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迁移C算子的循环融合和临时量消除

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CGH0S7
2026-03-03 15:57:10 +08:00
parent 7bb9042b18
commit f1fe9fd443
1 changed files with 186 additions and 186 deletions
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AMSS_NCKU_source/bssn_rhs.f90
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@@ -91,6 +91,8 @@
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
@@ -653,192 +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