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5 Commits
cjy-dystop
...
chb-parall
| Author | SHA1 | Date | |
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9c44d1c885
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4b9de28feb
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4eb5dc4ddb
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| 688bdb6708 | |||
| 524d1d1512 |
@@ -36,18 +36,12 @@ using namespace std;
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#include "myglobal.h"
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#include "myglobal.h"
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#endif
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#endif
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#include "perf.h"
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#include "perf.h"
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#include "derivatives.h"
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#include "derivatives.h"
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#include "ricci_gamma.h"
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#include "ricci_gamma.h"
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// Compile-time switch for per-timestep memory usage collection/printing.
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//================================================================================================
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// Default is OFF to reduce overhead in production runs.
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#ifndef BSSN_ENABLE_MEM_USAGE_LOG
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#define BSSN_ENABLE_MEM_USAGE_LOG 0
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#endif
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//================================================================================================
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// define bssn_class
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// define bssn_class
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@@ -2135,10 +2129,8 @@ void bssn_class::Evolve(int Steps)
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#endif
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#endif
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*/
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*/
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#if BSSN_ENABLE_MEM_USAGE_LOG
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perf bssn_perf;
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perf bssn_perf;
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size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
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size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
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#endif
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for (int lev = 0; lev < GH->levels; lev++)
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for (int lev = 0; lev < GH->levels; lev++)
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GH->Lt[lev] = PhysTime;
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GH->Lt[lev] = PhysTime;
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@@ -2232,23 +2224,21 @@ void bssn_class::Evolve(int Steps)
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// fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
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// fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
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#endif
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#endif
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#if BSSN_ENABLE_MEM_USAGE_LOG
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// Retrieve memory usage information used during computation; master process prints it
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// Retrieve memory usage information used during computation; master process prints it
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bssn_perf.MemoryUsage(¤t_min, ¤t_avg, ¤t_max,
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bssn_perf.MemoryUsage(¤t_min, ¤t_avg, ¤t_max,
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&peak_min, &peak_avg, &peak_max, nprocs);
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&peak_min, &peak_avg, &peak_max, nprocs);
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if (myrank == 0)
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if (myrank == 0)
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{
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{
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printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
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printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
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"peak %0.4lg/%0.4lg/%0.4lgMB\n",
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"peak %0.4lg/%0.4lg/%0.4lgMB\n",
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(double)current_min / (1024.0 * 1024.0),
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(double)current_min / (1024.0 * 1024.0),
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(double)current_avg / (1024.0 * 1024.0),
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(double)current_avg / (1024.0 * 1024.0),
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(double)current_max / (1024.0 * 1024.0),
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(double)current_max / (1024.0 * 1024.0),
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(double)peak_min / (1024.0 * 1024.0),
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(double)peak_min / (1024.0 * 1024.0),
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(double)peak_avg / (1024.0 * 1024.0),
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(double)peak_avg / (1024.0 * 1024.0),
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(double)peak_max / (1024.0 * 1024.0));
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(double)peak_max / (1024.0 * 1024.0));
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cout << endl;
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cout << endl;
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}
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}
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#endif
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// Output puncture positions at each step
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// Output puncture positions at each step
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if (myrank == 0)
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if (myrank == 0)
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@@ -5755,11 +5745,17 @@ void bssn_class::SHStep()
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//================================================================================================
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//================================================================================================
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// 0: do not use mixing two levels data for OutBD; 1: do use
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// 0: do not use mixing two levels data for OutBD; 1: do use
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#define MIXOUTB 0
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#define MIXOUTB 0
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void bssn_class::RestrictProlong(int lev, int YN, bool BB,
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// In the cached Restrict->OutBdLow2Hi path, coarse Sync is usually redundant:
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MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
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// OutBdLow2Hi_cached reads coarse owned cells (build_owned_gsl type-4), not coarse ghost/buffer cells.
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// Keep a switch to restore the old behavior if needed for debugging.
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#ifndef RP_SYNC_COARSE_AFTER_RESTRICT
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#define RP_SYNC_COARSE_AFTER_RESTRICT 0
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#endif
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void bssn_class::RestrictProlong(int lev, int YN, bool BB,
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MyList<var> *SL, MyList<var> *OL, MyList<var> *corL)
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// we assume
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// we assume
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// StateList 1 -----------
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// StateList 1 -----------
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//
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//
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@@ -5821,7 +5817,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
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// misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
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// misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (PSTR == 1 || PSTR == 2)
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#if (PSTR == 1 || PSTR == 2)
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// a_stream.clear();
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// a_stream.clear();
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@@ -5872,7 +5870,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB,
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// misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
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// misc::tillherecheck(GH->Commlev[GH->mylev],GH->start_rank[GH->mylev],a_stream.str());
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (PSTR == 1 || PSTR == 2)
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#if (PSTR == 1 || PSTR == 2)
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// a_stream.clear();
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// a_stream.clear();
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@@ -5958,7 +5958,9 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SynchList_pre, GH->rsul[lev], Symmetry);
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (RPB == 0)
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#if (RPB == 0)
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#if (MIXOUTB == 0)
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#if (MIXOUTB == 0)
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@@ -5980,7 +5982,9 @@ void bssn_class::RestrictProlong_aux(int lev, int YN, bool BB,
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SL, SL, GH->rsul[lev], Symmetry);
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], SL, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (RPB == 0)
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#if (RPB == 0)
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#if (MIXOUTB == 0)
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#if (MIXOUTB == 0)
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@@ -6045,7 +6049,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, SynchList_pre, GH->rsul[lev], Symmetry);
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], SynchList_pre, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (RPB == 0)
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#if (RPB == 0)
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#if (MIXOUTB == 0)
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#if (MIXOUTB == 0)
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@@ -6069,7 +6075,9 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
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Parallel::Restrict_bam(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, GH->rsul[lev], Symmetry);
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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#if (RPB == 0)
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#if (RPB == 0)
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#if (MIXOUTB == 0)
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#if (MIXOUTB == 0)
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@@ -6093,7 +6101,7 @@ void bssn_class::RestrictProlong(int lev, int YN, bool BB)
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//================================================================================================
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//================================================================================================
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void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
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void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
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{
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{
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if (lev > 0)
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if (lev > 0)
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{
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{
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@@ -6146,15 +6154,18 @@ void bssn_class::ProlongRestrict(int lev, int YN, bool BB)
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#else
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#else
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Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
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Parallel::Restrict_after(GH->PatL[lev - 1], GH->PatL[lev], SynchList_cor, StateList, Symmetry);
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#endif
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#endif
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Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
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#if (RP_SYNC_COARSE_AFTER_RESTRICT == 1)
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Parallel::Sync_cached(GH->PatL[lev - 1], StateList, Symmetry, sync_cache_rp_coarse[lev]);
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#endif
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}
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}
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Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
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Parallel::Sync_cached(GH->PatL[lev], SynchList_cor, Symmetry, sync_cache_rp_fine[lev]);
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}
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}
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}
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}
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#undef MIXOUTB
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#undef MIXOUTB
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#undef RP_SYNC_COARSE_AFTER_RESTRICT
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//================================================================================================
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//================================================================================================
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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, 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,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) :: 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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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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! gont = 0: success; gont = 1: something wrong
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integer::gont
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integer::gont
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integer :: i,j,k
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!~~~~~~> Other variables:
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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)) :: 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(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,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 :: dX, dY, dZ, PI
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real*8 :: divb_loc,det_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 :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
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real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
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real*8 :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
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real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
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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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double precision,parameter::FF = 0.75d0,eta=2.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 :: 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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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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real*8, dimension(ex(1),ex(2),ex(3)) :: reta
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#endif
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#endif
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#if (GAUGE == 6 || GAUGE == 7)
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#if (GAUGE == 6 || GAUGE == 7)
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integer :: BHN
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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(9) :: Porg
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real*8, dimension(3) :: Mass
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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 :: 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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real*8, dimension(ex(1),ex(2),ex(3)) :: reta
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call getpbh(BHN,Porg,Mass)
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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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dY = Y(2) - Y(1)
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dZ = Z(2) - Z(1)
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dZ = Z(2) - Z(1)
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do k=1,ex(3)
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alpn1 = Lap + ONE
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do j=1,ex(2)
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chin1 = chi + ONE
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do i=1,ex(1)
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gxx = dxx + ONE
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alpn1(i,j,k) = Lap(i,j,k) + ONE
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gyy = dyy + ONE
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chin1(i,j,k) = chi(i,j,k) + ONE
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gzz = dzz + 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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call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
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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,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,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)
|
chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
|
||||||
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,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||||
call fderivs(ex,dyy,gyyx,gyyy,gyyz,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,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
|
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
|
||||||
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,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)
|
||||||
do k=1,ex(3)
|
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
|
||||||
do j=1,ex(2)
|
|
||||||
do i=1,ex(1)
|
gxx_rhs = - TWO * alpn1 * Axx - F2o3 * gxx * div_beta + &
|
||||||
divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
|
TWO *( gxx * betaxx + gxy * betayx + gxz * betazx)
|
||||||
div_beta(i,j,k) = divb_loc
|
|
||||||
|
gyy_rhs = - TWO * alpn1 * Ayy - F2o3 * gyy * div_beta + &
|
||||||
chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
|
TWO *( gxy * betaxy + gyy * betayy + gyz * betazy)
|
||||||
|
|
||||||
gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
|
gzz_rhs = - TWO * alpn1 * Azz - F2o3 * gzz * div_beta + &
|
||||||
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) )
|
TWO *( gxz * betaxz + gyz * betayz + gzz * betazz)
|
||||||
|
|
||||||
gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
|
gxy_rhs = - TWO * alpn1 * Axy + F1o3 * gxy * div_beta + &
|
||||||
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) )
|
gxx * betaxy + gxz * betazy + &
|
||||||
|
gyy * betayx + gyz * betazx &
|
||||||
gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
|
- gxy * betazz
|
||||||
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) )
|
|
||||||
|
gyz_rhs = - TWO * alpn1 * Ayz + F1o3 * gyz * div_beta + &
|
||||||
gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
|
gxy * betaxz + gyy * betayz + &
|
||||||
gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
|
gxz * betaxy + gzz * betazy &
|
||||||
gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
|
- gyz * betaxx
|
||||||
|
|
||||||
gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
|
gxz_rhs = - TWO * alpn1 * Axz + F1o3 * gxz * div_beta + &
|
||||||
gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
|
gxx * betaxz + gxy * betayz + &
|
||||||
gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
|
gyz * betayx + gzz * betazx &
|
||||||
|
- gxz * betayy !rhs for gij
|
||||||
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) + &
|
! invert tilted metric
|
||||||
gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
|
gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
|
||||||
|
gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
|
||||||
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) + &
|
gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
|
||||||
gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
|
gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
|
||||||
gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
|
gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
|
||||||
gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
|
gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
|
||||||
gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
|
gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
|
||||||
gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
|
gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
|
||||||
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
|
if(co == 0)then
|
||||||
gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
|
! Gam^i_Res = Gam^i + gup^ij_,j
|
||||||
gupxx(i,j,k) = gupxx_loc
|
Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
|
||||||
gupxy(i,j,k) = gupxy_loc
|
+gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
|
||||||
gupxz(i,j,k) = gupxz_loc
|
+gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
|
||||||
gupyy(i,j,k) = gupyy_loc
|
+gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
|
||||||
gupyz(i,j,k) = gupyz_loc
|
+gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
|
||||||
gupzz(i,j,k) = gupzz_loc
|
+gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
|
||||||
|
+gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||||
if(co == 0)then
|
+gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||||
Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
|
+gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||||
gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
|
Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
|
||||||
gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
|
+gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
|
||||||
gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
|
+gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
|
||||||
gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
|
+gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
|
||||||
gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
|
+gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
|
||||||
gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
|
+gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
|
||||||
gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
+gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||||
gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
+gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||||
gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
+gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||||
Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
|
Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
|
||||||
gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
|
+gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
|
||||||
gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
|
+gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
|
||||||
gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
|
+gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
|
||||||
gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
|
+gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
|
||||||
gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
|
+gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
|
||||||
gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
|
+gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
|
||||||
gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
+gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
|
||||||
gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
+gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
|
||||||
gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
endif
|
||||||
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)) + &
|
! second kind of connection
|
||||||
gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
|
Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
|
||||||
gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
|
Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
|
||||||
gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
|
Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
|
||||||
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)) + &
|
Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
|
||||||
gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
|
Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
|
||||||
gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
|
Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
|
||||||
gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
|
|
||||||
endif
|
Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
|
||||||
|
Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
|
||||||
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)))
|
Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
|
||||||
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)))
|
Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
|
||||||
|
Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
|
||||||
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)))
|
Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
|
||||||
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)))
|
Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
|
||||||
|
Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
|
||||||
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))
|
Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
|
||||||
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))
|
Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
|
||||||
|
Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
|
||||||
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)) )
|
Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
|
||||||
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)) )
|
! Raise indices of \tilde A_{ij} and store in R_ij
|
||||||
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)) )
|
|
||||||
|
Rxx = gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
|
||||||
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) )
|
TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
|
||||||
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) )
|
Ryy = gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
|
||||||
|
TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
|
||||||
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) )
|
Rzz = gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
|
||||||
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) )
|
TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
|
||||||
enddo
|
|
||||||
enddo
|
Rxy = gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
|
||||||
enddo
|
(gupxx * gupyy + gupxy * gupxy)* Axy + &
|
||||||
! Raise indices of \tilde A_{ij} and store in R_ij
|
(gupxx * gupyz + gupxz * gupxy)* Axz + &
|
||||||
|
(gupxy * gupyz + gupxz * gupyy)* 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)
|
Rxz = gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
|
||||||
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
|
(gupxx * gupyz + gupxy * gupxz)* Axy + &
|
||||||
do k=1,ex(3)
|
(gupxx * gupzz + gupxz * gupxz)* Axz + &
|
||||||
do j=1,ex(2)
|
(gupxy * gupzz + gupxz * gupyz)* Ayz
|
||||||
do i=1,ex(1)
|
|
||||||
gupxx_loc = gupxx(i,j,k)
|
Ryz = gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
|
||||||
gupxy_loc = gupxy(i,j,k)
|
(gupxy * gupyz + gupyy * gupxz)* Axy + &
|
||||||
gupxz_loc = gupxz(i,j,k)
|
(gupxy * gupzz + gupyz * gupxz)* Axz + &
|
||||||
gupyy_loc = gupyy(i,j,k)
|
(gupyy * gupzz + gupyz * gupyz)* Ayz
|
||||||
gupyz_loc = gupyz(i,j,k)
|
|
||||||
gupzz_loc = gupzz(i,j,k)
|
! Right hand side for Gam^i without shift terms...
|
||||||
|
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||||
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) + &
|
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
|
||||||
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) + &
|
Gamx_rhs = - TWO * ( Lapx * Rxx + Lapy * Rxy + Lapz * Rxz ) + &
|
||||||
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))
|
TWO * alpn1 * ( &
|
||||||
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) + &
|
-F3o2/chin1 * ( chix * Rxx + chiy * Rxy + chiz * Rxz ) - &
|
||||||
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))
|
gupxx * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||||
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) + &
|
gupxy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||||
(gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
|
gupxz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||||
(gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
|
Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz + &
|
||||||
(gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
|
TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
|
||||||
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) + &
|
Gamy_rhs = - TWO * ( Lapx * Rxy + Lapy * Ryy + Lapz * Ryz ) + &
|
||||||
(gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
|
TWO * alpn1 * ( &
|
||||||
(gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
|
-F3o2/chin1 * ( chix * Rxy + chiy * Ryy + chiz * Ryz ) - &
|
||||||
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 * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||||
(gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
|
gupyy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||||
(gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
|
gupyz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||||
(gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
|
Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz + &
|
||||||
Rxx(i,j,k) = Rxx_loc
|
TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
|
||||||
Ryy(i,j,k) = Ryy_loc
|
|
||||||
Rzz(i,j,k) = Rzz_loc
|
Gamz_rhs = - TWO * ( Lapx * Rxz + Lapy * Ryz + Lapz * Rzz ) + &
|
||||||
Rxy(i,j,k) = Rxy_loc
|
TWO * alpn1 * ( &
|
||||||
Rxz(i,j,k) = Rxz_loc
|
-F3o2/chin1 * ( chix * Rxz + chiy * Ryz + chiz * Rzz ) - &
|
||||||
Ryz(i,j,k) = Ryz_loc
|
gupxz * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
|
||||||
|
gupyz * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
|
||||||
Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
|
gupzz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
|
||||||
TWO * alpn1(i,j,k) * ( &
|
Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz + &
|
||||||
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
|
TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
|
||||||
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
|
|
||||||
|
|
||||||
call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
|
call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
|
||||||
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
|
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
|
||||||
@@ -359,54 +321,38 @@
|
|||||||
call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
|
call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
|
||||||
X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
|
X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
|
||||||
|
|
||||||
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
|
fxx = gxxx + gxyy + gxzz
|
||||||
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
|
fxy = gxyx + gyyy + gyzz
|
||||||
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
|
fxz = gxzx + gyzy + gzzz
|
||||||
do k=1,ex(3)
|
|
||||||
do j=1,ex(2)
|
Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
|
||||||
do i=1,ex(1)
|
TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
|
||||||
divb_loc = div_beta(i,j,k)
|
Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
|
||||||
fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
|
TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
|
||||||
fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
|
Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
|
||||||
fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
|
TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
|
||||||
|
|
||||||
gupxx_loc = gupxx(i,j,k)
|
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
|
||||||
gupxy_loc = gupxy(i,j,k)
|
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
|
||||||
gupxz_loc = gupxz(i,j,k)
|
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
|
||||||
gupyy_loc = gupyy(i,j,k)
|
|
||||||
gupyz_loc = gupyz(i,j,k)
|
Gamx_rhs = Gamx_rhs + F2o3 * Gamxa * div_beta - &
|
||||||
gupzz_loc = gupzz(i,j,k)
|
Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz + &
|
||||||
|
F1o3 * (gupxx * fxx + gupxy * fxy + gupxz * fxz ) + &
|
||||||
Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
|
gupxx * gxxx + gupyy * gyyx + gupzz * gzzx + &
|
||||||
TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
|
TWO * (gupxy * gxyx + gupxz * gxzx + gupyz * gyzx )
|
||||||
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))
|
Gamy_rhs = Gamy_rhs + F2o3 * Gamya * div_beta - &
|
||||||
Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
|
Gamxa * betayx - Gamya * betayy - Gamza * betayz + &
|
||||||
TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
|
F1o3 * (gupxy * fxx + gupyy * fxy + gupyz * fxz ) + &
|
||||||
Gamxa(i,j,k) = Gamxa_loc
|
gupxx * gxxy + gupyy * gyyy + gupzz * gzzy + &
|
||||||
Gamya(i,j,k) = Gamya_loc
|
TWO * (gupxy * gxyy + gupxz * gxzy + gupyz * gyzy )
|
||||||
Gamza(i,j,k) = Gamza_loc
|
|
||||||
|
Gamz_rhs = Gamz_rhs + F2o3 * Gamza * div_beta - &
|
||||||
Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
|
Gamxa * betazx - Gamya * betazy - Gamza * betazz + &
|
||||||
Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
|
F1o3 * (gupxz * fxx + gupyz * fxy + gupzz * fxz ) + &
|
||||||
F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
|
gupxx * gxxz + gupyy * gyyz + gupzz * gzzz + &
|
||||||
gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
|
TWO * (gupxy * gxyz + gupxz * gxzz + gupyz * gyzz ) !rhs for Gam^i
|
||||||
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
|
|
||||||
|
|
||||||
!first kind of connection stored in gij,k
|
!first kind of connection stored in gij,k
|
||||||
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
|
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
|
||||||
@@ -655,190 +601,192 @@
|
|||||||
Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz + &
|
Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz + &
|
||||||
Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy + &
|
Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy + &
|
||||||
Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
|
Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
|
||||||
!covariant second derivative of chi respect to tilted metric
|
!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)
|
call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
|
||||||
|
|
||||||
do k=1,ex(3)
|
fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
|
||||||
do j=1,ex(2)
|
fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
|
||||||
do i=1,ex(1)
|
fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * chiz
|
||||||
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)
|
fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * chiz
|
||||||
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)
|
fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * chiz
|
||||||
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)
|
fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
|
||||||
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)
|
! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
|
||||||
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)
|
f = gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
|
||||||
|
gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
|
||||||
chin_loc = chin1(i,j,k)
|
gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
|
||||||
f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
|
TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
|
||||||
gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
|
TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
|
||||||
gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
|
TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz )
|
||||||
TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
|
! Add chi part to Ricci tensor:
|
||||||
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))
|
Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
|
||||||
f(i,j,k) = f_loc
|
Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
|
||||||
|
Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
|
||||||
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
|
Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/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
|
Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/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
|
Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/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
|
! covariant second derivatives of the lapse respect to physical metric
|
||||||
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
|
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
|
||||||
enddo
|
SYM,SYM,SYM,symmetry,Lev)
|
||||||
enddo
|
|
||||||
enddo
|
gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
|
||||||
|
gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
|
||||||
! covariant second derivatives of the lapse respect to physical metric
|
gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
|
||||||
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
|
! now get physical second kind of connection
|
||||||
SYM,SYM,SYM,symmetry,Lev)
|
Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
|
||||||
|
Gamyxx = Gamyxx - ( - gxx * gxxy )*HALF
|
||||||
do k=1,ex(3)
|
Gamzxx = Gamzxx - ( - gxx * gxxz )*HALF
|
||||||
do j=1,ex(2)
|
Gamxyy = Gamxyy - ( - gyy * gxxx )*HALF
|
||||||
do i=1,ex(1)
|
Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
|
||||||
chin_loc = chin1(i,j,k)
|
Gamzyy = Gamzyy - ( - gyy * gxxz )*HALF
|
||||||
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
|
Gamxzz = Gamxzz - ( - gzz * gxxx )*HALF
|
||||||
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
|
Gamyzz = Gamyzz - ( - gzz * gxxy )*HALF
|
||||||
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
|
Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
|
||||||
|
Gamxxy = Gamxxy - ( chiy /chin1 - gxy * gxxx )*HALF
|
||||||
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
|
Gamyxy = Gamyxy - ( chix /chin1 - gxy * gxxy )*HALF
|
||||||
Gamyxx(i,j,k) = Gamyxx(i,j,k) - ( - gxx(i,j,k) * gxxy(i,j,k) )*HALF
|
Gamzxy = Gamzxy - ( - gxy * gxxz )*HALF
|
||||||
Gamzxx(i,j,k) = Gamzxx(i,j,k) - ( - gxx(i,j,k) * gxxz(i,j,k) )*HALF
|
Gamxxz = Gamxxz - ( chiz /chin1 - gxz * gxxx )*HALF
|
||||||
Gamxyy(i,j,k) = Gamxyy(i,j,k) - ( - gyy(i,j,k) * gxxx(i,j,k) )*HALF
|
Gamyxz = Gamyxz - ( - gxz * gxxy )*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
|
Gamzxz = Gamzxz - ( chix /chin1 - gxz * gxxz )*HALF
|
||||||
Gamzyy(i,j,k) = Gamzyy(i,j,k) - ( - gyy(i,j,k) * gxxz(i,j,k) )*HALF
|
Gamxyz = Gamxyz - ( - gyz * gxxx )*HALF
|
||||||
Gamxzz(i,j,k) = Gamxzz(i,j,k) - ( - gzz(i,j,k) * gxxx(i,j,k) )*HALF
|
Gamyyz = Gamyyz - ( chiz /chin1 - gyz * gxxy )*HALF
|
||||||
Gamyzz(i,j,k) = Gamyzz(i,j,k) - ( - gzz(i,j,k) * gxxy(i,j,k) )*HALF
|
Gamzyz = Gamzyz - ( chiy /chin1 - gyz * gxxz )*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
|
fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
|
||||||
Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
|
fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
|
||||||
Gamzxy(i,j,k) = Gamzxy(i,j,k) - ( - gxy(i,j,k) * gxxz(i,j,k) )*HALF
|
fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
|
||||||
Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
|
fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
|
||||||
Gamyxz(i,j,k) = Gamyxz(i,j,k) - ( - gxz(i,j,k) * gxxy(i,j,k) )*HALF
|
fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
|
||||||
Gamzxz(i,j,k) = Gamzxz(i,j,k) - ( chix(i,j,k) /chin_loc - gxz(i,j,k) * gxxz(i,j,k) )*HALF
|
fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz
|
||||||
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
|
! store D^i D_i Lap in trK_rhs upto chi
|
||||||
Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
|
trK_rhs = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||||
|
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz )
|
||||||
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)
|
#if 1
|
||||||
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)
|
!! follow bam code
|
||||||
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)
|
S = chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
|
||||||
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)
|
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
|
||||||
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)
|
f = F2o3 * trK * trK -(&
|
||||||
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)
|
gupxx * ( &
|
||||||
|
gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
|
||||||
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 * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
|
||||||
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))
|
gupyy * ( &
|
||||||
enddo
|
gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
|
||||||
enddo
|
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
|
||||||
enddo
|
gupzz * ( &
|
||||||
do k=1,ex(3)
|
gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
|
||||||
do j=1,ex(2)
|
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
|
||||||
do i=1,ex(1)
|
TWO * ( &
|
||||||
divb_loc = div_beta(i,j,k)
|
gupxy * ( &
|
||||||
chin_loc = chin1(i,j,k)
|
gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
|
||||||
|
gupxy * (Axx * Ayy + Axy * Axy) + &
|
||||||
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) + &
|
gupxz * (Axx * Ayz + Axz * Axy) + &
|
||||||
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)) )
|
gupyz * (Axy * Ayz + Axz * Ayy) ) + &
|
||||||
S(i,j,k) = S_loc
|
gupxz * ( &
|
||||||
|
gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
|
||||||
f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
|
gupxy * (Axx * Ayz + Axy * Axz) + &
|
||||||
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) + &
|
gupxz * (Axx * Azz + Axz * Axz) + &
|
||||||
gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + &
|
gupyz * (Axy * Azz + Axz * Ayz) ) + &
|
||||||
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 * ( &
|
||||||
gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
|
gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
|
||||||
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) + &
|
gupxy * (Axy * Ayz + Ayy * Axz) + &
|
||||||
gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
|
gupxz * (Axy * Azz + Ayz * Axz) + &
|
||||||
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 * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
|
||||||
gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
|
f = - F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||||
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) + &
|
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
|
||||||
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) + &
|
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
|
||||||
gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
|
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
|
||||||
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) + &
|
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
|
||||||
gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
|
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
|
||||||
gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
|
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
|
||||||
gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
|
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
|
||||||
gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k)) ) + &
|
#else
|
||||||
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) + &
|
! Add lapse and S_ij parts to Ricci tensor:
|
||||||
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)) + &
|
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
|
||||||
gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
|
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
|
||||||
gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k)) ) + &
|
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
|
||||||
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) + &
|
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
|
||||||
gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + &
|
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
|
||||||
gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
|
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
|
||||||
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)) ) ) ) - &
|
! Compute trace-free part (note: chi^-1 and chi cancel!):
|
||||||
F16 * PI * rho(i,j,k) + EIGHT * PI * S_loc
|
|
||||||
|
f = F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||||
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 * fxy + gupxz * fxz + gupyz * fyz ) )
|
||||||
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)) + &
|
#endif
|
||||||
alpn1(i,j,k)/chin_loc * f_loc )
|
|
||||||
f(i,j,k) = f_loc
|
Axx_rhs = fxx - gxx * f
|
||||||
|
Ayy_rhs = fyy - gyy * f
|
||||||
l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
|
Azz_rhs = fzz - gzz * f
|
||||||
l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
|
Axy_rhs = fxy - gxy * f
|
||||||
l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
|
Axz_rhs = fxz - gxz * f
|
||||||
l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
|
Ayz_rhs = fyz - gyz * f
|
||||||
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)
|
! Now: store A_il A^l_j into fij:
|
||||||
|
|
||||||
Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
|
fxx = gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
|
||||||
Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
|
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
|
||||||
Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
|
fyy = gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
|
||||||
Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
|
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
|
||||||
Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
|
fzz = gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
|
||||||
Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
|
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
|
||||||
|
fxy = gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
|
||||||
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) + &
|
gupxy *(Axx * Ayy + Axy * Axy) + &
|
||||||
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 *(Axx * Ayz + Axz * Axy) + &
|
||||||
gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
|
gupyz *(Axy * Ayz + Axz * Ayy)
|
||||||
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) + &
|
fxz = gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
|
||||||
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) + &
|
gupxy *(Axx * Ayz + Axy * Axz) + &
|
||||||
gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
|
gupxz *(Axx * Azz + Axz * Axz) + &
|
||||||
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) + &
|
gupyz *(Axy * Azz + Axz * Ayz)
|
||||||
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) + &
|
fyz = gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
|
||||||
gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k))
|
gupxy *(Axy * Ayz + Ayy * Axz) + &
|
||||||
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) + &
|
gupxz *(Axy * Azz + Ayz * Axz) + &
|
||||||
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)) + &
|
gupyz *(Ayy * Azz + Ayz * Ayz)
|
||||||
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))
|
f = chin1
|
||||||
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) + &
|
! store D^i D_i Lap in trK_rhs
|
||||||
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)) + &
|
trK_rhs = f*trK_rhs
|
||||||
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))
|
Axx_rhs = f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx) + &
|
||||||
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) + &
|
TWO * ( Axx * betaxx + Axy * betayx + Axz * betazx )- &
|
||||||
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)) + &
|
F2o3 * Axx * div_beta
|
||||||
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))
|
Ayy_rhs = f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy) + &
|
||||||
|
TWO * ( Axy * betaxy + Ayy * betayy + Ayz * betazy )- &
|
||||||
trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
|
F2o3 * Ayy * div_beta
|
||||||
|
|
||||||
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)) + &
|
Azz_rhs = f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz) + &
|
||||||
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)) - &
|
TWO * ( Axz * betaxz + Ayz * betayz + Azz * betazz )- &
|
||||||
F2o3 * Axx(i,j,k) * divb_loc
|
F2o3 * Azz * div_beta
|
||||||
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)) - &
|
Axy_rhs = f * Axy_rhs+ alpn1 *( trK * Axy - TWO * fxy )+ &
|
||||||
F2o3 * Ayy(i,j,k) * divb_loc
|
Axx * betaxy + Axz * betazy + &
|
||||||
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)) + &
|
Ayy * betayx + Ayz * betazx + &
|
||||||
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)) - &
|
F1o3 * Axy * div_beta - Axy * betazz
|
||||||
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)) + &
|
Ayz_rhs = f * Ayz_rhs+ alpn1 *( trK * Ayz - TWO * fyz )+ &
|
||||||
Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
|
Axy * betaxz + Ayy * betayz + &
|
||||||
Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
|
Axz * betaxy + Azz * betazy + &
|
||||||
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)) + &
|
F1o3 * Ayz * div_beta - Ayz * betaxx
|
||||||
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 = f * Axz_rhs+ alpn1 *( trK * Axz - TWO * fxz )+ &
|
||||||
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 * betaxz + Axy * betayz + &
|
||||||
Axx(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
|
Ayz * betayx + Azz * betazx + &
|
||||||
Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
|
F1o3 * Axz * div_beta - Axz * betayy !rhs for Aij
|
||||||
|
|
||||||
trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(i,j,k) + &
|
! Compute trace of S_ij
|
||||||
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)) + &
|
S = f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
|
||||||
FOUR * PI * (rho(i,j,k) + S_loc) )
|
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
|
||||||
enddo
|
|
||||||
enddo
|
trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK + &
|
||||||
enddo
|
gupxx * fxx + gupyy * fyy + gupzz * fzz + &
|
||||||
|
TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
|
||||||
|
FOUR * PI * ( rho + S )) !rhs for trK
|
||||||
|
|
||||||
!!!! gauge variable part
|
!!!! gauge variable part
|
||||||
|
|
||||||
@@ -1000,15 +948,15 @@
|
|||||||
!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
|
!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
|
||||||
! lopsided_kodis shares the symmetry_bd buffer between advection and
|
! lopsided_kodis shares the symmetry_bd buffer between advection and
|
||||||
! dissipation, eliminating redundant full-grid copies. For metric variables
|
! dissipation, eliminating redundant full-grid copies. For metric variables
|
||||||
! gxx/gyy/gzz (=dxx/dyy/dzz+1): stencil coefficients sum to zero,
|
! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
|
||||||
! so the constant offset has no effect on dissipation.
|
! 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,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,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,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,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,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)
|
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,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)
|
call lopsided_kodis(ex,X,Y,Z,Axy,Axy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
|
||||||
|
|||||||
@@ -716,7 +716,6 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
|||||||
|
|
||||||
// 24ms //
|
// 24ms //
|
||||||
fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
|
fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
|
||||||
fderivs(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev);
|
|
||||||
|
|
||||||
// 6ms //
|
// 6ms //
|
||||||
for (int i=0;i<all;i+=1) {
|
for (int i=0;i<all;i+=1) {
|
||||||
@@ -1014,12 +1013,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
|||||||
betaz_rhs[i] = FF * dtSfz[i];
|
betaz_rhs[i] = FF * dtSfz[i];
|
||||||
|
|
||||||
reta[i] =
|
reta[i] =
|
||||||
gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
|
gupxx[i] * chix[i] * chix[i]
|
||||||
+ gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
|
+ gupyy[i] * chiy[i] * chiy[i]
|
||||||
+ gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
|
+ gupzz[i] * chiz[i] * chiz[i]
|
||||||
+ TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
|
+ TWO * ( gupxy[i] * chix[i] * chiy[i]
|
||||||
+ gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
|
+ gupxz[i] * chix[i] * chiz[i]
|
||||||
+ gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
|
+ gupyz[i] * chiy[i] * chiz[i] );
|
||||||
|
|
||||||
#if (GAUGE == 2)
|
#if (GAUGE == 2)
|
||||||
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
||||||
@@ -1032,12 +1031,12 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
|||||||
dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
|
dtSfz_rhs[i] = Gamz_rhs[i] - reta[i] * dtSfz[i];
|
||||||
#elif (GAUGE == 4 || GAUGE == 5)
|
#elif (GAUGE == 4 || GAUGE == 5)
|
||||||
reta[i] =
|
reta[i] =
|
||||||
gupxx[i] * dtSfx_rhs[i] * dtSfx_rhs[i]
|
gupxx[i] * chix[i] * chix[i]
|
||||||
+ gupyy[i] * dtSfy_rhs[i] * dtSfy_rhs[i]
|
+ gupyy[i] * chiy[i] * chiy[i]
|
||||||
+ gupzz[i] * dtSfz_rhs[i] * dtSfz_rhs[i]
|
+ gupzz[i] * chiz[i] * chiz[i]
|
||||||
+ TWO * ( gupxy[i] * dtSfx_rhs[i] * dtSfy_rhs[i]
|
+ TWO * ( gupxy[i] * chix[i] * chiy[i]
|
||||||
+ gupxz[i] * dtSfx_rhs[i] * dtSfz_rhs[i]
|
+ gupxz[i] * chix[i] * chiz[i]
|
||||||
+ gupyz[i] * dtSfy_rhs[i] * dtSfz_rhs[i] );
|
+ gupyz[i] * chiy[i] * chiz[i] );
|
||||||
|
|
||||||
#if (GAUGE == 4)
|
#if (GAUGE == 4)
|
||||||
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
reta[i] = 1.31 / 2.0 * sqrt( reta[i] / chin1[i] ) / pow( (ONE - sqrt(chin1[i])), 2.0 );
|
||||||
@@ -1139,59 +1138,59 @@ int f_compute_rhs_bssn(int *ex, double &T,
|
|||||||
fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
|
fderivs(ex,Ayy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
|
||||||
fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
|
fderivs(ex,Ayz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,0);
|
||||||
fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
|
fderivs(ex,Azz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,0);
|
||||||
}
|
// 7ms //
|
||||||
// 7ms //
|
for (int i=0;i<all;i+=1) {
|
||||||
for (int i=0;i<all;i+=1) {
|
gxxx[i] = gxxx[i] - ( Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
|
||||||
gxxx[i] = gxxx[i] - ( Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]
|
+ Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
|
||||||
+ Gamxxx[i] * Axx[i] + Gamyxx[i] * Axy[i] + Gamzxx[i] * Axz[i]) - chix[i]*Axx[i]/chin1[i];
|
gxyx[i] = gxyx[i] - ( Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
|
||||||
gxyx[i] = gxyx[i] - ( Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
|
+ Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
|
||||||
+ Gamxxx[i] * Axy[i] + Gamyxx[i] * Ayy[i] + Gamzxx[i] * Ayz[i]) - chix[i]*Axy[i]/chin1[i];
|
gxzx[i] = gxzx[i] - ( Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
|
||||||
gxzx[i] = gxzx[i] - ( Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
|
+ Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
|
||||||
+ Gamxxx[i] * Axz[i] + Gamyxx[i] * Ayz[i] + Gamzxx[i] * Azz[i]) - chix[i]*Axz[i]/chin1[i];
|
gyyx[i] = gyyx[i] - ( Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
|
||||||
gyyx[i] = gyyx[i] - ( Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]
|
+ Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
|
||||||
+ Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chix[i]*Ayy[i]/chin1[i];
|
gyzx[i] = gyzx[i] - ( Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
|
||||||
gyzx[i] = gyzx[i] - ( Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]
|
+ Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
|
||||||
+ Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chix[i]*Ayz[i]/chin1[i];
|
gzzx[i] = gzzx[i] - ( Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
|
||||||
gzzx[i] = gzzx[i] - ( Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]
|
+ Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
|
||||||
+ Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chix[i]*Azz[i]/chin1[i];
|
gxxy[i] = gxxy[i] - ( Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
|
||||||
gxxy[i] = gxxy[i] - ( Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]
|
+ Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
|
||||||
+ Gamxxy[i] * Axx[i] + Gamyxy[i] * Axy[i] + Gamzxy[i] * Axz[i]) - chiy[i]*Axx[i]/chin1[i];
|
gxyy[i] = gxyy[i] - ( Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
|
||||||
gxyy[i] = gxyy[i] - ( Gamxyy[i] * Axx[i] + Gamyyy[i] * Axy[i] + Gamzyy[i] * Axz[i]
|
+ Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
|
||||||
+ Gamxxy[i] * Axy[i] + Gamyxy[i] * Ayy[i] + Gamzxy[i] * Ayz[i]) - chiy[i]*Axy[i]/chin1[i];
|
gxzy[i] = gxzy[i] - ( Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
|
||||||
gxzy[i] = gxzy[i] - ( Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
|
+ Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
|
||||||
+ Gamxxy[i] * Axz[i] + Gamyxy[i] * Ayz[i] + Gamzxy[i] * Azz[i]) - chiy[i]*Axz[i]/chin1[i];
|
gyyy[i] = gyyy[i] - ( Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
|
||||||
gyyy[i] = gyyy[i] - ( Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]
|
+ Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
|
||||||
+ Gamxyy[i] * Axy[i] + Gamyyy[i] * Ayy[i] + Gamzyy[i] * Ayz[i]) - chiy[i]*Ayy[i]/chin1[i];
|
gyzy[i] = gyzy[i] - ( Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
|
||||||
gyzy[i] = gyzy[i] - ( Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
|
+ Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
|
||||||
+ Gamxyy[i] * Axz[i] + Gamyyy[i] * Ayz[i] + Gamzyy[i] * Azz[i]) - chiy[i]*Ayz[i]/chin1[i];
|
gzzy[i] = gzzy[i] - ( Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
|
||||||
gzzy[i] = gzzy[i] - ( Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]
|
+ Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
|
||||||
+ Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiy[i]*Azz[i]/chin1[i];
|
gxxz[i] = gxxz[i] - ( Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
|
||||||
gxxz[i] = gxxz[i] - ( Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]
|
+ Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
|
||||||
+ Gamxxz[i] * Axx[i] + Gamyxz[i] * Axy[i] + Gamzxz[i] * Axz[i]) - chiz[i]*Axx[i]/chin1[i];
|
gxyz[i] = gxyz[i] - ( Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
|
||||||
gxyz[i] = gxyz[i] - ( Gamxyz[i] * Axx[i] + Gamyyz[i] * Axy[i] + Gamzyz[i] * Axz[i]
|
+ Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
|
||||||
+ Gamxxz[i] * Axy[i] + Gamyxz[i] * Ayy[i] + Gamzxz[i] * Ayz[i]) - chiz[i]*Axy[i]/chin1[i];
|
gxzz[i] = gxzz[i] - ( Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
|
||||||
gxzz[i] = gxzz[i] - ( Gamxzz[i] * Axx[i] + Gamyzz[i] * Axy[i] + Gamzzz[i] * Axz[i]
|
+ Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
|
||||||
+ Gamxxz[i] * Axz[i] + Gamyxz[i] * Ayz[i] + Gamzxz[i] * Azz[i]) - chiz[i]*Axz[i]/chin1[i];
|
gyyz[i] = gyyz[i] - ( Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
|
||||||
gyyz[i] = gyyz[i] - ( Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]
|
+ Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
|
||||||
+ Gamxyz[i] * Axy[i] + Gamyyz[i] * Ayy[i] + Gamzyz[i] * Ayz[i]) - chiz[i]*Ayy[i]/chin1[i];
|
gyzz[i] = gyzz[i] - ( Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
|
||||||
gyzz[i] = gyzz[i] - ( Gamxzz[i] * Axy[i] + Gamyzz[i] * Ayy[i] + Gamzzz[i] * Ayz[i]
|
+ Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
|
||||||
+ Gamxyz[i] * Axz[i] + Gamyyz[i] * Ayz[i] + Gamzyz[i] * Azz[i]) - chiz[i]*Ayz[i]/chin1[i];
|
gzzz[i] = gzzz[i] - ( Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
|
||||||
gzzz[i] = gzzz[i] - ( Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]
|
+ Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
|
||||||
+ Gamxzz[i] * Axz[i] + Gamyzz[i] * Ayz[i] + Gamzzz[i] * Azz[i]) - chiz[i]*Azz[i]/chin1[i];
|
|
||||||
|
|
||||||
movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
|
movx_Res[i] = gupxx[i]*gxxx[i] + gupyy[i]*gxyy[i] + gupzz[i]*gxzz[i]
|
||||||
+ gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
|
+ gupxy[i]*gxyx[i] + gupxz[i]*gxzx[i] + gupyz[i]*gxzy[i]
|
||||||
+ gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
|
+ gupxy[i]*gxxy[i] + gupxz[i]*gxxz[i] + gupyz[i]*gxyz[i];
|
||||||
movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
|
movy_Res[i] = gupxx[i]*gxyx[i] + gupyy[i]*gyyy[i] + gupzz[i]*gyzz[i]
|
||||||
+ gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
|
+ gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[i]
|
||||||
+ gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
|
+ gupxy[i]*gxyy[i] + gupxz[i]*gxyz[i] + gupyz[i]*gyyz[i];
|
||||||
movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
|
movz_Res[i] = gupxx[i]*gxzx[i] + gupyy[i]*gyzy[i] + gupzz[i]*gzzz[i]
|
||||||
+ gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
|
+ gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
|
||||||
+ gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
|
+ gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[i];
|
||||||
|
|
||||||
movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
|
movx_Res[i] = movx_Res[i] - F2o3*Kx[i] - F8*PI*Sx[i];
|
||||||
movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
|
movy_Res[i] = movy_Res[i] - F2o3*Ky[i] - F8*PI*Sy[i];
|
||||||
movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
|
movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
|
||||||
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
|
||||||
|
|||||||
@@ -71,106 +71,131 @@ void fdderivs(const int ex[3],
|
|||||||
const double Fdxdz = F1o144 / (dX * dZ);
|
const double Fdxdz = F1o144 / (dX * dZ);
|
||||||
const double Fdydz = F1o144 / (dY * dZ);
|
const double Fdydz = F1o144 / (dY * dZ);
|
||||||
|
|
||||||
const size_t all = (size_t)ex1 * (size_t)ex2 * (size_t)ex3;
|
/* 只清零不被主循环覆盖的边界面 */
|
||||||
for (size_t p = 0; p < all; ++p) {
|
{
|
||||||
fxx[p] = ZEO; fxy[p] = ZEO; fxz[p] = ZEO;
|
/* 高边界：k0=ex3-1 */
|
||||||
fyy[p] = ZEO; fyz[p] = ZEO; fzz[p] = ZEO;
|
for (int j0 = 0; j0 < ex2; ++j0)
|
||||||
|
for (int i0 = 0; i0 < ex1; ++i0) {
|
||||||
|
const size_t p = idx_ex(i0, j0, ex3 - 1, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
/* 高边界：j0=ex2-1 */
|
||||||
|
for (int k0 = 0; k0 < ex3 - 1; ++k0)
|
||||||
|
for (int i0 = 0; i0 < ex1; ++i0) {
|
||||||
|
const size_t p = idx_ex(i0, ex2 - 1, k0, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
/* 高边界：i0=ex1-1 */
|
||||||
|
for (int k0 = 0; k0 < ex3 - 1; ++k0)
|
||||||
|
for (int j0 = 0; j0 < ex2 - 1; ++j0) {
|
||||||
|
const size_t p = idx_ex(ex1 - 1, j0, k0, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
|
||||||
|
/* 低边界：当二阶模板也不可用时，对应 i0/j0/k0=0 面 */
|
||||||
|
if (kminF == 1) {
|
||||||
|
for (int j0 = 0; j0 < ex2; ++j0)
|
||||||
|
for (int i0 = 0; i0 < ex1; ++i0) {
|
||||||
|
const size_t p = idx_ex(i0, j0, 0, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if (jminF == 1) {
|
||||||
|
for (int k0 = 0; k0 < ex3; ++k0)
|
||||||
|
for (int i0 = 0; i0 < ex1; ++i0) {
|
||||||
|
const size_t p = idx_ex(i0, 0, k0, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
}
|
||||||
|
if (iminF == 1) {
|
||||||
|
for (int k0 = 0; k0 < ex3; ++k0)
|
||||||
|
for (int j0 = 0; j0 < ex2; ++j0) {
|
||||||
|
const size_t p = idx_ex(0, j0, k0, ex);
|
||||||
|
fxx[p]=ZEO; fyy[p]=ZEO; fzz[p]=ZEO;
|
||||||
|
fxy[p]=ZEO; fxz[p]=ZEO; fyz[p]=ZEO;
|
||||||
|
}
|
||||||
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
// Match Fortran (ghost_width=3, "for bam comparison") exactly:
|
/*
|
||||||
// only compute when x/y/z all satisfy the same-order stencil at this point.
|
* 两段式：
|
||||||
for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
|
* 1) 二阶可用区域先计算二阶模板
|
||||||
const int kF = k0 + 1;
|
* 2) 高阶可用区域再覆盖四阶模板
|
||||||
for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
|
*/
|
||||||
const int jF = j0 + 1;
|
const int i2_lo = (iminF > 0) ? iminF : 0;
|
||||||
for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
|
const int j2_lo = (jminF > 0) ? jminF : 0;
|
||||||
const int iF = i0 + 1;
|
const int k2_lo = (kminF > 0) ? kminF : 0;
|
||||||
const size_t p = idx_ex(i0, j0, k0, ex);
|
const int i2_hi = ex1 - 2;
|
||||||
|
const int j2_hi = ex2 - 2;
|
||||||
|
const int k2_hi = ex3 - 2;
|
||||||
|
|
||||||
|
const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
|
||||||
|
const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
|
||||||
|
const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
|
||||||
|
const int i4_hi = ex1 - 3;
|
||||||
|
const int j4_hi = ex2 - 3;
|
||||||
|
const int k4_hi = ex3 - 3;
|
||||||
|
|
||||||
|
/*
|
||||||
|
* Strategy A:
|
||||||
|
* Avoid redundant work in overlap of 2nd/4th-order regions.
|
||||||
|
* Only compute 2nd-order on shell points that are NOT overwritten by
|
||||||
|
* the 4th-order pass.
|
||||||
|
*/
|
||||||
|
const int has4 = (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi);
|
||||||
|
|
||||||
|
if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
|
||||||
|
for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
|
||||||
|
const int kF = k0 + 1;
|
||||||
|
for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
|
||||||
|
const int jF = j0 + 1;
|
||||||
|
for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
|
||||||
|
if (has4 &&
|
||||||
|
i0 >= i4_lo && i0 <= i4_hi &&
|
||||||
|
j0 >= j4_lo && j0 <= j4_hi &&
|
||||||
|
k0 >= k4_lo && k0 <= k4_hi) {
|
||||||
|
continue;
|
||||||
|
}
|
||||||
|
const int iF = i0 + 1;
|
||||||
|
const size_t p = idx_ex(i0, j0, k0, ex);
|
||||||
|
|
||||||
if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
|
|
||||||
(jF + 2 <= jmaxF && jF - 2 >= jminF) &&
|
|
||||||
(kF + 2 <= kmaxF && kF - 2 >= kminF)) {
|
|
||||||
fxx[p] = Fdxdx * (
|
|
||||||
-fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] -
|
|
||||||
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
|
||||||
);
|
|
||||||
fyy[p] = Fdydy * (
|
|
||||||
-fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] -
|
|
||||||
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
|
||||||
);
|
|
||||||
fzz[p] = Fdzdz * (
|
|
||||||
-fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] -
|
|
||||||
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)] +
|
|
||||||
F16 * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
|
||||||
);
|
|
||||||
fxy[p] = Fdxdy * (
|
|
||||||
(fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)])
|
|
||||||
- F8 * (fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)])
|
|
||||||
+ F8 * (fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)])
|
|
||||||
- (fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)] - fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)])
|
|
||||||
);
|
|
||||||
fxz[p] = Fdxdz * (
|
|
||||||
(fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)])
|
|
||||||
- F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)])
|
|
||||||
+ F8 * (fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)])
|
|
||||||
- (fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)] - fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)])
|
|
||||||
);
|
|
||||||
fyz[p] = Fdydz * (
|
|
||||||
(fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)])
|
|
||||||
- F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)])
|
|
||||||
+ F8 * (fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)])
|
|
||||||
- (fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)] - F8 * fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)] +
|
|
||||||
F8 * fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)] - fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)])
|
|
||||||
);
|
|
||||||
} else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
|
|
||||||
(jF + 1 <= jmaxF && jF - 1 >= jminF) &&
|
|
||||||
(kF + 1 <= kmaxF && kF - 1 >= kminF)) {
|
|
||||||
fxx[p] = Sdxdx * (
|
fxx[p] = Sdxdx * (
|
||||||
fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] -
|
fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] -
|
||||||
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fyy[p] = Sdydy * (
|
fyy[p] = Sdydy * (
|
||||||
fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] -
|
fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] -
|
||||||
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fzz[p] = Sdzdz * (
|
fzz[p] = Sdzdz * (
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] -
|
fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] -
|
||||||
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
TWO * fh[idx_fh_F_ord2(iF, jF, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fxy[p] = Sdxdy * (
|
fxy[p] = Sdxdy * (
|
||||||
fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
|
fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)] -
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
|
fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)] -
|
||||||
fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
|
fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
|
fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fxz[p] = Sdxdz * (
|
fxz[p] = Sdxdz * (
|
||||||
fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
|
fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)] -
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
|
fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)] -
|
||||||
fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
|
fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
|
fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fyz[p] = Sdydz * (
|
fyz[p] = Sdydz * (
|
||||||
fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
|
fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)] -
|
||||||
fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
|
fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)] -
|
||||||
@@ -182,5 +207,126 @@ void fdderivs(const int ex[3],
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
if (has4) {
|
||||||
|
for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
|
||||||
|
const int kF = k0 + 1;
|
||||||
|
for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
|
||||||
|
const int jF = j0 + 1;
|
||||||
|
for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
|
||||||
|
const int iF = i0 + 1;
|
||||||
|
const size_t p = idx_ex(i0, j0, k0, ex);
|
||||||
|
|
||||||
|
fxx[p] = Fdxdx * (
|
||||||
|
-fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] -
|
||||||
|
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
||||||
|
);
|
||||||
|
|
||||||
|
fyy[p] = Fdydy * (
|
||||||
|
-fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] -
|
||||||
|
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
||||||
|
);
|
||||||
|
|
||||||
|
fzz[p] = Fdzdz * (
|
||||||
|
-fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] -
|
||||||
|
F30 * fh[idx_fh_F_ord2(iF, jF, kF, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)] +
|
||||||
|
F16 * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
||||||
|
);
|
||||||
|
|
||||||
|
{
|
||||||
|
const double t_jm2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF - 2, kF, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF - 2, kF, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF - 2, kF, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF - 2, kF, ex)] );
|
||||||
|
|
||||||
|
const double t_jm1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF - 1, kF, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF - 1, kF, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF - 1, kF, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF - 1, kF, ex)] );
|
||||||
|
|
||||||
|
const double t_jp1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF + 1, kF, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF + 1, kF, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF + 1, kF, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF + 1, kF, ex)] );
|
||||||
|
|
||||||
|
const double t_jp2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF + 2, kF, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF + 2, kF, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF + 2, kF, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF + 2, kF, ex)] );
|
||||||
|
|
||||||
|
fxy[p] = Fdxdy * ( t_jm2 - F8 * t_jm1 + F8 * t_jp1 - t_jp2 );
|
||||||
|
}
|
||||||
|
|
||||||
|
{
|
||||||
|
const double t_km2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF, kF - 2, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 2, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 2, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF, kF - 2, ex)] );
|
||||||
|
|
||||||
|
const double t_km1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF, kF - 1, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF, kF - 1, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF, kF - 1, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF, kF - 1, ex)] );
|
||||||
|
|
||||||
|
const double t_kp1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF, kF + 1, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 1, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 1, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF, kF + 1, ex)] );
|
||||||
|
|
||||||
|
const double t_kp2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF - 2, jF, kF + 2, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF - 1, jF, kF + 2, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF + 1, jF, kF + 2, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF + 2, jF, kF + 2, ex)] );
|
||||||
|
|
||||||
|
fxz[p] = Fdxdz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
|
||||||
|
}
|
||||||
|
|
||||||
|
{
|
||||||
|
const double t_km2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF, jF - 2, kF - 2, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 2, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 2, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF, jF + 2, kF - 2, ex)] );
|
||||||
|
|
||||||
|
const double t_km1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF, jF - 2, kF - 1, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF, jF - 1, kF - 1, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF, jF + 1, kF - 1, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF, jF + 2, kF - 1, ex)] );
|
||||||
|
|
||||||
|
const double t_kp1 =
|
||||||
|
( fh[idx_fh_F_ord2(iF, jF - 2, kF + 1, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 1, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 1, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF, jF + 2, kF + 1, ex)] );
|
||||||
|
|
||||||
|
const double t_kp2 =
|
||||||
|
( fh[idx_fh_F_ord2(iF, jF - 2, kF + 2, ex)]
|
||||||
|
-F8*fh[idx_fh_F_ord2(iF, jF - 1, kF + 2, ex)]
|
||||||
|
+F8*fh[idx_fh_F_ord2(iF, jF + 1, kF + 2, ex)]
|
||||||
|
- fh[idx_fh_F_ord2(iF, jF + 2, kF + 2, ex)] );
|
||||||
|
|
||||||
|
fyz[p] = Fdydz * ( t_km2 - F8 * t_km1 + F8 * t_kp1 - t_kp2 );
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
// free(fh);
|
// free(fh);
|
||||||
}
|
}
|
||||||
|
|||||||
@@ -80,48 +80,46 @@ void fderivs(const int ex[3],
|
|||||||
fz[p] = ZEO;
|
fz[p] = ZEO;
|
||||||
}
|
}
|
||||||
|
|
||||||
// Match Fortran (ghost_width=3, "for bam comparison") exactly:
|
/*
|
||||||
// only compute when x/y/z all satisfy the same-order stencil at this point.
|
* 两段式：
|
||||||
for (int k0 = 0; k0 <= ex3 - 2; ++k0) {
|
* 1) 先在二阶可用区域计算二阶模板
|
||||||
const int kF = k0 + 1;
|
* 2) 再在高阶可用区域覆盖为四阶模板
|
||||||
for (int j0 = 0; j0 <= ex2 - 2; ++j0) {
|
*
|
||||||
const int jF = j0 + 1;
|
* 与原 if/elseif 逻辑等价，但减少逐点分支判断。
|
||||||
for (int i0 = 0; i0 <= ex1 - 2; ++i0) {
|
*/
|
||||||
const int iF = i0 + 1;
|
const int i2_lo = (iminF > 0) ? iminF : 0;
|
||||||
const size_t p = idx_ex(i0, j0, k0, ex);
|
const int j2_lo = (jminF > 0) ? jminF : 0;
|
||||||
|
const int k2_lo = (kminF > 0) ? kminF : 0;
|
||||||
|
const int i2_hi = ex1 - 2;
|
||||||
|
const int j2_hi = ex2 - 2;
|
||||||
|
const int k2_hi = ex3 - 2;
|
||||||
|
|
||||||
|
const int i4_lo = (iminF + 1 > 0) ? (iminF + 1) : 0;
|
||||||
|
const int j4_lo = (jminF + 1 > 0) ? (jminF + 1) : 0;
|
||||||
|
const int k4_lo = (kminF + 1 > 0) ? (kminF + 1) : 0;
|
||||||
|
const int i4_hi = ex1 - 3;
|
||||||
|
const int j4_hi = ex2 - 3;
|
||||||
|
const int k4_hi = ex3 - 3;
|
||||||
|
|
||||||
|
if (i2_lo <= i2_hi && j2_lo <= j2_hi && k2_lo <= k2_hi) {
|
||||||
|
for (int k0 = k2_lo; k0 <= k2_hi; ++k0) {
|
||||||
|
const int kF = k0 + 1;
|
||||||
|
for (int j0 = j2_lo; j0 <= j2_hi; ++j0) {
|
||||||
|
const int jF = j0 + 1;
|
||||||
|
for (int i0 = i2_lo; i0 <= i2_hi; ++i0) {
|
||||||
|
const int iF = i0 + 1;
|
||||||
|
const size_t p = idx_ex(i0, j0, k0, ex);
|
||||||
|
|
||||||
if ((iF + 2 <= imaxF && iF - 2 >= iminF) &&
|
|
||||||
(jF + 2 <= jmaxF && jF - 2 >= jminF) &&
|
|
||||||
(kF + 2 <= kmaxF && kF - 2 >= kminF)) {
|
|
||||||
fx[p] = d12dx * (
|
|
||||||
fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] -
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] +
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)]
|
|
||||||
);
|
|
||||||
fy[p] = d12dy * (
|
|
||||||
fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] -
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] +
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)]
|
|
||||||
);
|
|
||||||
fz[p] = d12dz * (
|
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] -
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] +
|
|
||||||
EIT * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] -
|
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)]
|
|
||||||
);
|
|
||||||
} else if ((iF + 1 <= imaxF && iF - 1 >= iminF) &&
|
|
||||||
(jF + 1 <= jmaxF && jF - 1 >= jminF) &&
|
|
||||||
(kF + 1 <= kmaxF && kF - 1 >= kminF)) {
|
|
||||||
fx[p] = d2dx * (
|
fx[p] = d2dx * (
|
||||||
-fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] +
|
-fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fy[p] = d2dy * (
|
fy[p] = d2dy * (
|
||||||
-fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] +
|
-fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)]
|
||||||
);
|
);
|
||||||
|
|
||||||
fz[p] = d2dz * (
|
fz[p] = d2dz * (
|
||||||
-fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] +
|
-fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] +
|
||||||
fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)]
|
||||||
@@ -131,5 +129,39 @@ void fderivs(const int ex[3],
|
|||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
|
if (i4_lo <= i4_hi && j4_lo <= j4_hi && k4_lo <= k4_hi) {
|
||||||
|
for (int k0 = k4_lo; k0 <= k4_hi; ++k0) {
|
||||||
|
const int kF = k0 + 1;
|
||||||
|
for (int j0 = j4_lo; j0 <= j4_hi; ++j0) {
|
||||||
|
const int jF = j0 + 1;
|
||||||
|
for (int i0 = i4_lo; i0 <= i4_hi; ++i0) {
|
||||||
|
const int iF = i0 + 1;
|
||||||
|
const size_t p = idx_ex(i0, j0, k0, ex);
|
||||||
|
|
||||||
|
fx[p] = d12dx * (
|
||||||
|
fh[idx_fh_F_ord2(iF - 2, jF, kF, ex)] -
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF - 1, jF, kF, ex)] +
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF + 1, jF, kF, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF + 2, jF, kF, ex)]
|
||||||
|
);
|
||||||
|
|
||||||
|
fy[p] = d12dy * (
|
||||||
|
fh[idx_fh_F_ord2(iF, jF - 2, kF, ex)] -
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF, jF - 1, kF, ex)] +
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF, jF + 1, kF, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF, jF + 2, kF, ex)]
|
||||||
|
);
|
||||||
|
|
||||||
|
fz[p] = d12dz * (
|
||||||
|
fh[idx_fh_F_ord2(iF, jF, kF - 2, ex)] -
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF, jF, kF - 1, ex)] +
|
||||||
|
EIT * fh[idx_fh_F_ord2(iF, jF, kF + 1, ex)] -
|
||||||
|
fh[idx_fh_F_ord2(iF, jF, kF + 2, ex)]
|
||||||
|
);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
// free(fh);
|
// free(fh);
|
||||||
}
|
}
|
||||||
|
|||||||
@@ -64,8 +64,8 @@ lopsided_c.o: lopsided_c.C
|
|||||||
lopsided_kodis_c.o: lopsided_kodis_c.C
|
lopsided_kodis_c.o: lopsided_kodis_c.C
|
||||||
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
||||||
|
|
||||||
#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
|
interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
|
||||||
# ${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
|
||||||
|
|
||||||
## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
|
## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
|
||||||
TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
|
TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata
|
||||||
|
|||||||
@@ -46,12 +46,12 @@ endif
|
|||||||
## Kernel implementation switch
|
## Kernel implementation switch
|
||||||
## 1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
|
## 1 (default) : use C++ rewrite of bssn_rhs and helper kernels (faster)
|
||||||
## 0 : fall back to original Fortran kernels
|
## 0 : fall back to original Fortran kernels
|
||||||
USE_CXX_KERNELS ?= 0
|
USE_CXX_KERNELS ?= 1
|
||||||
|
|
||||||
## RK4 kernel implementation switch
|
## RK4 kernel implementation switch
|
||||||
## 1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
|
## 1 (default) : use C/C++ rewrite of rungekutta4_rout (for optimization experiments)
|
||||||
## 0 : use original Fortran rungekutta4_rout.o
|
## 0 : use original Fortran rungekutta4_rout.o
|
||||||
USE_CXX_RK4 ?= 0
|
USE_CXX_RK4 ?= 1
|
||||||
|
|
||||||
f90 = ifx
|
f90 = ifx
|
||||||
f77 = ifx
|
f77 = ifx
|
||||||
|
|||||||
Reference in New Issue
Block a user