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merge into: 64-BitBrainstorm_2026:chb-parallel
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64-BitBrainstorm_2026:main 64-BitBrainstorm_2026:chb-parallel 64-BitBrainstorm_2026:cjy-dystopia 64-BitBrainstorm_2026:yx-prolong 64-BitBrainstorm_2026:chb-rebase-wip 64-BitBrainstorm_2026:hxh-omp 64-BitBrainstorm_2026:hxh-new 64-BitBrainstorm_2026:yx_new_split 64-BitBrainstorm_2026:cjy-oneapi-opus-hotfix 64-BitBrainstorm_2026:chb-replace 64-BitBrainstorm_2026:yx-vacation 64-BitBrainstorm_2026:chb-new 64-BitBrainstorm_2026:yx-mpi 64-BitBrainstorm_2026:cjy-oneapi-opus-windfall 64-BitBrainstorm_2026:chb-copilot-test 64-BitBrainstorm_2026:chb-twopunctures 64-BitBrainstorm_2026:yx-fmisc 64-BitBrainstorm_2026:cjy-oneapi-opus-rhs-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-openmp 64-BitBrainstorm_2026:cjy-oneapi 64-BitBrainstorm_2026:cjy-oneapi-openmp 64-BitBrainstorm_2026:baseline 64-BitBrainstorm_2026:cjy-oneapi-parallel 64-BitBrainstorm_2026:chb-local 64-BitBrainstorm_2026:cjy-oneapi-laptop 64-BitBrainstorm_2026:cjy-oneapi-test 64-BitBrainstorm_2026:cjy-oneapi-preview 64-BitBrainstorm_2026:cjy
...
pull from: 64-BitBrainstorm_2026:main
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64-BitBrainstorm_2026:main 64-BitBrainstorm_2026:chb-parallel 64-BitBrainstorm_2026:cjy-dystopia 64-BitBrainstorm_2026:yx-prolong 64-BitBrainstorm_2026:chb-rebase-wip 64-BitBrainstorm_2026:hxh-omp 64-BitBrainstorm_2026:hxh-new 64-BitBrainstorm_2026:yx_new_split 64-BitBrainstorm_2026:cjy-oneapi-opus-hotfix 64-BitBrainstorm_2026:chb-replace 64-BitBrainstorm_2026:yx-vacation 64-BitBrainstorm_2026:chb-new 64-BitBrainstorm_2026:yx-mpi 64-BitBrainstorm_2026:cjy-oneapi-opus-windfall 64-BitBrainstorm_2026:chb-copilot-test 64-BitBrainstorm_2026:chb-twopunctures 64-BitBrainstorm_2026:yx-fmisc 64-BitBrainstorm_2026:cjy-oneapi-opus-rhs-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-preview 64-BitBrainstorm_2026:cjy-oneapi-opus-openmp 64-BitBrainstorm_2026:cjy-oneapi 64-BitBrainstorm_2026:cjy-oneapi-openmp 64-BitBrainstorm_2026:baseline 64-BitBrainstorm_2026:cjy-oneapi-parallel 64-BitBrainstorm_2026:chb-local 64-BitBrainstorm_2026:cjy-oneapi-laptop 64-BitBrainstorm_2026:cjy-oneapi-test 64-BitBrainstorm_2026:cjy-oneapi-preview 64-BitBrainstorm_2026:cjy

5 Commits
chb-parall ... main

Author SHA1 Message Date
CGH0S7
8c1f4d8108 迁移C算子的循环融合和临时量消除 2026-03-03 16:20:15 +08:00
CGH0S7
d310ef918b bssn_rhs(fortran): migrate C kernel loop-fusion optimizations 2026-03-03 16:20:15 +08:00
CGH0S7
b35e1b289f 设置开关关闭内存打印统计 2026-03-03 16:17:47 +08:00
CGH0S7
05851b2c59 关闭静态负载 2026-03-03 16:17:47 +08:00
ianchb
3b39583d67 fix(bssn_rhs) 2026-03-03 16:06:33 +08:00
4 changed files with 540 additions and 478 deletions
Expand all files Collapse all files

56
AMSS_NCKU_source/bssn_class.C
View File

@@ -36,12 +36,18 @@ using namespace std;
#include "myglobal.h"
#endif
#include "perf.h"
#include "derivatives.h"
#include "ricci_gamma.h"
//================================================================================================
#include "perf.h"
#include "derivatives.h"
#include "ricci_gamma.h"
// Compile-time switch for per-timestep memory usage collection/printing.
// Default is OFF to reduce overhead in production runs.
#ifndef BSSN_ENABLE_MEM_USAGE_LOG
#define BSSN_ENABLE_MEM_USAGE_LOG 0
#endif
//================================================================================================
// define bssn_class
@@ -2129,8 +2135,10 @@ void bssn_class::Evolve(int Steps)
#endif
*/
perf bssn_perf;
size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
#if BSSN_ENABLE_MEM_USAGE_LOG
perf bssn_perf;
size_t current_min, current_avg, current_max, peak_min, peak_avg, peak_max;
#endif
for (int lev = 0; lev < GH->levels; lev++)
GH->Lt[lev] = PhysTime;
@@ -2224,21 +2232,23 @@ void bssn_class::Evolve(int Steps)
// fgt(PhysTime-dT_mon,StartTime,dT_mon/2),ErrorMonitor);
#endif
// Retrieve memory usage information used during computation; master process prints it
bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
&peak_min, &peak_avg, &peak_max, nprocs);
if (myrank == 0)
{
printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
"peak %0.4lg/%0.4lg/%0.4lgMB\n",
(double)current_min / (1024.0 * 1024.0),
(double)current_avg / (1024.0 * 1024.0),
(double)current_max / (1024.0 * 1024.0),
(double)peak_min / (1024.0 * 1024.0),
(double)peak_avg / (1024.0 * 1024.0),
(double)peak_max / (1024.0 * 1024.0));
cout << endl;
}
#if BSSN_ENABLE_MEM_USAGE_LOG
// Retrieve memory usage information used during computation; master process prints it
bssn_perf.MemoryUsage(&current_min, &current_avg, &current_max,
&peak_min, &peak_avg, &peak_max, nprocs);
if (myrank == 0)
{
printf(" Memory usage: current %0.4lg/%0.4lg/%0.4lgMB, "
"peak %0.4lg/%0.4lg/%0.4lgMB\n",
(double)current_min / (1024.0 * 1024.0),
(double)current_avg / (1024.0 * 1024.0),
(double)current_max / (1024.0 * 1024.0),
(double)peak_min / (1024.0 * 1024.0),
(double)peak_avg / (1024.0 * 1024.0),
(double)peak_max / (1024.0 * 1024.0));
cout << endl;
}
#endif
// Output puncture positions at each step
if (myrank == 0)

856
AMSS_NCKU_source/bssn_rhs.f90
View File

@@ -59,9 +59,10 @@
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Rxx,Rxy,Rxz,Ryy,Ryz,Rzz
real*8,intent(in) :: eps
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: ham_Res, movx_Res, movy_Res, movz_Res
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
! gont = 0: success; gont = 1: something wrong
integer::gont
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Gmx_Res, Gmy_Res, Gmz_Res
! gont = 0: success; gont = 1: something wrong
integer::gont
integer :: i,j,k
!~~~~~~> Other variables:
@@ -83,11 +84,18 @@
real*8, dimension(ex(1),ex(2),ex(3)) :: gupxx,gupxy,gupxz
real*8, dimension(ex(1),ex(2),ex(3)) :: gupyy,gupyz,gupzz
real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
real*8 :: dX, dY, dZ, PI
real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
real*8,dimension(3) ::SSS,AAS,ASA,SAA,ASS,SAS,SSA
real*8 :: dX, dY, dZ, PI
real*8 :: divb_loc,det_loc
real*8 :: gupxx_loc,gupxy_loc,gupxz_loc,gupyy_loc,gupyz_loc,gupzz_loc
real*8 :: Rxx_loc,Rxy_loc,Rxz_loc,Ryy_loc,Ryz_loc,Rzz_loc
real*8 :: fxx_loc,fxy_loc,fxz_loc
real*8 :: Gamxa_loc,Gamya_loc,Gamza_loc
real*8 :: f_loc,chin_loc
real*8 :: l_fxx,l_fxy,l_fxz,l_fyy,l_fyz,l_fzz,S_loc
real*8, parameter :: ZEO = 0.d0,ONE = 1.D0, TWO = 2.D0, FOUR = 4.D0
real*8, parameter :: EIGHT = 8.D0, HALF = 0.5D0, THR = 3.d0
real*8, parameter :: SYM = 1.D0, ANTI= - 1.D0
double precision,parameter::FF = 0.75d0,eta=2.d0
real*8, parameter :: F1o3 = 1.D0/3.D0, F2o3 = 2.D0/3.D0,F3o2=1.5d0, F1o6 = 1.D0/6.D0
real*8, parameter :: F16=1.6d1,F8=8.d0
@@ -96,11 +104,11 @@
real*8, dimension(ex(1),ex(2),ex(3)) :: reta
#endif
#if (GAUGE == 6 || GAUGE == 7)
integer :: BHN,i,j,k
real*8, dimension(9) :: Porg
real*8, dimension(3) :: Mass
real*8 :: r1,r2,M,A,w1,w2,C1,C2
#if (GAUGE == 6 || GAUGE == 7)
integer :: BHN
real*8, dimension(9) :: Porg
real*8, dimension(3) :: Mass
real*8 :: r1,r2,M,A,w1,w2,C1,C2
real*8, dimension(ex(1),ex(2),ex(3)) :: reta
call getpbh(BHN,Porg,Mass)
@@ -145,174 +153,204 @@
dY = Y(2) - Y(1)
dZ = Z(2) - Z(1)
alpn1 = Lap + ONE
chin1 = chi + ONE
gxx = dxx + ONE
gyy = dyy + ONE
gzz = dzz + ONE
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
alpn1(i,j,k) = Lap(i,j,k) + ONE
chin1(i,j,k) = chi(i,j,k) + ONE
gxx(i,j,k) = dxx(i,j,k) + ONE
gyy(i,j,k) = dyy(i,j,k) + ONE
gzz(i,j,k) = dzz(i,j,k) + ONE
enddo
enddo
enddo
call fderivs(ex,betax,betaxx,betaxy,betaxz,X,Y,Z,ANTI, SYM, SYM,Symmetry,Lev)
call fderivs(ex,betay,betayx,betayy,betayz,X,Y,Z, SYM,ANTI, SYM,Symmetry,Lev)
call fderivs(ex,betaz,betazx,betazy,betazz,X,Y,Z, SYM, SYM,ANTI,Symmetry,Lev)
div_beta = betaxx + betayy + betazz
call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
call fderivs(ex,chi,chix,chiy,chiz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
gxx_rhs = - TWO * alpn1 * Axx - F2o3 * gxx * div_beta + &
TWO *( gxx * betaxx + gxy * betayx + gxz * betazx)
gyy_rhs = - TWO * alpn1 * Ayy - F2o3 * gyy * div_beta + &
TWO *( gxy * betaxy + gyy * betayy + gyz * betazy)
gzz_rhs = - TWO * alpn1 * Azz - F2o3 * gzz * div_beta + &
TWO *( gxz * betaxz + gyz * betayz + gzz * betazz)
gxy_rhs = - TWO * alpn1 * Axy + F1o3 * gxy * div_beta + &
gxx * betaxy + gxz * betazy + &
gyy * betayx + gyz * betazx &
- gxy * betazz
gyz_rhs = - TWO * alpn1 * Ayz + F1o3 * gyz * div_beta + &
gxy * betaxz + gyy * betayz + &
gxz * betaxy + gzz * betazy &
- gyz * betaxx
gxz_rhs = - TWO * alpn1 * Axz + F1o3 * gxz * div_beta + &
gxx * betaxz + gxy * betayz + &
gyz * betayx + gzz * betazx &
- gxz * betayy !rhs for gij
! invert tilted metric
gupzz = gxx * gyy * gzz + gxy * gyz * gxz + gxz * gxy * gyz - &
gxz * gyy * gxz - gxy * gxy * gzz - gxx * gyz * gyz
gupxx = ( gyy * gzz - gyz * gyz ) / gupzz
gupxy = - ( gxy * gzz - gyz * gxz ) / gupzz
gupxz = ( gxy * gyz - gyy * gxz ) / gupzz
gupyy = ( gxx * gzz - gxz * gxz ) / gupzz
gupyz = - ( gxx * gyz - gxy * gxz ) / gupzz
gupzz = ( gxx * gyy - gxy * gxy ) / gupzz
if(co == 0)then
! Gam^i_Res = Gam^i + gup^ij_,j
Gmx_Res = Gamx - (gupxx*(gupxx*gxxx+gupxy*gxyx+gupxz*gxzx)&
+gupxy*(gupxx*gxyx+gupxy*gyyx+gupxz*gyzx)&
+gupxz*(gupxx*gxzx+gupxy*gyzx+gupxz*gzzx)&
+gupxx*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+gupxy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+gupxz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+gupxx*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupxy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupxz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
Gmy_Res = Gamy - (gupxx*(gupxy*gxxx+gupyy*gxyx+gupyz*gxzx)&
+gupxy*(gupxy*gxyx+gupyy*gyyx+gupyz*gyzx)&
+gupxz*(gupxy*gxzx+gupyy*gyzx+gupyz*gzzx)&
+gupxy*(gupxy*gxxy+gupyy*gxyy+gupyz*gxzy)&
+gupyy*(gupxy*gxyy+gupyy*gyyy+gupyz*gyzy)&
+gupyz*(gupxy*gxzy+gupyy*gyzy+gupyz*gzzy)&
+gupxy*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupyy*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupyz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
Gmz_Res = Gamz - (gupxx*(gupxz*gxxx+gupyz*gxyx+gupzz*gxzx)&
+gupxy*(gupxz*gxyx+gupyz*gyyx+gupzz*gyzx)&
+gupxz*(gupxz*gxzx+gupyz*gyzx+gupzz*gzzx)&
+gupxy*(gupxz*gxxy+gupyz*gxyy+gupzz*gxzy)&
+gupyy*(gupxz*gxyy+gupyz*gyyy+gupzz*gyzy)&
+gupyz*(gupxz*gxzy+gupyz*gyzy+gupzz*gzzy)&
+gupxz*(gupxz*gxxz+gupyz*gxyz+gupzz*gxzz)&
+gupyz*(gupxz*gxyz+gupyz*gyyz+gupzz*gyzz)&
+gupzz*(gupxz*gxzz+gupyz*gyzz+gupzz*gzzz))
endif
! second kind of connection
Gamxxx =HALF*( gupxx*gxxx + gupxy*(TWO*gxyx - gxxy ) + gupxz*(TWO*gxzx - gxxz ))
Gamyxx =HALF*( gupxy*gxxx + gupyy*(TWO*gxyx - gxxy ) + gupyz*(TWO*gxzx - gxxz ))
Gamzxx =HALF*( gupxz*gxxx + gupyz*(TWO*gxyx - gxxy ) + gupzz*(TWO*gxzx - gxxz ))
Gamxyy =HALF*( gupxx*(TWO*gxyy - gyyx ) + gupxy*gyyy + gupxz*(TWO*gyzy - gyyz ))
Gamyyy =HALF*( gupxy*(TWO*gxyy - gyyx ) + gupyy*gyyy + gupyz*(TWO*gyzy - gyyz ))
Gamzyy =HALF*( gupxz*(TWO*gxyy - gyyx ) + gupyz*gyyy + gupzz*(TWO*gyzy - gyyz ))
Gamxzz =HALF*( gupxx*(TWO*gxzz - gzzx ) + gupxy*(TWO*gyzz - gzzy ) + gupxz*gzzz)
Gamyzz =HALF*( gupxy*(TWO*gxzz - gzzx ) + gupyy*(TWO*gyzz - gzzy ) + gupyz*gzzz)
Gamzzz =HALF*( gupxz*(TWO*gxzz - gzzx ) + gupyz*(TWO*gyzz - gzzy ) + gupzz*gzzz)
Gamxxy =HALF*( gupxx*gxxy + gupxy*gyyx + gupxz*( gxzy + gyzx - gxyz ) )
Gamyxy =HALF*( gupxy*gxxy + gupyy*gyyx + gupyz*( gxzy + gyzx - gxyz ) )
Gamzxy =HALF*( gupxz*gxxy + gupyz*gyyx + gupzz*( gxzy + gyzx - gxyz ) )
Gamxxz =HALF*( gupxx*gxxz + gupxy*( gxyz + gyzx - gxzy ) + gupxz*gzzx )
Gamyxz =HALF*( gupxy*gxxz + gupyy*( gxyz + gyzx - gxzy ) + gupyz*gzzx )
Gamzxz =HALF*( gupxz*gxxz + gupyz*( gxyz + gyzx - gxzy ) + gupzz*gzzx )
Gamxyz =HALF*( gupxx*( gxyz + gxzy - gyzx ) + gupxy*gyyz + gupxz*gzzy )
Gamyyz =HALF*( gupxy*( gxyz + gxzy - gyzx ) + gupyy*gyyz + gupyz*gzzy )
Gamzyz =HALF*( gupxz*( gxyz + gxzy - gyzx ) + gupyz*gyyz + gupzz*gzzy )
! Raise indices of \tilde A_{ij} and store in R_ij
Rxx = gupxx * gupxx * Axx + gupxy * gupxy * Ayy + gupxz * gupxz * Azz + &
TWO*(gupxx * gupxy * Axy + gupxx * gupxz * Axz + gupxy * gupxz * Ayz)
Ryy = gupxy * gupxy * Axx + gupyy * gupyy * Ayy + gupyz * gupyz * Azz + &
TWO*(gupxy * gupyy * Axy + gupxy * gupyz * Axz + gupyy * gupyz * Ayz)
Rzz = gupxz * gupxz * Axx + gupyz * gupyz * Ayy + gupzz * gupzz * Azz + &
TWO*(gupxz * gupyz * Axy + gupxz * gupzz * Axz + gupyz * gupzz * Ayz)
Rxy = gupxx * gupxy * Axx + gupxy * gupyy * Ayy + gupxz * gupyz * Azz + &
(gupxx * gupyy + gupxy * gupxy)* Axy + &
(gupxx * gupyz + gupxz * gupxy)* Axz + &
(gupxy * gupyz + gupxz * gupyy)* Ayz
Rxz = gupxx * gupxz * Axx + gupxy * gupyz * Ayy + gupxz * gupzz * Azz + &
(gupxx * gupyz + gupxy * gupxz)* Axy + &
(gupxx * gupzz + gupxz * gupxz)* Axz + &
(gupxy * gupzz + gupxz * gupyz)* Ayz
Ryz = gupxy * gupxz * Axx + gupyy * gupyz * Ayy + gupyz * gupzz * Azz + &
(gupxy * gupyz + gupyy * gupxz)* Axy + &
(gupxy * gupzz + gupyz * gupxz)* Axz + &
(gupyy * gupzz + gupyz * gupyz)* Ayz
! Right hand side for Gam^i without shift terms...
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
Gamx_rhs = - TWO * ( Lapx * Rxx + Lapy * Rxy + Lapz * Rxz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxx + chiy * Rxy + chiz * Rxz ) - &
gupxx * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupxy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupxz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz + &
TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
Gamy_rhs = - TWO * ( Lapx * Rxy + Lapy * Ryy + Lapz * Ryz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxy + chiy * Ryy + chiz * Ryz ) - &
gupxy * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupyz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz + &
TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
Gamz_rhs = - TWO * ( Lapx * Rxz + Lapy * Ryz + Lapz * Rzz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxz + chiy * Ryz + chiz * Rzz ) - &
gupxz * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyz * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupzz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz + &
TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
call fderivs(ex,dxx,gxxx,gxxy,gxxz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,gxy,gxyx,gxyy,gxyz,X,Y,Z,ANTI,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,gxz,gxzx,gxzy,gxzz,X,Y,Z,ANTI,SYM ,ANTI,Symmetry,Lev)
call fderivs(ex,dyy,gyyx,gyyy,gyyz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,gyz,gyzx,gyzy,gyzz,X,Y,Z,SYM ,ANTI,ANTI,Symmetry,Lev)
call fderivs(ex,dzz,gzzx,gzzy,gzzz,X,Y,Z,SYM ,SYM ,SYM ,Symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
divb_loc = betaxx(i,j,k) + betayy(i,j,k) + betazz(i,j,k)
div_beta(i,j,k) = divb_loc
chi_rhs(i,j,k) = F2o3 * chin1(i,j,k) * (alpn1(i,j,k) * trK(i,j,k) - divb_loc)
gxx_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axx(i,j,k) - F2o3 * gxx(i,j,k) * divb_loc + &
TWO * ( gxx(i,j,k) * betaxx(i,j,k) + gxy(i,j,k) * betayx(i,j,k) + gxz(i,j,k) * betazx(i,j,k) )
gyy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayy(i,j,k) - F2o3 * gyy(i,j,k) * divb_loc + &
TWO * ( gxy(i,j,k) * betaxy(i,j,k) + gyy(i,j,k) * betayy(i,j,k) + gyz(i,j,k) * betazy(i,j,k) )
gzz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Azz(i,j,k) - F2o3 * gzz(i,j,k) * divb_loc + &
TWO * ( gxz(i,j,k) * betaxz(i,j,k) + gyz(i,j,k) * betayz(i,j,k) + gzz(i,j,k) * betazz(i,j,k) )
gxy_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axy(i,j,k) + F1o3 * gxy(i,j,k) * divb_loc + &
gxx(i,j,k) * betaxy(i,j,k) + gxz(i,j,k) * betazy(i,j,k) + gyy(i,j,k) * betayx(i,j,k) + &
gyz(i,j,k) * betazx(i,j,k) - gxy(i,j,k) * betazz(i,j,k)
gyz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Ayz(i,j,k) + F1o3 * gyz(i,j,k) * divb_loc + &
gxy(i,j,k) * betaxz(i,j,k) + gyy(i,j,k) * betayz(i,j,k) + gxz(i,j,k) * betaxy(i,j,k) + &
gzz(i,j,k) * betazy(i,j,k) - gyz(i,j,k) * betaxx(i,j,k)
gxz_rhs(i,j,k) = - TWO * alpn1(i,j,k) * Axz(i,j,k) + F1o3 * gxz(i,j,k) * divb_loc + &
gxx(i,j,k) * betaxz(i,j,k) + gxy(i,j,k) * betayz(i,j,k) + gyz(i,j,k) * betayx(i,j,k) + &
gzz(i,j,k) * betazx(i,j,k) - gxz(i,j,k) * betayy(i,j,k)
det_loc = gxx(i,j,k) * gyy(i,j,k) * gzz(i,j,k) + gxy(i,j,k) * gyz(i,j,k) * gxz(i,j,k) + &
gxz(i,j,k) * gxy(i,j,k) * gyz(i,j,k) - gxz(i,j,k) * gyy(i,j,k) * gxz(i,j,k) - &
gxy(i,j,k) * gxy(i,j,k) * gzz(i,j,k) - gxx(i,j,k) * gyz(i,j,k) * gyz(i,j,k)
gupxx_loc = ( gyy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gyz(i,j,k) ) / det_loc
gupxy_loc = - ( gxy(i,j,k) * gzz(i,j,k) - gyz(i,j,k) * gxz(i,j,k) ) / det_loc
gupxz_loc = ( gxy(i,j,k) * gyz(i,j,k) - gyy(i,j,k) * gxz(i,j,k) ) / det_loc
gupyy_loc = ( gxx(i,j,k) * gzz(i,j,k) - gxz(i,j,k) * gxz(i,j,k) ) / det_loc
gupyz_loc = - ( gxx(i,j,k) * gyz(i,j,k) - gxy(i,j,k) * gxz(i,j,k) ) / det_loc
gupzz_loc = ( gxx(i,j,k) * gyy(i,j,k) - gxy(i,j,k) * gxy(i,j,k) ) / det_loc
gupxx(i,j,k) = gupxx_loc
gupxy(i,j,k) = gupxy_loc
gupxz(i,j,k) = gupxz_loc
gupyy(i,j,k) = gupyy_loc
gupyz(i,j,k) = gupyz_loc
gupzz(i,j,k) = gupzz_loc
if(co == 0)then
Gmx_Res(i,j,k) = Gamx(i,j,k) - ( &
gupxx_loc*(gupxx_loc*gxxx(i,j,k)+gupxy_loc*gxyx(i,j,k)+gupxz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxx_loc*gxyx(i,j,k)+gupxy_loc*gyyx(i,j,k)+gupxz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxx_loc*gxzx(i,j,k)+gupxy_loc*gyzx(i,j,k)+gupxz_loc*gzzx(i,j,k)) + &
gupxx_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
gupxz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
gupxx_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
Gmy_Res(i,j,k) = Gamy(i,j,k) - ( &
gupxx_loc*(gupxy_loc*gxxx(i,j,k)+gupyy_loc*gxyx(i,j,k)+gupyz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxyx(i,j,k)+gupyy_loc*gyyx(i,j,k)+gupyz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxy_loc*gxzx(i,j,k)+gupyy_loc*gyzx(i,j,k)+gupyz_loc*gzzx(i,j,k)) + &
gupxy_loc*(gupxy_loc*gxxy(i,j,k)+gupyy_loc*gxyy(i,j,k)+gupyz_loc*gxzy(i,j,k)) + &
gupyy_loc*(gupxy_loc*gxyy(i,j,k)+gupyy_loc*gyyy(i,j,k)+gupyz_loc*gyzy(i,j,k)) + &
gupyz_loc*(gupxy_loc*gxzy(i,j,k)+gupyy_loc*gyzy(i,j,k)+gupyz_loc*gzzy(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupyy_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
Gmz_Res(i,j,k) = Gamz(i,j,k) - ( &
gupxx_loc*(gupxz_loc*gxxx(i,j,k)+gupyz_loc*gxyx(i,j,k)+gupzz_loc*gxzx(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxyx(i,j,k)+gupyz_loc*gyyx(i,j,k)+gupzz_loc*gyzx(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxzx(i,j,k)+gupyz_loc*gyzx(i,j,k)+gupzz_loc*gzzx(i,j,k)) + &
gupxy_loc*(gupxz_loc*gxxy(i,j,k)+gupyz_loc*gxyy(i,j,k)+gupzz_loc*gxzy(i,j,k)) + &
gupyy_loc*(gupxz_loc*gxyy(i,j,k)+gupyz_loc*gyyy(i,j,k)+gupzz_loc*gyzy(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxzy(i,j,k)+gupyz_loc*gyzy(i,j,k)+gupzz_loc*gzzy(i,j,k)) + &
gupxz_loc*(gupxz_loc*gxxz(i,j,k)+gupyz_loc*gxyz(i,j,k)+gupzz_loc*gxzz(i,j,k)) + &
gupyz_loc*(gupxz_loc*gxyz(i,j,k)+gupyz_loc*gyyz(i,j,k)+gupzz_loc*gyzz(i,j,k)) + &
gupzz_loc*(gupxz_loc*gxzz(i,j,k)+gupyz_loc*gyzz(i,j,k)+gupzz_loc*gzzz(i,j,k)))
endif
Gamxxx(i,j,k)=HALF*( gupxx_loc*gxxx(i,j,k) + gupxy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupxz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamyxx(i,j,k)=HALF*( gupxy_loc*gxxx(i,j,k) + gupyy_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupyz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamzxx(i,j,k)=HALF*( gupxz_loc*gxxx(i,j,k) + gupyz_loc*(TWO*gxyx(i,j,k) - gxxy(i,j,k)) + gupzz_loc*(TWO*gxzx(i,j,k) - gxxz(i,j,k)))
Gamxyy(i,j,k)=HALF*( gupxx_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupxy_loc*gyyy(i,j,k) + gupxz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamyyy(i,j,k)=HALF*( gupxy_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyy_loc*gyyy(i,j,k) + gupyz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamzyy(i,j,k)=HALF*( gupxz_loc*(TWO*gxyy(i,j,k) - gyyx(i,j,k)) + gupyz_loc*gyyy(i,j,k) + gupzz_loc*(TWO*gyzy(i,j,k) - gyyz(i,j,k)))
Gamxzz(i,j,k)=HALF*( gupxx_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupxy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupxz_loc*gzzz(i,j,k))
Gamyzz(i,j,k)=HALF*( gupxy_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyy_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupyz_loc*gzzz(i,j,k))
Gamzzz(i,j,k)=HALF*( gupxz_loc*(TWO*gxzz(i,j,k) - gzzx(i,j,k)) + gupyz_loc*(TWO*gyzz(i,j,k) - gzzy(i,j,k)) + gupzz_loc*gzzz(i,j,k))
Gamxxy(i,j,k)=HALF*( gupxx_loc*gxxy(i,j,k) + gupxy_loc*gyyx(i,j,k) + gupxz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamyxy(i,j,k)=HALF*( gupxy_loc*gxxy(i,j,k) + gupyy_loc*gyyx(i,j,k) + gupyz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamzxy(i,j,k)=HALF*( gupxz_loc*gxxy(i,j,k) + gupyz_loc*gyyx(i,j,k) + gupzz_loc*(gxzy(i,j,k) + gyzx(i,j,k) - gxyz(i,j,k)) )
Gamxxz(i,j,k)=HALF*( gupxx_loc*gxxz(i,j,k) + gupxy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupxz_loc*gzzx(i,j,k) )
Gamyxz(i,j,k)=HALF*( gupxy_loc*gxxz(i,j,k) + gupyy_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupyz_loc*gzzx(i,j,k) )
Gamzxz(i,j,k)=HALF*( gupxz_loc*gxxz(i,j,k) + gupyz_loc*(gxyz(i,j,k) + gyzx(i,j,k) - gxzy(i,j,k)) + gupzz_loc*gzzx(i,j,k) )
Gamxyz(i,j,k)=HALF*( gupxx_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupxy_loc*gyyz(i,j,k) + gupxz_loc*gzzy(i,j,k) )
Gamyyz(i,j,k)=HALF*( gupxy_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyy_loc*gyyz(i,j,k) + gupyz_loc*gzzy(i,j,k) )
Gamzyz(i,j,k)=HALF*( gupxz_loc*(gxyz(i,j,k) + gxzy(i,j,k) - gyzx(i,j,k)) + gupyz_loc*gyyz(i,j,k) + gupzz_loc*gzzy(i,j,k) )
enddo
enddo
enddo
! Raise indices of \tilde A_{ij} and store in R_ij
! Right hand side for Gam^i without shift terms...
call fderivs(ex,Lap,Lapx,Lapy,Lapz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
call fderivs(ex,trK,Kx,Ky,Kz,X,Y,Z,SYM,SYM,SYM,symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
gupxx_loc = gupxx(i,j,k)
gupxy_loc = gupxy(i,j,k)
gupxz_loc = gupxz(i,j,k)
gupyy_loc = gupyy(i,j,k)
gupyz_loc = gupyz(i,j,k)
gupzz_loc = gupzz(i,j,k)
Rxx_loc = gupxx_loc * gupxx_loc * Axx(i,j,k) + gupxy_loc * gupxy_loc * Ayy(i,j,k) + gupxz_loc * gupxz_loc * Azz(i,j,k) + &
TWO * (gupxx_loc * gupxy_loc * Axy(i,j,k) + gupxx_loc * gupxz_loc * Axz(i,j,k) + gupxy_loc * gupxz_loc * Ayz(i,j,k))
Ryy_loc = gupxy_loc * gupxy_loc * Axx(i,j,k) + gupyy_loc * gupyy_loc * Ayy(i,j,k) + gupyz_loc * gupyz_loc * Azz(i,j,k) + &
TWO * (gupxy_loc * gupyy_loc * Axy(i,j,k) + gupxy_loc * gupyz_loc * Axz(i,j,k) + gupyy_loc * gupyz_loc * Ayz(i,j,k))
Rzz_loc = gupxz_loc * gupxz_loc * Axx(i,j,k) + gupyz_loc * gupyz_loc * Ayy(i,j,k) + gupzz_loc * gupzz_loc * Azz(i,j,k) + &
TWO * (gupxz_loc * gupyz_loc * Axy(i,j,k) + gupxz_loc * gupzz_loc * Axz(i,j,k) + gupyz_loc * gupzz_loc * Ayz(i,j,k))
Rxy_loc = gupxx_loc * gupxy_loc * Axx(i,j,k) + gupxy_loc * gupyy_loc * Ayy(i,j,k) + gupxz_loc * gupyz_loc * Azz(i,j,k) + &
(gupxx_loc * gupyy_loc + gupxy_loc * gupxy_loc) * Axy(i,j,k) + &
(gupxx_loc * gupyz_loc + gupxz_loc * gupxy_loc) * Axz(i,j,k) + &
(gupxy_loc * gupyz_loc + gupxz_loc * gupyy_loc) * Ayz(i,j,k)
Rxz_loc = gupxx_loc * gupxz_loc * Axx(i,j,k) + gupxy_loc * gupyz_loc * Ayy(i,j,k) + gupxz_loc * gupzz_loc * Azz(i,j,k) + &
(gupxx_loc * gupyz_loc + gupxy_loc * gupxz_loc) * Axy(i,j,k) + &
(gupxx_loc * gupzz_loc + gupxz_loc * gupxz_loc) * Axz(i,j,k) + &
(gupxy_loc * gupzz_loc + gupxz_loc * gupyz_loc) * Ayz(i,j,k)
Ryz_loc = gupxy_loc * gupxz_loc * Axx(i,j,k) + gupyy_loc * gupyz_loc * Ayy(i,j,k) + gupyz_loc * gupzz_loc * Azz(i,j,k) + &
(gupxy_loc * gupyz_loc + gupyy_loc * gupxz_loc) * Axy(i,j,k) + &
(gupxy_loc * gupzz_loc + gupyz_loc * gupxz_loc) * Axz(i,j,k) + &
(gupyy_loc * gupzz_loc + gupyz_loc * gupyz_loc) * Ayz(i,j,k)
Rxx(i,j,k) = Rxx_loc
Ryy(i,j,k) = Ryy_loc
Rzz(i,j,k) = Rzz_loc
Rxy(i,j,k) = Rxy_loc
Rxz(i,j,k) = Rxz_loc
Ryz(i,j,k) = Ryz_loc
Gamx_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxx_loc + Lapy(i,j,k) * Rxy_loc + Lapz(i,j,k) * Rxz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxx_loc + chiy(i,j,k) * Rxy_loc + chiz(i,j,k) * Rxz_loc) - &
gupxx_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupxy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupxz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamxxx(i,j,k) * Rxx_loc + Gamxyy(i,j,k) * Ryy_loc + Gamxzz(i,j,k) * Rzz_loc + &
TWO * (Gamxxy(i,j,k) * Rxy_loc + Gamxxz(i,j,k) * Rxz_loc + Gamxyz(i,j,k) * Ryz_loc))
Gamy_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxy_loc + Lapy(i,j,k) * Ryy_loc + Lapz(i,j,k) * Ryz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxy_loc + chiy(i,j,k) * Ryy_loc + chiz(i,j,k) * Ryz_loc) - &
gupxy_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupyy_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupyz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamyxx(i,j,k) * Rxx_loc + Gamyyy(i,j,k) * Ryy_loc + Gamyzz(i,j,k) * Rzz_loc + &
TWO * (Gamyxy(i,j,k) * Rxy_loc + Gamyxz(i,j,k) * Rxz_loc + Gamyyz(i,j,k) * Ryz_loc))
Gamz_rhs(i,j,k) = - TWO * (Lapx(i,j,k) * Rxz_loc + Lapy(i,j,k) * Ryz_loc + Lapz(i,j,k) * Rzz_loc) + &
TWO * alpn1(i,j,k) * ( &
-F3o2/chin1(i,j,k) * (chix(i,j,k) * Rxz_loc + chiy(i,j,k) * Ryz_loc + chiz(i,j,k) * Rzz_loc) - &
gupxz_loc * (F2o3 * Kx(i,j,k) + EIGHT * PI * Sx(i,j,k)) - &
gupyz_loc * (F2o3 * Ky(i,j,k) + EIGHT * PI * Sy(i,j,k)) - &
gupzz_loc * (F2o3 * Kz(i,j,k) + EIGHT * PI * Sz(i,j,k)) + &
Gamzxx(i,j,k) * Rxx_loc + Gamzyy(i,j,k) * Ryy_loc + Gamzzz(i,j,k) * Rzz_loc + &
TWO * (Gamzxy(i,j,k) * Rxy_loc + Gamzxz(i,j,k) * Rxz_loc + Gamzyz(i,j,k) * Ryz_loc))
enddo
enddo
enddo
call fdderivs(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,&
X,Y,Z,ANTI,SYM, SYM ,Symmetry,Lev)
@@ -321,38 +359,54 @@
call fdderivs(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,&
X,Y,Z,SYM ,SYM, ANTI,Symmetry,Lev)
fxx = gxxx + gxyy + gxzz
fxy = gxyx + gyyy + gyzz
fxz = gxzx + gyzy + gzzz
Gamxa = gupxx * Gamxxx + gupyy * Gamxyy + gupzz * Gamxzz + &
TWO*( gupxy * Gamxxy + gupxz * Gamxxz + gupyz * Gamxyz )
Gamya = gupxx * Gamyxx + gupyy * Gamyyy + gupzz * Gamyzz + &
TWO*( gupxy * Gamyxy + gupxz * Gamyxz + gupyz * Gamyyz )
Gamza = gupxx * Gamzxx + gupyy * Gamzyy + gupzz * Gamzzz + &
TWO*( gupxy * Gamzxy + gupxz * Gamzxz + gupyz * Gamzyz )
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
Gamx_rhs = Gamx_rhs + F2o3 * Gamxa * div_beta - &
Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz + &
F1o3 * (gupxx * fxx + gupxy * fxy + gupxz * fxz ) + &
gupxx * gxxx + gupyy * gyyx + gupzz * gzzx + &
TWO * (gupxy * gxyx + gupxz * gxzx + gupyz * gyzx )
Gamy_rhs = Gamy_rhs + F2o3 * Gamya * div_beta - &
Gamxa * betayx - Gamya * betayy - Gamza * betayz + &
F1o3 * (gupxy * fxx + gupyy * fxy + gupyz * fxz ) + &
gupxx * gxxy + gupyy * gyyy + gupzz * gzzy + &
TWO * (gupxy * gxyy + gupxz * gxzy + gupyz * gyzy )
Gamz_rhs = Gamz_rhs + F2o3 * Gamza * div_beta - &
Gamxa * betazx - Gamya * betazy - Gamza * betazz + &
F1o3 * (gupxz * fxx + gupyz * fxy + gupzz * fxz ) + &
gupxx * gxxz + gupyy * gyyz + gupzz * gzzz + &
TWO * (gupxy * gxyz + gupxz * gxzz + gupyz * gyzz ) !rhs for Gam^i
call fderivs(ex,Gamx,Gamxx,Gamxy,Gamxz,X,Y,Z,ANTI,SYM ,SYM ,Symmetry,Lev)
call fderivs(ex,Gamy,Gamyx,Gamyy,Gamyz,X,Y,Z,SYM ,ANTI,SYM ,Symmetry,Lev)
call fderivs(ex,Gamz,Gamzx,Gamzy,Gamzz,X,Y,Z,SYM ,SYM ,ANTI,Symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
divb_loc = div_beta(i,j,k)
fxx_loc = gxxx(i,j,k) + gxyy(i,j,k) + gxzz(i,j,k)
fxy_loc = gxyx(i,j,k) + gyyy(i,j,k) + gyzz(i,j,k)
fxz_loc = gxzx(i,j,k) + gyzy(i,j,k) + gzzz(i,j,k)
gupxx_loc = gupxx(i,j,k)
gupxy_loc = gupxy(i,j,k)
gupxz_loc = gupxz(i,j,k)
gupyy_loc = gupyy(i,j,k)
gupyz_loc = gupyz(i,j,k)
gupzz_loc = gupzz(i,j,k)
Gamxa_loc = gupxx_loc * Gamxxx(i,j,k) + gupyy_loc * Gamxyy(i,j,k) + gupzz_loc * Gamxzz(i,j,k) + &
TWO * (gupxy_loc * Gamxxy(i,j,k) + gupxz_loc * Gamxxz(i,j,k) + gupyz_loc * Gamxyz(i,j,k))
Gamya_loc = gupxx_loc * Gamyxx(i,j,k) + gupyy_loc * Gamyyy(i,j,k) + gupzz_loc * Gamyzz(i,j,k) + &
TWO * (gupxy_loc * Gamyxy(i,j,k) + gupxz_loc * Gamyxz(i,j,k) + gupyz_loc * Gamyyz(i,j,k))
Gamza_loc = gupxx_loc * Gamzxx(i,j,k) + gupyy_loc * Gamzyy(i,j,k) + gupzz_loc * Gamzzz(i,j,k) + &
TWO * (gupxy_loc * Gamzxy(i,j,k) + gupxz_loc * Gamzxz(i,j,k) + gupyz_loc * Gamzyz(i,j,k))
Gamxa(i,j,k) = Gamxa_loc
Gamya(i,j,k) = Gamya_loc
Gamza(i,j,k) = Gamza_loc
Gamx_rhs(i,j,k) = Gamx_rhs(i,j,k) + F2o3 * Gamxa_loc * divb_loc - &
Gamxa_loc * betaxx(i,j,k) - Gamya_loc * betaxy(i,j,k) - Gamza_loc * betaxz(i,j,k) + &
F1o3 * (gupxx_loc * fxx_loc + gupxy_loc * fxy_loc + gupxz_loc * fxz_loc) + &
gupxx_loc * gxxx(i,j,k) + gupyy_loc * gyyx(i,j,k) + gupzz_loc * gzzx(i,j,k) + &
TWO * (gupxy_loc * gxyx(i,j,k) + gupxz_loc * gxzx(i,j,k) + gupyz_loc * gyzx(i,j,k))
Gamy_rhs(i,j,k) = Gamy_rhs(i,j,k) + F2o3 * Gamya_loc * divb_loc - &
Gamxa_loc * betayx(i,j,k) - Gamya_loc * betayy(i,j,k) - Gamza_loc * betayz(i,j,k) + &
F1o3 * (gupxy_loc * fxx_loc + gupyy_loc * fxy_loc + gupyz_loc * fxz_loc) + &
gupxx_loc * gxxy(i,j,k) + gupyy_loc * gyyy(i,j,k) + gupzz_loc * gzzy(i,j,k) + &
TWO * (gupxy_loc * gxyy(i,j,k) + gupxz_loc * gxzy(i,j,k) + gupyz_loc * gyzy(i,j,k))
Gamz_rhs(i,j,k) = Gamz_rhs(i,j,k) + F2o3 * Gamza_loc * divb_loc - &
Gamxa_loc * betazx(i,j,k) - Gamya_loc * betazy(i,j,k) - Gamza_loc * betazz(i,j,k) + &
F1o3 * (gupxz_loc * fxx_loc + gupyz_loc * fxy_loc + gupzz_loc * fxz_loc) + &
gupxx_loc * gxxz(i,j,k) + gupyy_loc * gyyz(i,j,k) + gupzz_loc * gzzz(i,j,k) + &
TWO * (gupxy_loc * gxyz(i,j,k) + gupxz_loc * gxzz(i,j,k) + gupyz_loc * gyzz(i,j,k))
enddo
enddo
enddo
!first kind of connection stored in gij,k
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
@@ -601,192 +655,190 @@
Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz + &
Gamxzz * gxzy + Gamyzz * gyzy + Gamzzz * gzzy + &
Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )
!covariant second derivative of chi respect to tilted metric
call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
fxx = fxx - Gamxxx * chix - Gamyxx * chiy - Gamzxx * chiz
fxy = fxy - Gamxxy * chix - Gamyxy * chiy - Gamzxy * chiz
fxz = fxz - Gamxxz * chix - Gamyxz * chiy - Gamzxz * chiz
fyy = fyy - Gamxyy * chix - Gamyyy * chiy - Gamzyy * chiz
fyz = fyz - Gamxyz * chix - Gamyyz * chiy - Gamzyz * chiz
fzz = fzz - Gamxzz * chix - Gamyzz * chiy - Gamzzz * chiz
! Store D^l D_l chi - 3/(2*chi) D^l chi D_l chi in f
f = gupxx * ( fxx - F3o2/chin1 * chix * chix ) + &
gupyy * ( fyy - F3o2/chin1 * chiy * chiy ) + &
gupzz * ( fzz - F3o2/chin1 * chiz * chiz ) + &
TWO * gupxy * ( fxy - F3o2/chin1 * chix * chiy ) + &
TWO * gupxz * ( fxz - F3o2/chin1 * chix * chiz ) + &
TWO * gupyz * ( fyz - F3o2/chin1 * chiy * chiz )
! Add chi part to Ricci tensor:
Rxx = Rxx + (fxx - chix*chix/chin1/TWO + gxx * f)/chin1/TWO
Ryy = Ryy + (fyy - chiy*chiy/chin1/TWO + gyy * f)/chin1/TWO
Rzz = Rzz + (fzz - chiz*chiz/chin1/TWO + gzz * f)/chin1/TWO
Rxy = Rxy + (fxy - chix*chiy/chin1/TWO + gxy * f)/chin1/TWO
Rxz = Rxz + (fxz - chix*chiz/chin1/TWO + gxz * f)/chin1/TWO
Ryz = Ryz + (fyz - chiy*chiz/chin1/TWO + gyz * f)/chin1/TWO
! covariant second derivatives of the lapse respect to physical metric
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM,SYM,SYM,symmetry,Lev)
gxxx = (gupxx * chix + gupxy * chiy + gupxz * chiz)/chin1
gxxy = (gupxy * chix + gupyy * chiy + gupyz * chiz)/chin1
gxxz = (gupxz * chix + gupyz * chiy + gupzz * chiz)/chin1
! now get physical second kind of connection
Gamxxx = Gamxxx - ( (chix + chix)/chin1 - gxx * gxxx )*HALF
Gamyxx = Gamyxx - ( - gxx * gxxy )*HALF
Gamzxx = Gamzxx - ( - gxx * gxxz )*HALF
Gamxyy = Gamxyy - ( - gyy * gxxx )*HALF
Gamyyy = Gamyyy - ( (chiy + chiy)/chin1 - gyy * gxxy )*HALF
Gamzyy = Gamzyy - ( - gyy * gxxz )*HALF
Gamxzz = Gamxzz - ( - gzz * gxxx )*HALF
Gamyzz = Gamyzz - ( - gzz * gxxy )*HALF
Gamzzz = Gamzzz - ( (chiz + chiz)/chin1 - gzz * gxxz )*HALF
Gamxxy = Gamxxy - ( chiy /chin1 - gxy * gxxx )*HALF
Gamyxy = Gamyxy - ( chix /chin1 - gxy * gxxy )*HALF
Gamzxy = Gamzxy - ( - gxy * gxxz )*HALF
Gamxxz = Gamxxz - ( chiz /chin1 - gxz * gxxx )*HALF
Gamyxz = Gamyxz - ( - gxz * gxxy )*HALF
Gamzxz = Gamzxz - ( chix /chin1 - gxz * gxxz )*HALF
Gamxyz = Gamxyz - ( - gyz * gxxx )*HALF
Gamyyz = Gamyyz - ( chiz /chin1 - gyz * gxxy )*HALF
Gamzyz = Gamzyz - ( chiy /chin1 - gyz * gxxz )*HALF
fxx = fxx - Gamxxx*Lapx - Gamyxx*Lapy - Gamzxx*Lapz
fyy = fyy - Gamxyy*Lapx - Gamyyy*Lapy - Gamzyy*Lapz
fzz = fzz - Gamxzz*Lapx - Gamyzz*Lapy - Gamzzz*Lapz
fxy = fxy - Gamxxy*Lapx - Gamyxy*Lapy - Gamzxy*Lapz
fxz = fxz - Gamxxz*Lapx - Gamyxz*Lapy - Gamzxz*Lapz
fyz = fyz - Gamxyz*Lapx - Gamyyz*Lapy - Gamzyz*Lapz
! store D^i D_i Lap in trK_rhs upto chi
trK_rhs = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz )
#if 1
!! follow bam code
S = chin1 * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
f = F2o3 * trK * trK -(&
gupxx * ( &
gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz) ) + &
gupyy * ( &
gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz) ) + &
gupzz * ( &
gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz) ) + &
TWO * ( &
gupxy * ( &
gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
gupxy * (Axx * Ayy + Axy * Axy) + &
gupxz * (Axx * Ayz + Axz * Axy) + &
gupyz * (Axy * Ayz + Axz * Ayy) ) + &
gupxz * ( &
gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
gupxy * (Axx * Ayz + Axy * Axz) + &
gupxz * (Axx * Azz + Axz * Axz) + &
gupyz * (Axy * Azz + Axz * Ayz) ) + &
gupyz * ( &
gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
gupxy * (Axy * Ayz + Ayy * Axz) + &
gupxz * (Axy * Azz + Ayz * Axz) + &
gupyz * (Ayy * Azz + Ayz * Ayz) ) )) -1.6d1*PI*rho + EIGHT * PI * S
f = - F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + alpn1/chin1*f)
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
#else
! Add lapse and S_ij parts to Ricci tensor:
fxx = alpn1 * (Rxx - EIGHT * PI * Sxx) - fxx
fxy = alpn1 * (Rxy - EIGHT * PI * Sxy) - fxy
fxz = alpn1 * (Rxz - EIGHT * PI * Sxz) - fxz
fyy = alpn1 * (Ryy - EIGHT * PI * Syy) - fyy
fyz = alpn1 * (Ryz - EIGHT * PI * Syz) - fyz
fzz = alpn1 * (Rzz - EIGHT * PI * Szz) - fzz
! Compute trace-free part (note: chi^-1 and chi cancel!):
f = F1o3 *( gupxx * fxx + gupyy * fyy + gupzz * fzz + &
TWO* ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) )
#endif
Axx_rhs = fxx - gxx * f
Ayy_rhs = fyy - gyy * f
Azz_rhs = fzz - gzz * f
Axy_rhs = fxy - gxy * f
Axz_rhs = fxz - gxz * f
Ayz_rhs = fyz - gyz * f
! Now: store A_il A^l_j into fij:
fxx = gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
fyy = gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
fzz = gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
fxy = gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
gupxy *(Axx * Ayy + Axy * Axy) + &
gupxz *(Axx * Ayz + Axz * Axy) + &
gupyz *(Axy * Ayz + Axz * Ayy)
fxz = gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
gupxy *(Axx * Ayz + Axy * Axz) + &
gupxz *(Axx * Azz + Axz * Axz) + &
gupyz *(Axy * Azz + Axz * Ayz)
fyz = gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
gupxy *(Axy * Ayz + Ayy * Axz) + &
gupxz *(Axy * Azz + Ayz * Axz) + &
gupyz *(Ayy * Azz + Ayz * Ayz)
f = chin1
! store D^i D_i Lap in trK_rhs
trK_rhs = f*trK_rhs
Axx_rhs = f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx) + &
TWO * ( Axx * betaxx + Axy * betayx + Axz * betazx )- &
F2o3 * Axx * div_beta
Ayy_rhs = f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy) + &
TWO * ( Axy * betaxy + Ayy * betayy + Ayz * betazy )- &
F2o3 * Ayy * div_beta
Azz_rhs = f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz) + &
TWO * ( Axz * betaxz + Ayz * betayz + Azz * betazz )- &
F2o3 * Azz * div_beta
Axy_rhs = f * Axy_rhs+ alpn1 *( trK * Axy - TWO * fxy )+ &
Axx * betaxy + Axz * betazy + &
Ayy * betayx + Ayz * betazx + &
F1o3 * Axy * div_beta - Axy * betazz
Ayz_rhs = f * Ayz_rhs+ alpn1 *( trK * Ayz - TWO * fyz )+ &
Axy * betaxz + Ayy * betayz + &
Axz * betaxy + Azz * betazy + &
F1o3 * Ayz * div_beta - Ayz * betaxx
Axz_rhs = f * Axz_rhs+ alpn1 *( trK * Axz - TWO * fxz )+ &
Axx * betaxz + Axy * betayz + &
Ayz * betayx + Azz * betazx + &
F1o3 * Axz * div_beta - Axz * betayy !rhs for Aij
! Compute trace of S_ij
S = f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK + &
gupxx * fxx + gupyy * fyy + gupzz * fzz + &
TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
FOUR * PI * ( rho + S )) !rhs for trK
!covariant second derivative of chi respect to tilted metric
call fdderivs(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z,SYM,SYM,SYM,Symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k) * chix(i,j,k) - Gamyxx(i,j,k) * chiy(i,j,k) - Gamzxx(i,j,k) * chiz(i,j,k)
fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k) * chix(i,j,k) - Gamyxy(i,j,k) * chiy(i,j,k) - Gamzxy(i,j,k) * chiz(i,j,k)
fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k) * chix(i,j,k) - Gamyxz(i,j,k) * chiy(i,j,k) - Gamzxz(i,j,k) * chiz(i,j,k)
fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k) * chix(i,j,k) - Gamyyy(i,j,k) * chiy(i,j,k) - Gamzyy(i,j,k) * chiz(i,j,k)
fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k) * chix(i,j,k) - Gamyyz(i,j,k) * chiy(i,j,k) - Gamzyz(i,j,k) * chiz(i,j,k)
fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k) * chix(i,j,k) - Gamyzz(i,j,k) * chiy(i,j,k) - Gamzzz(i,j,k) * chiz(i,j,k)
chin_loc = chin1(i,j,k)
f_loc = gupxx(i,j,k) * (fxx(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chix(i,j,k)) + &
gupyy(i,j,k) * (fyy(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiy(i,j,k)) + &
gupzz(i,j,k) * (fzz(i,j,k) - F3o2/chin_loc * chiz(i,j,k) * chiz(i,j,k)) + &
TWO * gupxy(i,j,k) * (fxy(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiy(i,j,k)) + &
TWO * gupxz(i,j,k) * (fxz(i,j,k) - F3o2/chin_loc * chix(i,j,k) * chiz(i,j,k)) + &
TWO * gupyz(i,j,k) * (fyz(i,j,k) - F3o2/chin_loc * chiy(i,j,k) * chiz(i,j,k))
f(i,j,k) = f_loc
Rxx(i,j,k) = Rxx(i,j,k) + (fxx(i,j,k) - chix(i,j,k)*chix(i,j,k)/chin_loc/TWO + gxx(i,j,k) * f_loc)/chin_loc/TWO
Ryy(i,j,k) = Ryy(i,j,k) + (fyy(i,j,k) - chiy(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gyy(i,j,k) * f_loc)/chin_loc/TWO
Rzz(i,j,k) = Rzz(i,j,k) + (fzz(i,j,k) - chiz(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gzz(i,j,k) * f_loc)/chin_loc/TWO
Rxy(i,j,k) = Rxy(i,j,k) + (fxy(i,j,k) - chix(i,j,k)*chiy(i,j,k)/chin_loc/TWO + gxy(i,j,k) * f_loc)/chin_loc/TWO
Rxz(i,j,k) = Rxz(i,j,k) + (fxz(i,j,k) - chix(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gxz(i,j,k) * f_loc)/chin_loc/TWO
Ryz(i,j,k) = Ryz(i,j,k) + (fyz(i,j,k) - chiy(i,j,k)*chiz(i,j,k)/chin_loc/TWO + gyz(i,j,k) * f_loc)/chin_loc/TWO
enddo
enddo
enddo
! covariant second derivatives of the lapse respect to physical metric
call fdderivs(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM,SYM,SYM,symmetry,Lev)
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
chin_loc = chin1(i,j,k)
gxxx(i,j,k) = (gupxx(i,j,k) * chix(i,j,k) + gupxy(i,j,k) * chiy(i,j,k) + gupxz(i,j,k) * chiz(i,j,k)) / chin_loc
gxxy(i,j,k) = (gupxy(i,j,k) * chix(i,j,k) + gupyy(i,j,k) * chiy(i,j,k) + gupyz(i,j,k) * chiz(i,j,k)) / chin_loc
gxxz(i,j,k) = (gupxz(i,j,k) * chix(i,j,k) + gupyz(i,j,k) * chiy(i,j,k) + gupzz(i,j,k) * chiz(i,j,k)) / chin_loc
Gamxxx(i,j,k) = Gamxxx(i,j,k) - ( (chix(i,j,k) + chix(i,j,k))/chin_loc - gxx(i,j,k) * gxxx(i,j,k) )*HALF
Gamyxx(i,j,k) = Gamyxx(i,j,k) - ( - gxx(i,j,k) * gxxy(i,j,k) )*HALF
Gamzxx(i,j,k) = Gamzxx(i,j,k) - ( - gxx(i,j,k) * gxxz(i,j,k) )*HALF
Gamxyy(i,j,k) = Gamxyy(i,j,k) - ( - gyy(i,j,k) * gxxx(i,j,k) )*HALF
Gamyyy(i,j,k) = Gamyyy(i,j,k) - ( (chiy(i,j,k) + chiy(i,j,k))/chin_loc - gyy(i,j,k) * gxxy(i,j,k) )*HALF
Gamzyy(i,j,k) = Gamzyy(i,j,k) - ( - gyy(i,j,k) * gxxz(i,j,k) )*HALF
Gamxzz(i,j,k) = Gamxzz(i,j,k) - ( - gzz(i,j,k) * gxxx(i,j,k) )*HALF
Gamyzz(i,j,k) = Gamyzz(i,j,k) - ( - gzz(i,j,k) * gxxy(i,j,k) )*HALF
Gamzzz(i,j,k) = Gamzzz(i,j,k) - ( (chiz(i,j,k) + chiz(i,j,k))/chin_loc - gzz(i,j,k) * gxxz(i,j,k) )*HALF
Gamxxy(i,j,k) = Gamxxy(i,j,k) - ( chiy(i,j,k) /chin_loc - gxy(i,j,k) * gxxx(i,j,k) )*HALF
Gamyxy(i,j,k) = Gamyxy(i,j,k) - ( chix(i,j,k) /chin_loc - gxy(i,j,k) * gxxy(i,j,k) )*HALF
Gamzxy(i,j,k) = Gamzxy(i,j,k) - ( - gxy(i,j,k) * gxxz(i,j,k) )*HALF
Gamxxz(i,j,k) = Gamxxz(i,j,k) - ( chiz(i,j,k) /chin_loc - gxz(i,j,k) * gxxx(i,j,k) )*HALF
Gamyxz(i,j,k) = Gamyxz(i,j,k) - ( - gxz(i,j,k) * gxxy(i,j,k) )*HALF
Gamzxz(i,j,k) = Gamzxz(i,j,k) - ( chix(i,j,k) /chin_loc - gxz(i,j,k) * gxxz(i,j,k) )*HALF
Gamxyz(i,j,k) = Gamxyz(i,j,k) - ( - gyz(i,j,k) * gxxx(i,j,k) )*HALF
Gamyyz(i,j,k) = Gamyyz(i,j,k) - ( chiz(i,j,k) /chin_loc - gyz(i,j,k) * gxxy(i,j,k) )*HALF
Gamzyz(i,j,k) = Gamzyz(i,j,k) - ( chiy(i,j,k) /chin_loc - gyz(i,j,k) * gxxz(i,j,k) )*HALF
fxx(i,j,k) = fxx(i,j,k) - Gamxxx(i,j,k)*Lapx(i,j,k) - Gamyxx(i,j,k)*Lapy(i,j,k) - Gamzxx(i,j,k)*Lapz(i,j,k)
fyy(i,j,k) = fyy(i,j,k) - Gamxyy(i,j,k)*Lapx(i,j,k) - Gamyyy(i,j,k)*Lapy(i,j,k) - Gamzyy(i,j,k)*Lapz(i,j,k)
fzz(i,j,k) = fzz(i,j,k) - Gamxzz(i,j,k)*Lapx(i,j,k) - Gamyzz(i,j,k)*Lapy(i,j,k) - Gamzzz(i,j,k)*Lapz(i,j,k)
fxy(i,j,k) = fxy(i,j,k) - Gamxxy(i,j,k)*Lapx(i,j,k) - Gamyxy(i,j,k)*Lapy(i,j,k) - Gamzxy(i,j,k)*Lapz(i,j,k)
fxz(i,j,k) = fxz(i,j,k) - Gamxxz(i,j,k)*Lapx(i,j,k) - Gamyxz(i,j,k)*Lapy(i,j,k) - Gamzxz(i,j,k)*Lapz(i,j,k)
fyz(i,j,k) = fyz(i,j,k) - Gamxyz(i,j,k)*Lapx(i,j,k) - Gamyyz(i,j,k)*Lapy(i,j,k) - Gamzyz(i,j,k)*Lapz(i,j,k)
trK_rhs(i,j,k) = gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k))
enddo
enddo
enddo
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
divb_loc = div_beta(i,j,k)
chin_loc = chin1(i,j,k)
S_loc = chin_loc * ( gupxx(i,j,k) * Sxx(i,j,k) + gupyy(i,j,k) * Syy(i,j,k) + gupzz(i,j,k) * Szz(i,j,k) + &
TWO * (gupxy(i,j,k) * Sxy(i,j,k) + gupxz(i,j,k) * Sxz(i,j,k) + gupyz(i,j,k) * Syz(i,j,k)) )
S(i,j,k) = S_loc
f_loc = F2o3 * trK(i,j,k) * trK(i,j,k) - ( &
gupxx(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + &
TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + &
gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k)) ) + &
gupyy(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k)) ) + &
gupzz(i,j,k) * ( gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + &
TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k)) ) + &
TWO * ( gupxy(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k)) ) + &
gupxz(i,j,k) * ( gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + &
gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k)) ) + &
gupyz(i,j,k) * ( gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + &
gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k)) ) ) ) - &
F16 * PI * rho(i,j,k) + EIGHT * PI * S_loc
f_loc = -F1o3 * ( gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
alpn1(i,j,k)/chin_loc * f_loc )
f(i,j,k) = f_loc
l_fxx = alpn1(i,j,k) * (Rxx(i,j,k) - EIGHT * PI * Sxx(i,j,k)) - fxx(i,j,k)
l_fxy = alpn1(i,j,k) * (Rxy(i,j,k) - EIGHT * PI * Sxy(i,j,k)) - fxy(i,j,k)
l_fxz = alpn1(i,j,k) * (Rxz(i,j,k) - EIGHT * PI * Sxz(i,j,k)) - fxz(i,j,k)
l_fyy = alpn1(i,j,k) * (Ryy(i,j,k) - EIGHT * PI * Syy(i,j,k)) - fyy(i,j,k)
l_fyz = alpn1(i,j,k) * (Ryz(i,j,k) - EIGHT * PI * Syz(i,j,k)) - fyz(i,j,k)
l_fzz = alpn1(i,j,k) * (Rzz(i,j,k) - EIGHT * PI * Szz(i,j,k)) - fzz(i,j,k)
Axx_rhs(i,j,k) = l_fxx - gxx(i,j,k) * f_loc
Ayy_rhs(i,j,k) = l_fyy - gyy(i,j,k) * f_loc
Azz_rhs(i,j,k) = l_fzz - gzz(i,j,k) * f_loc
Axy_rhs(i,j,k) = l_fxy - gxy(i,j,k) * f_loc
Axz_rhs(i,j,k) = l_fxz - gxz(i,j,k) * f_loc
Ayz_rhs(i,j,k) = l_fyz - gyz(i,j,k) * f_loc
fxx(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axx(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + TWO * (gupxy(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + &
gupxz(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyz(i,j,k) * Axy(i,j,k) * Axz(i,j,k))
fyy(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayy(i,j,k) + &
gupzz(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + TWO * (gupxy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
gupxz(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + gupyz(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k))
fzz(i,j,k) = gupxx(i,j,k) * Axz(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayz(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Azz(i,j,k) * Azz(i,j,k) + TWO * (gupxy(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + &
gupxz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupyz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k))
fxy(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axy(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayy(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Ayz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayy(i,j,k) + Axy(i,j,k) * Axy(i,j,k)) + &
gupxz(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Axy(i,j,k)) + &
gupyz(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Axz(i,j,k) * Ayy(i,j,k))
fxz(i,j,k) = gupxx(i,j,k) * Axx(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Axy(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Axz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axx(i,j,k) * Ayz(i,j,k) + Axy(i,j,k) * Axz(i,j,k)) + &
gupxz(i,j,k) * (Axx(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Axz(i,j,k)) + &
gupyz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Axz(i,j,k) * Ayz(i,j,k))
fyz(i,j,k) = gupxx(i,j,k) * Axy(i,j,k) * Axz(i,j,k) + gupyy(i,j,k) * Ayy(i,j,k) * Ayz(i,j,k) + &
gupzz(i,j,k) * Ayz(i,j,k) * Azz(i,j,k) + gupxy(i,j,k) * (Axy(i,j,k) * Ayz(i,j,k) + Ayy(i,j,k) * Axz(i,j,k)) + &
gupxz(i,j,k) * (Axy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Axz(i,j,k)) + &
gupyz(i,j,k) * (Ayy(i,j,k) * Azz(i,j,k) + Ayz(i,j,k) * Ayz(i,j,k))
trK_rhs(i,j,k) = chin_loc * trK_rhs(i,j,k)
Axx_rhs(i,j,k) = chin_loc * Axx_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axx(i,j,k) - TWO * fxx(i,j,k)) + &
TWO * (Axx(i,j,k) * betaxx(i,j,k) + Axy(i,j,k) * betayx(i,j,k) + Axz(i,j,k) * betazx(i,j,k)) - &
F2o3 * Axx(i,j,k) * divb_loc
Ayy_rhs(i,j,k) = chin_loc * Ayy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayy(i,j,k) - TWO * fyy(i,j,k)) + &
TWO * (Axy(i,j,k) * betaxy(i,j,k) + Ayy(i,j,k) * betayy(i,j,k) + Ayz(i,j,k) * betazy(i,j,k)) - &
F2o3 * Ayy(i,j,k) * divb_loc
Azz_rhs(i,j,k) = chin_loc * Azz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Azz(i,j,k) - TWO * fzz(i,j,k)) + &
TWO * (Axz(i,j,k) * betaxz(i,j,k) + Ayz(i,j,k) * betayz(i,j,k) + Azz(i,j,k) * betazz(i,j,k)) - &
F2o3 * Azz(i,j,k) * divb_loc
Axy_rhs(i,j,k) = chin_loc * Axy_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axy(i,j,k) - TWO * fxy(i,j,k)) + &
Axx(i,j,k) * betaxy(i,j,k) + Axz(i,j,k) * betazy(i,j,k) + Ayy(i,j,k) * betayx(i,j,k) + &
Ayz(i,j,k) * betazx(i,j,k) + F1o3 * Axy(i,j,k) * divb_loc - Axy(i,j,k) * betazz(i,j,k)
Ayz_rhs(i,j,k) = chin_loc * Ayz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Ayz(i,j,k) - TWO * fyz(i,j,k)) + &
Axy(i,j,k) * betaxz(i,j,k) + Ayy(i,j,k) * betayz(i,j,k) + Axz(i,j,k) * betaxy(i,j,k) + &
Azz(i,j,k) * betazy(i,j,k) + F1o3 * Ayz(i,j,k) * divb_loc - Ayz(i,j,k) * betaxx(i,j,k)
Axz_rhs(i,j,k) = chin_loc * Axz_rhs(i,j,k) + alpn1(i,j,k) * (trK(i,j,k) * Axz(i,j,k) - TWO * fxz(i,j,k)) + &
Axx(i,j,k) * betaxz(i,j,k) + Axy(i,j,k) * betayz(i,j,k) + Ayz(i,j,k) * betayx(i,j,k) + &
Azz(i,j,k) * betazx(i,j,k) + F1o3 * Axz(i,j,k) * divb_loc - Axz(i,j,k) * betayy(i,j,k)
trK_rhs(i,j,k) = - trK_rhs(i,j,k) + alpn1(i,j,k) * ( F1o3 * trK(i,j,k) * trK(i,j,k) + &
gupxx(i,j,k) * fxx(i,j,k) + gupyy(i,j,k) * fyy(i,j,k) + gupzz(i,j,k) * fzz(i,j,k) + &
TWO * (gupxy(i,j,k) * fxy(i,j,k) + gupxz(i,j,k) * fxz(i,j,k) + gupyz(i,j,k) * fyz(i,j,k)) + &
FOUR * PI * (rho(i,j,k) + S_loc) )
enddo
enddo
enddo
!!!! gauge variable part
@@ -948,15 +1000,15 @@
!!!!!!!!!advection term + Kreiss-Oliger dissipation (merged for cache efficiency)
! lopsided_kodis shares the symmetry_bd buffer between advection and
! dissipation, eliminating redundant full-grid copies. For metric variables
! gxx/gyy/gzz (=dxx/dyy/dzz+1): kodis stencil coefficients sum to zero,
! so the constant offset has no effect on dissipation.
call lopsided_kodis(ex,X,Y,Z,gxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
call lopsided_kodis(ex,X,Y,Z,gyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
call lopsided_kodis(ex,X,Y,Z,gzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
! gxx/gyy/gzz (=dxx/dyy/dzz+1): stencil coefficients sum to zero,
! so the constant offset has no effect on dissipation.
call lopsided_kodis(ex,X,Y,Z,dxx,gxx_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gxy,gxy_rhs,betax,betay,betaz,Symmetry,AAS,eps)
call lopsided_kodis(ex,X,Y,Z,gxz,gxz_rhs,betax,betay,betaz,Symmetry,ASA,eps)
call lopsided_kodis(ex,X,Y,Z,dyy,gyy_rhs,betax,betay,betaz,Symmetry,SSS,eps)
call lopsided_kodis(ex,X,Y,Z,gyz,gyz_rhs,betax,betay,betaz,Symmetry,SAA,eps)
call lopsided_kodis(ex,X,Y,Z,dzz,gzz_rhs,betax,betay,betaz,Symmetry,SSS,eps)
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)

102
AMSS_NCKU_source/bssn_rhs_c.C
View File

@@ -1139,59 +1139,59 @@ 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,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);
}
// 7ms //
for (int i=0;i<all;i+=1) {
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
// 7ms //
for (int i=0;i<all;i+=1) {
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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];
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]*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]
+ gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[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]
+ gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[i]
+ gupxy[i]*gxzy[i] + gupxz[i]*gxzz[i] + gupyz[i]*gyzz[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]*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]
+ gupxy[i]*gyyx[i] + gupxz[i]*gyzx[i] + gupyz[i]*gyzy[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]
+ gupxy[i]*gyzx[i] + gupxz[i]*gzzx[i] + gupyz[i]*gzzy[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];
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];
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];
movz_Res[i] = movz_Res[i] - F2o3*Kz[i] - F8*PI*Sz[i];
}
}

4
AMSS_NCKU_source/makefile
View File

@@ -64,8 +64,8 @@ lopsided_c.o: lopsided_c.C
lopsided_kodis_c.o: lopsided_kodis_c.C
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
#interp_lb_profile.o: interp_lb_profile.C interp_lb_profile.h
# ${CXX} $(CXXAPPFLAGS) -c $< $(filein) -o $@
## TwoPunctureABE uses fixed optimal flags with its own PGO profile, independent of CXXAPPFLAGS
TP_PROFDATA = /home/$(shell whoami)/AMSS-NCKU/pgo_profile/TwoPunctureABE.profdata