1 )
|
||||
elif ( stdin_abort_poll == "no" ):
|
||||
print( "#define BSSN_ENABLE_STDIN_ABORT_POLL 0", file=file1 )
|
||||
print( file=file1 )
|
||||
else:
|
||||
print( "Enable_Stdin_Abort_Poll setting error!!!" )
|
||||
print()
|
||||
print( "# Enable_Stdin_Abort_Poll setting error!!!", file=file1 )
|
||||
print( file=file1 )
|
||||
|
||||
# Define macro USE_GPU
|
||||
# use GPU or not
|
||||
|
||||
@@ -280,21 +224,6 @@ def generate_macrodef_h():
|
||||
print( "// 0: for every level;", file=file1 )
|
||||
print( "// 1: for all", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define BSSN_FINE_TIMING", file=file1 )
|
||||
print( "// enable fine-grained per-timestep timing monitor", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define BSSN_FINE_TIMING_EVERY", file=file1 )
|
||||
print( "// report timing every N coarse timesteps", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define BSSN_FINE_TIMING_TOPN", file=file1 )
|
||||
print( "// number of hottest timing buckets shown in stdout", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define BSSN_KERNEL_FINE_TIMING", file=file1 )
|
||||
print( "// enable split timing inside compute_rhs_bssn", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define BSSN_ENABLE_STDIN_ABORT_POLL", file=file1 )
|
||||
print( "// poll stdin and broadcast abort flag every coarse step", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
print( "// define USE_GPU", file=file1 )
|
||||
print( "// use gpu or not", file=file1 )
|
||||
print( "//", file=file1 )
|
||||
|
||||
Reference in New Issue
Block a user