#include "macrodef.fh"
function compute_rhs_bssn_ss(ex, T,crho,sigma,R,x,y,z, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz, &
chi , trK , &
dxx , gxy , gxz , dyy , gyz , dzz, &
Axx , Axy , Axz , Ayy , Ayz , Azz, &
Gamx , Gamy , Gamz , &
Lap , betax , betay , betaz , &
dtSfx , dtSfy , dtSfz , &
chi_rhs, trK_rhs, &
gxx_rhs, gxy_rhs, gxz_rhs, gyy_rhs, gyz_rhs, gzz_rhs, &
Axx_rhs, Axy_rhs, Axz_rhs, Ayy_rhs, Ayz_rhs, Azz_rhs, &
Gamx_rhs, Gamy_rhs, Gamz_rhs, &
Lap_rhs, betax_rhs, betay_rhs, betaz_rhs, &
dtSfx_rhs, dtSfy_rhs, dtSfz_rhs, &
rho,Sx,Sy,Sz,Sxx,Sxy,Sxz,Syy,Syz,Szz, &
Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz, &
Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz, &
Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz, &
Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
ham_Res, movx_Res, movy_Res, movz_Res, &
Gmx_Res, Gmy_Res, Gmz_Res, &
Symmetry,Lev,eps,sst,co) result(gont)
! calculate constraint violation when co=0
implicit none
!~~~~~~> Input parameters:
integer,intent(in ):: ex(1:3), Symmetry,Lev,sst,co
real*8, intent(in ):: T
double precision,intent(in),dimension(ex(1))::crho
double precision,intent(in),dimension(ex(2))::sigma
double precision,intent(in),dimension(ex(3))::R
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::x,y,z
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::drhodx, drhody, drhodz
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dsigmadx,dsigmady,dsigmadz
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dRdx,dRdy,dRdz
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz
double precision,intent(in),dimension(ex(1),ex(2),ex(3))::dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: chi,dxx,dyy,dzz
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: trK
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: gxy,gxz,gyz
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Axx,Axy,Axz,Ayy,Ayz,Azz
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Gamx,Gamy,Gamz
real*8, dimension(ex(1),ex(2),ex(3)),intent(inout) :: Lap, betax, betay, betaz
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: dtSfx, dtSfy, dtSfz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: chi_rhs,trK_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: gxx_rhs,gxy_rhs,gxz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: gyy_rhs,gyz_rhs,gzz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Axx_rhs,Axy_rhs,Axz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Ayy_rhs,Ayz_rhs,Azz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamx_rhs,Gamy_rhs,Gamz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Lap_rhs, betax_rhs, betay_rhs, betaz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: dtSfx_rhs,dtSfy_rhs,dtSfz_rhs
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: rho,Sx,Sy,Sz
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ) :: Sxx,Sxy,Sxz,Syy,Syz,Szz
! when out, physical second kind of connection
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxxx, Gamxxy, Gamxxz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamxyy, Gamxyz, Gamxzz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyxx, Gamyxy, Gamyxz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamyyy, Gamyyz, Gamyzz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzxx, Gamzxy, Gamzxz
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gamzyy, Gamzyz, Gamzzz
! when out, physical Ricci tensor
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(out) :: ham_Res, movx_Res, movy_Res, movz_Res
real*8, dimension(ex(1),ex(2),ex(3)),intent(out) :: Gmx_Res, Gmy_Res, Gmz_Res
! gont = 0: success; gont = 1: something wrong
integer::gont
!~~~~~~> Other variables:
real*8, dimension(ex(1),ex(2),ex(3)) :: gxx,gyy,gzz
real*8, dimension(ex(1),ex(2),ex(3)) :: chix,chiy,chiz
real*8, dimension(ex(1),ex(2),ex(3)) :: gxxx,gxyx,gxzx,gyyx,gyzx,gzzx
real*8, dimension(ex(1),ex(2),ex(3)) :: gxxy,gxyy,gxzy,gyyy,gyzy,gzzy
real*8, dimension(ex(1),ex(2),ex(3)) :: gxxz,gxyz,gxzz,gyyz,gyzz,gzzz
real*8, dimension(ex(1),ex(2),ex(3)) :: Lapx,Lapy,Lapz
real*8, dimension(ex(1),ex(2),ex(3)) :: betaxx,betaxy,betaxz
real*8, dimension(ex(1),ex(2),ex(3)) :: betayx,betayy,betayz
real*8, dimension(ex(1),ex(2),ex(3)) :: betazx,betazy,betazz
real*8, dimension(ex(1),ex(2),ex(3)) :: Gamxx,Gamxy,Gamxz
real*8, dimension(ex(1),ex(2),ex(3)) :: Gamyx,Gamyy,Gamyz
real*8, dimension(ex(1),ex(2),ex(3)) :: Gamzx,Gamzy,Gamzz
real*8, dimension(ex(1),ex(2),ex(3)) :: Kx,Ky,Kz,div_beta,S
real*8, dimension(ex(1),ex(2),ex(3)) :: f,fxx,fxy,fxz,fyy,fyz,fzz
real*8, dimension(ex(1),ex(2),ex(3)) :: Gamxa,Gamya,Gamza,alpn1,chin1
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
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
#if (GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5)
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
real*8, dimension(ex(1),ex(2),ex(3)) :: reta
call getpbh(BHN,Porg,Mass)
#endif
!!! sanity check
dX = sum(chi)+sum(trK)+sum(dxx)+sum(gxy)+sum(gxz)+sum(dyy)+sum(gyz)+sum(dzz) &
+sum(Axx)+sum(Axy)+sum(Axz)+sum(Ayy)+sum(Ayz)+sum(Azz) &
+sum(Gamx)+sum(Gamy)+sum(Gamz) &
+sum(Lap)+sum(betax)+sum(betay)+sum(betaz)
if(dX.ne.dX) then
if(sum(chi).ne.sum(chi))write(*,*)"bssn.f90: find NaN in chi"
if(sum(trK).ne.sum(trK))write(*,*)"bssn.f90: find NaN in trk"
if(sum(dxx).ne.sum(dxx))write(*,*)"bssn.f90: find NaN in dxx"
if(sum(gxy).ne.sum(gxy))write(*,*)"bssn.f90: find NaN in gxy"
if(sum(gxz).ne.sum(gxz))write(*,*)"bssn.f90: find NaN in gxz"
if(sum(dyy).ne.sum(dyy))write(*,*)"bssn.f90: find NaN in dyy"
if(sum(gyz).ne.sum(gyz))write(*,*)"bssn.f90: find NaN in gyz"
if(sum(dzz).ne.sum(dzz))write(*,*)"bssn.f90: find NaN in dzz"
if(sum(Axx).ne.sum(Axx))write(*,*)"bssn.f90: find NaN in Axx"
if(sum(Axy).ne.sum(Axy))write(*,*)"bssn.f90: find NaN in Axy"
if(sum(Axz).ne.sum(Axz))write(*,*)"bssn.f90: find NaN in Axz"
if(sum(Ayy).ne.sum(Ayy))write(*,*)"bssn.f90: find NaN in Ayy"
if(sum(Ayz).ne.sum(Ayz))write(*,*)"bssn.f90: find NaN in Ayz"
if(sum(Azz).ne.sum(Azz))write(*,*)"bssn.f90: find NaN in Azz"
if(sum(Gamx).ne.sum(Gamx))write(*,*)"bssn.f90: find NaN in Gamx"
if(sum(Gamy).ne.sum(Gamy))write(*,*)"bssn.f90: find NaN in Gamy"
if(sum(Gamz).ne.sum(Gamz))write(*,*)"bssn.f90: find NaN in Gamz"
if(sum(Lap).ne.sum(Lap))write(*,*)"bssn.f90: find NaN in Lap"
if(sum(betax).ne.sum(betax))write(*,*)"bssn.f90: find NaN in betax"
if(sum(betay).ne.sum(betay))write(*,*)"bssn.f90: find NaN in betay"
if(sum(betaz).ne.sum(betaz))write(*,*)"bssn.f90: find NaN in betaz"
gont = 1
return
endif
PI = dacos(-ONE)
dX = crho(2) - crho(1)
dY = sigma(2) - sigma(1)
dZ = R(2) - R(1)
alpn1 = Lap + ONE
chin1 = chi + ONE
gxx = dxx + ONE
gyy = dyy + ONE
gzz = dzz + ONE
call fderivs_shc(ex,betax,betaxx,betaxy,betaxz,crho,sigma,R,ANTI, SYM, SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,betay,betayx,betayy,betayz,crho,sigma,R, SYM,ANTI, SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,betaz,betazx,betazy,betazz,crho,sigma,R, SYM, SYM,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
div_beta = betaxx + betayy + betazz
call fderivs_shc(ex,chi,chix,chiy,chiz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
chi_rhs = F2o3 *chin1*( alpn1 * trK - div_beta ) !rhs for chi
call fderivs_shc(ex,dxx,gxxx,gxxy,gxxz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,gxy,gxyx,gxyy,gxyz,crho,sigma,R,ANTI,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,gxz,gxzx,gxzy,gxzz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,dyy,gyyx,gyyy,gyyz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,gyz,gyzx,gyzy,gyzz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,dzz,gzzx,gzzy,gzzz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
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
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
! 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_shc(ex,Lap,Lapx,Lapy,Lapz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,trK,Kx,Ky,Kz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Gamx_rhs = - TWO * ( Lapx * Rxx + Lapy * Rxy + Lapz * Rxz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxx + chiy * Rxy + chiz * Rxz ) - &
gupxx * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupxy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupxz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamxxx * Rxx + Gamxyy * Ryy + Gamxzz * Rzz + &
TWO * ( Gamxxy * Rxy + Gamxxz * Rxz + Gamxyz * Ryz ) )
Gamy_rhs = - TWO * ( Lapx * Rxy + Lapy * Ryy + Lapz * Ryz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxy + chiy * Ryy + chiz * Ryz ) - &
gupxy * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyy * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupyz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamyxx * Rxx + Gamyyy * Ryy + Gamyzz * Rzz + &
TWO * ( Gamyxy * Rxy + Gamyxz * Rxz + Gamyyz * Ryz ) )
Gamz_rhs = - TWO * ( Lapx * Rxz + Lapy * Ryz + Lapz * Rzz ) + &
TWO * alpn1 * ( &
-F3o2/chin1 * ( chix * Rxz + chiy * Ryz + chiz * Rzz ) - &
gupxz * ( F2o3 * Kx + EIGHT * PI * Sx ) - &
gupyz * ( F2o3 * Ky + EIGHT * PI * Sy ) - &
gupzz * ( F2o3 * Kz + EIGHT * PI * Sz ) + &
Gamzxx * Rxx + Gamzyy * Ryy + Gamzzz * Rzz + &
TWO * ( Gamzxy * Rxy + Gamzxz * Rxz + Gamzyz * Ryz ) )
call fdderivs_shc(ex,betax,gxxx,gxyx,gxzx,gyyx,gyzx,gzzx,crho,sigma,R,ANTI, SYM, SYM,Symmetry,Lev,sst,&
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
call fdderivs_shc(ex,betay,gxxy,gxyy,gxzy,gyyy,gyzy,gzzy,crho,sigma,R, SYM,ANTI, SYM,Symmetry,Lev,sst,&
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
call fdderivs_shc(ex,betaz,gxxz,gxyz,gxzz,gyyz,gyzz,gzzz,crho,sigma,R, SYM, SYM,ANTI,Symmetry,Lev,sst,&
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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_shc(ex,Gamx,Gamxx,Gamxy,Gamxz,crho,sigma,R,ANTI,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Gamy,Gamyx,Gamyy,Gamyz,crho,sigma,R,SYM ,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Gamz,Gamzx,Gamzy,Gamzz,crho,sigma,R,SYM ,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Gamx_rhs = Gamx_rhs + F2o3 * Gamxa * div_beta - &
Gamxa * betaxx - Gamya * betaxy - Gamza * betaxz + &
F1o3 * (gupxx * fxx + gupxy * fxy + gupxz * fxz ) + &
gupxx * gxxx + gupyy * gyyx + gupzz * gzzx + &
TWO * (gupxy * gxyx + gupxz * gxzx + gupyz * gyzx )
Gamy_rhs = Gamy_rhs + F2o3 * Gamya * div_beta - &
Gamxa * betayx - Gamya * betayy - Gamza * betayz + &
F1o3 * (gupxy * fxx + gupyy * fxy + gupyz * fxz ) + &
gupxx * gxxy + gupyy * gyyy + gupzz * gzzy + &
TWO * (gupxy * gxyy + gupxz * gxzy + gupyz * gyzy )
Gamz_rhs = Gamz_rhs + F2o3 * Gamza * div_beta - &
Gamxa * betazx - Gamya * betazy - Gamza * betazz + &
F1o3 * (gupxz * fxx + gupyz * fxy + gupzz * fxz ) + &
gupxx * gxxz + gupyy * gyyz + gupzz * gzzz + &
TWO * (gupxy * gxyz + gupxz * gxzz + gupyz * gyzz ) !rhs for Gam^i
!first kind of connection stored in gij,k
gxxx = gxx * Gamxxx + gxy * Gamyxx + gxz * Gamzxx
gxyx = gxx * Gamxxy + gxy * Gamyxy + gxz * Gamzxy
gxzx = gxx * Gamxxz + gxy * Gamyxz + gxz * Gamzxz
gyyx = gxx * Gamxyy + gxy * Gamyyy + gxz * Gamzyy
gyzx = gxx * Gamxyz + gxy * Gamyyz + gxz * Gamzyz
gzzx = gxx * Gamxzz + gxy * Gamyzz + gxz * Gamzzz
gxxy = gxy * Gamxxx + gyy * Gamyxx + gyz * Gamzxx
gxyy = gxy * Gamxxy + gyy * Gamyxy + gyz * Gamzxy
gxzy = gxy * Gamxxz + gyy * Gamyxz + gyz * Gamzxz
gyyy = gxy * Gamxyy + gyy * Gamyyy + gyz * Gamzyy
gyzy = gxy * Gamxyz + gyy * Gamyyz + gyz * Gamzyz
gzzy = gxy * Gamxzz + gyy * Gamyzz + gyz * Gamzzz
gxxz = gxz * Gamxxx + gyz * Gamyxx + gzz * Gamzxx
gxyz = gxz * Gamxxy + gyz * Gamyxy + gzz * Gamzxy
gxzz = gxz * Gamxxz + gyz * Gamyxz + gzz * Gamzxz
gyyz = gxz * Gamxyy + gyz * Gamyyy + gzz * Gamzyy
gyzz = gxz * Gamxyz + gyz * Gamyyz + gzz * Gamzyz
gzzz = gxz * Gamxzz + gyz * Gamyzz + gzz * Gamzzz
!compute Ricci tensor for tilted metric
call fdderivs_shc(ex,dxx,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Rxx = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
call fdderivs_shc(ex,dyy,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Ryy = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
call fdderivs_shc(ex,dzz,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R, SYM, SYM,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Rzz = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
call fdderivs_shc(ex,gxy,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,ANTI,ANTI,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Rxy = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
call fdderivs_shc(ex,gxz,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Rxz = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
call fdderivs_shc(ex,gyz,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
Ryz = gupxx * fxx + gupyy * fyy + gupzz * fzz + &
( gupxy * fxy + gupxz * fxz + gupyz * fyz ) * TWO
Rxx = - HALF * Rxx + &
gxx * Gamxx+ gxy * Gamyx + gxz * Gamzx + &
Gamxa * gxxx + Gamya * gxyx + Gamza * gxzx + &
gupxx *( &
TWO*(Gamxxx * gxxx + Gamyxx * gxyx + Gamzxx * gxzx) + &
Gamxxx * gxxx + Gamyxx * gxxy + Gamzxx * gxxz )+ &
gupxy *( &
TWO*(Gamxxx * gxyx + Gamyxx * gyyx + Gamzxx * gyzx + &
Gamxxy * gxxx + Gamyxy * gxyx + Gamzxy * gxzx) + &
Gamxxy * gxxx + Gamyxy * gxxy + Gamzxy * gxxz + &
Gamxxx * gxyx + Gamyxx * gxyy + Gamzxx * gxyz )+ &
gupxz *( &
TWO*(Gamxxx * gxzx + Gamyxx * gyzx + Gamzxx * gzzx + &
Gamxxz * gxxx + Gamyxz * gxyx + Gamzxz * gxzx) + &
Gamxxz * gxxx + Gamyxz * gxxy + Gamzxz * gxxz + &
Gamxxx * gxzx + Gamyxx * gxzy + Gamzxx * gxzz )+ &
gupyy *( &
TWO*(Gamxxy * gxyx + Gamyxy * gyyx + Gamzxy * gyzx) + &
Gamxxy * gxyx + Gamyxy * gxyy + Gamzxy * gxyz )+ &
gupyz *( &
TWO*(Gamxxy * gxzx + Gamyxy * gyzx + Gamzxy * gzzx + &
Gamxxz * gxyx + Gamyxz * gyyx + Gamzxz * gyzx) + &
Gamxxz * gxyx + Gamyxz * gxyy + Gamzxz * gxyz + &
Gamxxy * gxzx + Gamyxy * gxzy + Gamzxy * gxzz )+ &
gupzz *( &
TWO*(Gamxxz * gxzx + Gamyxz * gyzx + Gamzxz * gzzx) + &
Gamxxz * gxzx + Gamyxz * gxzy + Gamzxz * gxzz )
Ryy = - HALF * Ryy + &
gxy * Gamxy+ gyy * Gamyy + gyz * Gamzy + &
Gamxa * gxyy + Gamya * gyyy + Gamza * gyzy + &
gupxx *( &
TWO*(Gamxxy * gxxy + Gamyxy * gxyy + Gamzxy * gxzy) + &
Gamxxy * gxyx + Gamyxy * gxyy + Gamzxy * gxyz )+ &
gupxy *( &
TWO*(Gamxxy * gxyy + Gamyxy * gyyy + Gamzxy * gyzy + &
Gamxyy * gxxy + Gamyyy * gxyy + Gamzyy * gxzy) + &
Gamxyy * gxyx + Gamyyy * gxyy + Gamzyy * gxyz + &
Gamxxy * gyyx + Gamyxy * gyyy + Gamzxy * gyyz )+ &
gupxz *( &
TWO*(Gamxxy * gxzy + Gamyxy * gyzy + Gamzxy * gzzy + &
Gamxyz * gxxy + Gamyyz * gxyy + Gamzyz * gxzy) + &
Gamxyz * gxyx + Gamyyz * gxyy + Gamzyz * gxyz + &
Gamxxy * gyzx + Gamyxy * gyzy + Gamzxy * gyzz )+ &
gupyy *( &
TWO*(Gamxyy * gxyy + Gamyyy * gyyy + Gamzyy * gyzy) + &
Gamxyy * gyyx + Gamyyy * gyyy + Gamzyy * gyyz )+ &
gupyz *( &
TWO*(Gamxyy * gxzy + Gamyyy * gyzy + Gamzyy * gzzy + &
Gamxyz * gxyy + Gamyyz * gyyy + Gamzyz * gyzy) + &
Gamxyz * gyyx + Gamyyz * gyyy + Gamzyz * gyyz + &
Gamxyy * gyzx + Gamyyy * gyzy + Gamzyy * gyzz )+ &
gupzz *( &
TWO*(Gamxyz * gxzy + Gamyyz * gyzy + Gamzyz * gzzy) + &
Gamxyz * gyzx + Gamyyz * gyzy + Gamzyz * gyzz )
Rzz = - HALF * Rzz + &
gxz * Gamxz+ gyz * Gamyz + gzz * Gamzz + &
Gamxa * gxzz + Gamya * gyzz + Gamza * gzzz + &
gupxx *( &
TWO*(Gamxxz * gxxz + Gamyxz * gxyz + Gamzxz * gxzz) + &
Gamxxz * gxzx + Gamyxz * gxzy + Gamzxz * gxzz )+ &
gupxy *( &
TWO*(Gamxxz * gxyz + Gamyxz * gyyz + Gamzxz * gyzz + &
Gamxyz * gxxz + Gamyyz * gxyz + Gamzyz * gxzz) + &
Gamxyz * gxzx + Gamyyz * gxzy + Gamzyz * gxzz + &
Gamxxz * gyzx + Gamyxz * gyzy + Gamzxz * gyzz )+ &
gupxz *( &
TWO*(Gamxxz * gxzz + Gamyxz * gyzz + Gamzxz * gzzz + &
Gamxzz * gxxz + Gamyzz * gxyz + Gamzzz * gxzz) + &
Gamxzz * gxzx + Gamyzz * gxzy + Gamzzz * gxzz + &
Gamxxz * gzzx + Gamyxz * gzzy + Gamzxz * gzzz )+ &
gupyy *( &
TWO*(Gamxyz * gxyz + Gamyyz * gyyz + Gamzyz * gyzz) + &
Gamxyz * gyzx + Gamyyz * gyzy + Gamzyz * gyzz )+ &
gupyz *( &
TWO*(Gamxyz * gxzz + Gamyyz * gyzz + Gamzyz * gzzz + &
Gamxzz * gxyz + Gamyzz * gyyz + Gamzzz * gyzz) + &
Gamxzz * gyzx + Gamyzz * gyzy + Gamzzz * gyzz + &
Gamxyz * gzzx + Gamyyz * gzzy + Gamzyz * gzzz )+ &
gupzz *( &
TWO*(Gamxzz * gxzz + Gamyzz * gyzz + Gamzzz * gzzz) + &
Gamxzz * gzzx + Gamyzz * gzzy + Gamzzz * gzzz )
Rxy = HALF*( - Rxy + &
gxx * Gamxy + gxy * Gamyy + gxz * Gamzy + &
gxy * Gamxx + gyy * Gamyx + gyz * Gamzx + &
Gamxa * gxyx + Gamya * gyyx + Gamza * gyzx + &
Gamxa * gxxy + Gamya * gxyy + Gamza * gxzy )+ &
gupxx *( &
Gamxxx * gxxy + Gamyxx * gxyy + Gamzxx * gxzy + &
Gamxxy * gxxx + Gamyxy * gxyx + Gamzxy * gxzx + &
Gamxxx * gxyx + Gamyxx * gxyy + Gamzxx * gxyz )+ &
gupxy *( &
Gamxxx * gxyy + Gamyxx * gyyy + Gamzxx * gyzy + &
Gamxxy * gxyx + Gamyxy * gyyx + Gamzxy * gyzx + &
Gamxxy * gxyx + Gamyxy * gxyy + Gamzxy * gxyz + &
Gamxxy * gxxy + Gamyxy * gxyy + Gamzxy * gxzy + &
Gamxyy * gxxx + Gamyyy * gxyx + Gamzyy * gxzx + &
Gamxxx * gyyx + Gamyxx * gyyy + Gamzxx * gyyz )+ &
gupxz *( &
Gamxxx * gxzy + Gamyxx * gyzy + Gamzxx * gzzy + &
Gamxxy * gxzx + Gamyxy * gyzx + Gamzxy * gzzx + &
Gamxxz * gxyx + Gamyxz * gxyy + Gamzxz * gxyz + &
Gamxxz * gxxy + Gamyxz * gxyy + Gamzxz * gxzy + &
Gamxyz * gxxx + Gamyyz * gxyx + Gamzyz * gxzx + &
Gamxxx * gyzx + Gamyxx * gyzy + Gamzxx * gyzz )+ &
gupyy *( &
Gamxxy * gxyy + Gamyxy * gyyy + Gamzxy * gyzy + &
Gamxyy * gxyx + Gamyyy * gyyx + Gamzyy * gyzx + &
Gamxxy * gyyx + Gamyxy * gyyy + Gamzxy * gyyz )+ &
gupyz *( &
Gamxxy * gxzy + Gamyxy * gyzy + Gamzxy * gzzy + &
Gamxyy * gxzx + Gamyyy * gyzx + Gamzyy * gzzx + &
Gamxxz * gyyx + Gamyxz * gyyy + Gamzxz * gyyz + &
Gamxxz * gxyy + Gamyxz * gyyy + Gamzxz * gyzy + &
Gamxyz * gxyx + Gamyyz * gyyx + Gamzyz * gyzx + &
Gamxxy * gyzx + Gamyxy * gyzy + Gamzxy * gyzz )+ &
gupzz *( &
Gamxxz * gxzy + Gamyxz * gyzy + Gamzxz * gzzy + &
Gamxyz * gxzx + Gamyyz * gyzx + Gamzyz * gzzx + &
Gamxxz * gyzx + Gamyxz * gyzy + Gamzxz * gyzz )
Rxz = HALF*( - Rxz + &
gxx * Gamxz + gxy * Gamyz + gxz * Gamzz + &
gxz * Gamxx + gyz * Gamyx + gzz * Gamzx + &
Gamxa * gxzx + Gamya * gyzx + Gamza * gzzx + &
Gamxa * gxxz + Gamya * gxyz + Gamza * gxzz )+ &
gupxx *( &
Gamxxx * gxxz + Gamyxx * gxyz + Gamzxx * gxzz + &
Gamxxz * gxxx + Gamyxz * gxyx + Gamzxz * gxzx + &
Gamxxx * gxzx + Gamyxx * gxzy + Gamzxx * gxzz )+ &
gupxy *( &
Gamxxx * gxyz + Gamyxx * gyyz + Gamzxx * gyzz + &
Gamxxz * gxyx + Gamyxz * gyyx + Gamzxz * gyzx + &
Gamxxy * gxzx + Gamyxy * gxzy + Gamzxy * gxzz + &
Gamxxy * gxxz + Gamyxy * gxyz + Gamzxy * gxzz + &
Gamxyz * gxxx + Gamyyz * gxyx + Gamzyz * gxzx + &
Gamxxx * gyzx + Gamyxx * gyzy + Gamzxx * gyzz )+ &
gupxz *( &
Gamxxx * gxzz + Gamyxx * gyzz + Gamzxx * gzzz + &
Gamxxz * gxzx + Gamyxz * gyzx + Gamzxz * gzzx + &
Gamxxz * gxzx + Gamyxz * gxzy + Gamzxz * gxzz + &
Gamxxz * gxxz + Gamyxz * gxyz + Gamzxz * gxzz + &
Gamxzz * gxxx + Gamyzz * gxyx + Gamzzz * gxzx + &
Gamxxx * gzzx + Gamyxx * gzzy + Gamzxx * gzzz )+ &
gupyy *( &
Gamxxy * gxyz + Gamyxy * gyyz + Gamzxy * gyzz + &
Gamxyz * gxyx + Gamyyz * gyyx + Gamzyz * gyzx + &
Gamxxy * gyzx + Gamyxy * gyzy + Gamzxy * gyzz )+ &
gupyz *( &
Gamxxy * gxzz + Gamyxy * gyzz + Gamzxy * gzzz + &
Gamxyz * gxzx + Gamyyz * gyzx + Gamzyz * gzzx + &
Gamxxz * gyzx + Gamyxz * gyzy + Gamzxz * gyzz + &
Gamxxz * gxyz + Gamyxz * gyyz + Gamzxz * gyzz + &
Gamxzz * gxyx + Gamyzz * gyyx + Gamzzz * gyzx + &
Gamxxy * gzzx + Gamyxy * gzzy + Gamzxy * gzzz )+ &
gupzz *( &
Gamxxz * gxzz + Gamyxz * gyzz + Gamzxz * gzzz + &
Gamxzz * gxzx + Gamyzz * gyzx + Gamzzz * gzzx + &
Gamxxz * gzzx + Gamyxz * gzzy + Gamzxz * gzzz )
Ryz = HALF*( - Ryz + &
gxy * Gamxz + gyy * Gamyz + gyz * Gamzz + &
gxz * Gamxy + gyz * Gamyy + gzz * Gamzy + &
Gamxa * gxzy + Gamya * gyzy + Gamza * gzzy + &
Gamxa * gxyz + Gamya * gyyz + Gamza * gyzz )+ &
gupxx *( &
Gamxxy * gxxz + Gamyxy * gxyz + Gamzxy * gxzz + &
Gamxxz * gxxy + Gamyxz * gxyy + Gamzxz * gxzy + &
Gamxxy * gxzx + Gamyxy * gxzy + Gamzxy * gxzz )+ &
gupxy *( &
Gamxxy * gxyz + Gamyxy * gyyz + Gamzxy * gyzz + &
Gamxxz * gxyy + Gamyxz * gyyy + Gamzxz * gyzy + &
Gamxyy * gxzx + Gamyyy * gxzy + Gamzyy * gxzz + &
Gamxyy * gxxz + Gamyyy * gxyz + Gamzyy * gxzz + &
Gamxyz * gxxy + Gamyyz * gxyy + Gamzyz * gxzy + &
Gamxxy * gyzx + Gamyxy * gyzy + Gamzxy * gyzz )+ &
gupxz *( &
Gamxxy * gxzz + Gamyxy * gyzz + Gamzxy * gzzz + &
Gamxxz * gxzy + Gamyxz * gyzy + Gamzxz * gzzy + &
Gamxyz * gxzx + Gamyyz * gxzy + Gamzyz * gxzz + &
Gamxyz * gxxz + Gamyyz * gxyz + Gamzyz * gxzz + &
Gamxzz * gxxy + Gamyzz * gxyy + Gamzzz * gxzy + &
Gamxxy * gzzx + Gamyxy * gzzy + Gamzxy * gzzz )+ &
gupyy *( &
Gamxyy * gxyz + Gamyyy * gyyz + Gamzyy * gyzz + &
Gamxyz * gxyy + Gamyyz * gyyy + Gamzyz * gyzy + &
Gamxyy * gyzx + Gamyyy * gyzy + Gamzyy * gyzz )+ &
gupyz *( &
Gamxyy * gxzz + Gamyyy * gyzz + Gamzyy * gzzz + &
Gamxyz * gxzy + Gamyyz * gyzy + Gamzyz * gzzy + &
Gamxyz * gyzx + Gamyyz * gyzy + Gamzyz * gyzz + &
Gamxyz * gxyz + Gamyyz * gyyz + Gamzyz * gyzz + &
Gamxzz * gxyy + Gamyzz * gyyy + Gamzzz * gyzy + &
Gamxyy * gzzx + Gamyyy * gzzy + Gamzyy * gzzz )+ &
gupzz *( &
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_shc(ex,chi,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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_shc(ex,Lap,fxx,fxy,fxz,fyy,fyz,fzz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz)
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 )
! 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 ) )
Axx_rhs = fxx - gxx * f
Ayy_rhs = fyy - gyy * f
Azz_rhs = fzz - gzz * f
Axy_rhs = fxy - gxy * f
Axz_rhs = fxz - gxz * f
Ayz_rhs = fyz - gyz * f
! Now: store A_il A^l_j into fij:
fxx = gupxx * Axx * Axx + gupyy * Axy * Axy + gupzz * Axz * Axz + &
TWO * (gupxy * Axx * Axy + gupxz * Axx * Axz + gupyz * Axy * Axz)
fyy = gupxx * Axy * Axy + gupyy * Ayy * Ayy + gupzz * Ayz * Ayz + &
TWO * (gupxy * Axy * Ayy + gupxz * Axy * Ayz + gupyz * Ayy * Ayz)
fzz = gupxx * Axz * Axz + gupyy * Ayz * Ayz + gupzz * Azz * Azz + &
TWO * (gupxy * Axz * Ayz + gupxz * Axz * Azz + gupyz * Ayz * Azz)
fxy = gupxx * Axx * Axy + gupyy * Axy * Ayy + gupzz * Axz * Ayz + &
gupxy *(Axx * Ayy + Axy * Axy) + &
gupxz *(Axx * Ayz + Axz * Axy) + &
gupyz *(Axy * Ayz + Axz * Ayy)
fxz = gupxx * Axx * Axz + gupyy * Axy * Ayz + gupzz * Axz * Azz + &
gupxy *(Axx * Ayz + Axy * Axz) + &
gupxz *(Axx * Azz + Axz * Axz) + &
gupyz *(Axy * Azz + Axz * Ayz)
fyz = gupxx * Axy * Axz + gupyy * Ayy * Ayz + gupzz * Ayz * Azz + &
gupxy *(Axy * Ayz + Ayy * Axz) + &
gupxz *(Axy * Azz + Ayz * Axz) + &
gupyz *(Ayy * Azz + Ayz * Ayz)
f = chin1
! store D^i D_i Lap in trK_rhs
trK_rhs = f*trK_rhs
Axx_rhs = f * Axx_rhs+ alpn1 * (trK * Axx - TWO * fxx) + &
TWO * ( Axx * betaxx + Axy * betayx + Axz * betazx )- &
F2o3 * Axx * div_beta
Ayy_rhs = f * Ayy_rhs+ alpn1 * (trK * Ayy - TWO * fyy) + &
TWO * ( Axy * betaxy + Ayy * betayy + Ayz * betazy )- &
F2o3 * Ayy * div_beta
Azz_rhs = f * Azz_rhs+ alpn1 * (trK * Azz - TWO * fzz) + &
TWO * ( Axz * betaxz + Ayz * betayz + Azz * betazz )- &
F2o3 * Azz * div_beta
Axy_rhs = f * Axy_rhs+ alpn1 *( trK * Axy - TWO * fxy )+ &
Axx * betaxy + Axz * betazy + &
Ayy * betayx + Ayz * betazx + &
F1o3 * Axy * div_beta - Axy * betazz
Ayz_rhs = f * Ayz_rhs+ alpn1 *( trK * Ayz - TWO * fyz )+ &
Axy * betaxz + Ayy * betayz + &
Axz * betaxy + Azz * betazy + &
F1o3 * Ayz * div_beta - Ayz * betaxx
Axz_rhs = f * Axz_rhs+ alpn1 *( trK * Axz - TWO * fxz )+ &
Axx * betaxz + Axy * betayz + &
Ayz * betayx + Azz * betazx + &
F1o3 * Axz * div_beta - Axz * betayy !rhs for Aij
! Compute trace of S_ij
S = f * ( gupxx * Sxx + gupyy * Syy + gupzz * Szz + &
TWO * ( gupxy * Sxy + gupxz * Sxz + gupyz * Syz ) )
trK_rhs = - trK_rhs + alpn1 *( F1o3 * trK * trK + &
gupxx * fxx + gupyy * fyy + gupzz * fzz + &
TWO * ( gupxy * fxy + gupxz * fxz + gupyz * fyz ) + &
FOUR * PI * ( rho + S )) !rhs for trK
!!!! gauge variable part
Lap_rhs = -TWO*alpn1*trK
#if (GAUGE == 0)
betax_rhs = FF*dtSfx
betay_rhs = FF*dtSfy
betaz_rhs = FF*dtSfz
dtSfx_rhs = Gamx_rhs - eta*dtSfx
dtSfy_rhs = Gamy_rhs - eta*dtSfy
dtSfz_rhs = Gamz_rhs - eta*dtSfz
#elif (GAUGE == 1)
betax_rhs = Gamx - eta*betax
betay_rhs = Gamy - eta*betay
betaz_rhs = Gamz - eta*betaz
dtSfx_rhs = ZEO
dtSfy_rhs = ZEO
dtSfz_rhs = ZEO
#elif (GAUGE == 2)
betax_rhs = FF*dtSfx
betay_rhs = FF*dtSfy
betaz_rhs = FF*dtSfz
call fderivs_shc(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
reta = 1.31d0/2*dsqrt(reta/chin1)/(1-dsqrt(chin1))**2
dtSfx_rhs = Gamx_rhs - reta*dtSfx
dtSfy_rhs = Gamy_rhs - reta*dtSfy
dtSfz_rhs = Gamz_rhs - reta*dtSfz
#elif (GAUGE == 3)
betax_rhs = FF*dtSfx
betay_rhs = FF*dtSfy
betaz_rhs = FF*dtSfz
call fderivs_shc(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
reta = 1.31d0/2*dsqrt(reta/chin1)/(1-chin1)**2
dtSfx_rhs = Gamx_rhs - reta*dtSfx
dtSfy_rhs = Gamy_rhs - reta*dtSfy
dtSfz_rhs = Gamz_rhs - reta*dtSfz
#elif (GAUGE == 4)
call fderivs_shc(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
reta = 1.31d0/2*dsqrt(reta/chin1)/(1-dsqrt(chin1))**2
betax_rhs = FF*Gamx - reta*betax
betay_rhs = FF*Gamy - reta*betay
betaz_rhs = FF*Gamz - reta*betaz
dtSfx_rhs = ZEO
dtSfy_rhs = ZEO
dtSfz_rhs = ZEO
#elif (GAUGE == 5)
call fderivs_shc(ex,chi,dtSfx_rhs,dtSfy_rhs,dtSfz_rhs,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
reta = gupxx * dtSfx_rhs * dtSfx_rhs + gupyy * dtSfy_rhs * dtSfy_rhs + gupzz * dtSfz_rhs * dtSfz_rhs + &
TWO * (gupxy * dtSfx_rhs * dtSfy_rhs + gupxz * dtSfx_rhs * dtSfz_rhs + gupyz * dtSfy_rhs * dtSfz_rhs)
reta = 1.31d0/2*dsqrt(reta/chin1)/(1-chin1)**2
betax_rhs = FF*Gamx - reta*betax
betay_rhs = FF*Gamy - reta*betay
betaz_rhs = FF*Gamz - reta*betaz
dtSfx_rhs = ZEO
dtSfy_rhs = ZEO
dtSfz_rhs = ZEO
#elif (GAUGE == 6)
if(BHN==2)then
M = Mass(1)+Mass(2)
A = 2.d0/M
w1 = 1.2d1
w2 = w1
C1 = 1.d0/Mass(1) - A
C2 = 1.d0/Mass(2) - A
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
r1 = ((Porg(1)-X(i,j,k))**2+(Porg(2)-Y(i,j,k))**2+(Porg(3)-Z(i,j,k))**2)/ &
((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
r2 = ((Porg(4)-X(i,j,k))**2+(Porg(5)-Y(i,j,k))**2+(Porg(6)-Z(i,j,k))**2)/ &
((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
reta(i,j,k) = A + C1/(ONE+w1*r1) + C2/(ONE+w2*r2)
enddo
enddo
enddo
else
write(*,*) "not support BH_num in Jason's form 1",BHN
endif
betax_rhs = FF*dtSfx
betay_rhs = FF*dtSfy
betaz_rhs = FF*dtSfz
dtSfx_rhs = Gamx_rhs - reta*dtSfx
dtSfy_rhs = Gamy_rhs - reta*dtSfy
dtSfz_rhs = Gamz_rhs - reta*dtSfz
#elif (GAUGE == 7)
if(BHN==2)then
M = Mass(1)+Mass(2)
A = 2.d0/M
w1 = 1.2d1
w2 = w1
C1 = 1.d0/Mass(1) - A
C2 = 1.d0/Mass(2) - A
do k=1,ex(3)
do j=1,ex(2)
do i=1,ex(1)
r1 = ((Porg(1)-X(i,j,k))**2+(Porg(2)-Y(i,j,k))**2+(Porg(3)-Z(i,j,k))**2)/ &
((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
r2 = ((Porg(4)-X(i,j,k))**2+(Porg(5)-Y(i,j,k))**2+(Porg(6)-Z(i,j,k))**2)/ &
((Porg(1)-Porg(4))**2+(Porg(2)-Porg(5))**2+(Porg(3)-Porg(6))**2)
reta(i,j,k) = A + C1*dexp(-w1*r1) + C2*dexp(-w2*r2)
enddo
enddo
enddo
else
write(*,*) "not support BH_num in Jason's form 2",BHN
endif
betax_rhs = FF*dtSfx
betay_rhs = FF*dtSfy
betaz_rhs = FF*dtSfz
dtSfx_rhs = Gamx_rhs - reta*dtSfx
dtSfy_rhs = Gamy_rhs - reta*dtSfy
dtSfz_rhs = Gamz_rhs - reta*dtSfz
#endif
SSS(1)=SYM
SSS(2)=SYM
SSS(3)=SYM
AAS(1)=ANTI
AAS(2)=ANTI
AAS(3)=SYM
ASA(1)=ANTI
ASA(2)=SYM
ASA(3)=ANTI
SAA(1)=SYM
SAA(2)=ANTI
SAA(3)=ANTI
ASS(1)=ANTI
ASS(2)=SYM
ASS(3)=SYM
SAS(1)=SYM
SAS(2)=ANTI
SAS(3)=SYM
SSA(1)=SYM
SSA(2)=SYM
SSA(3)=ANTI
!!!!!!!!!advection term part
!g_ij
call fderivs_shc(ex,dxx,fxx,fxy,fxz,crho,sigma,R,SYM,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gxx_rhs = gxx_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,gxy,fxx,fxy,fxz,crho,sigma,R,ANTI,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gxy_rhs = gxy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,gxz,fxx,fxy,fxz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gxz_rhs = gxz_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,dyy,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gyy_rhs = gyy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,gyz,fxx,fxy,fxz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gyz_rhs = gyz_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,dzz,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gzz_rhs = gzz_rhs + betax*fxx+betay*fxy+betaz*fxz
!A_ij
call fderivs_shc(ex,Axx,fxx,fxy,fxz,crho,sigma,R,SYM,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Axx_rhs = Axx_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Axy,fxx,fxy,fxz,crho,sigma,R,ANTI,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Axy_rhs = Axy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Axz,fxx,fxy,fxz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Axz_rhs = Axz_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Ayy,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Ayy_rhs = Ayy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Ayz,fxx,fxy,fxz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Ayz_rhs = Ayz_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Azz,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM ,SYM ,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Azz_rhs = Azz_rhs + betax*fxx+betay*fxy+betaz*fxz
!chi and trK
call fderivs_shc(ex,chi,fxx,fxy,fxz,crho,sigma,R,SYM,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
chi_rhs = chi_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,trK,fxx,fxy,fxz,crho,sigma,R,SYM,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
trK_rhs = trK_rhs + betax*fxx+betay*fxy+betaz*fxz
!Gam^i
call fderivs_shc(ex,Gamx,fxx,fxy,fxz,crho,sigma,R,ANTI,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Gamx_rhs = Gamx_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Gamy,fxx,fxy,fxz,crho,sigma,R,SYM ,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Gamy_rhs = Gamy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,Gamz,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Gamz_rhs = Gamz_rhs + betax*fxx+betay*fxy+betaz*fxz
!gauge variables
call fderivs_shc(ex,Lap,fxx,fxy,fxz,crho,sigma,R,SYM,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
Lap_rhs = Lap_rhs + betax*fxx+betay*fxy+betaz*fxz
#if (GAUGE == 0 || GAUGE == 1 || GAUGE == 2 || GAUGE == 3 || GAUGE == 4 || GAUGE == 5 || GAUGE == 6 || GAUGE == 7)
call fderivs_shc(ex,betax,fxx,fxy,fxz,crho,sigma,R,ANTI,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
betax_rhs = betax_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,betay,fxx,fxy,fxz,crho,sigma,R,SYM ,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
betay_rhs = betay_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,betaz,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
betaz_rhs = betaz_rhs + betax*fxx+betay*fxy+betaz*fxz
#endif
#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
call fderivs_shc(ex,dtSfx,fxx,fxy,fxz,crho,sigma,R,ANTI,SYM ,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
dtSfx_rhs = dtSfx_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,dtSfy,fxx,fxy,fxz,crho,sigma,R,SYM ,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
dtSfy_rhs = dtSfy_rhs + betax*fxx+betay*fxy+betaz*fxz
call fderivs_shc(ex,dtSfz,fxx,fxy,fxz,crho,sigma,R,SYM ,SYM,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
dtSfz_rhs = dtSfz_rhs + betax*fxx+betay*fxy+betaz*fxz
#endif
if(eps>0)then
! usual Kreiss-Oliger dissipation
call kodis_sh(ex,crho,sigma,R,chi,chi_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,trK,trK_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,dxx,gxx_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,gxy,gxy_rhs,AAS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,gxz,gxz_rhs,ASA,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,dyy,gyy_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,gyz,gyz_rhs,SAA,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,dzz,gzz_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Axx,Axx_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Axy,Axy_rhs,AAS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Axz,Axz_rhs,ASA,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Ayy,Ayy_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Ayz,Ayz_rhs,SAA,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Azz,Azz_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Gamx,Gamx_rhs,ASS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Gamy,Gamy_rhs,SAS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Gamz,Gamz_rhs,SSA,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,Lap,Lap_rhs,SSS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,betax,betax_rhs,ASS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,betay,betay_rhs,SAS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,betaz,betaz_rhs,SSA,Symmetry,eps,sst)
#if (GAUGE == 0 || GAUGE == 2 || GAUGE == 3 || GAUGE == 6 || GAUGE == 7)
call kodis_sh(ex,crho,sigma,R,dtSfx,dtSfx_rhs,ASS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,dtSfy,dtSfy_rhs,SAS,Symmetry,eps,sst)
call kodis_sh(ex,crho,sigma,R,dtSfz,dtSfz_rhs,SSA,Symmetry,eps,sst)
#endif
endif
if(co == 0)then
! ham_Res = trR + 2/3 * K^2 - A_ij * A^ij - 16 * PI * rho
! here trR is respect to physical metric
ham_Res = gupxx * Rxx + gupyy * Ryy + gupzz * Rzz + &
TWO* ( gupxy * Rxy + gupxz * Rxz + gupyz * Ryz )
ham_Res = chin1*ham_Res + 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) ) ))- F16 * PI * rho
! mov_Res_j = gupkj*(-1/chi d_k chi*A_ij + D_k A_ij) - 2/3 d_j trK - 8 PI s_j where D respect to physical metric
! store D_i A_jk - 1/chi d_i chi*A_jk in gjk_i
call fderivs_shc(ex,Axx,gxxx,gxxy,gxxz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Axy,gxyx,gxyy,gxyz,crho,sigma,R,ANTI,ANTI,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Axz,gxzx,gxzy,gxzz,crho,sigma,R,ANTI,SYM ,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Ayy,gyyx,gyyy,gyyz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Ayz,gyzx,gyzy,gyzz,crho,sigma,R,SYM ,ANTI,ANTI,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
call fderivs_shc(ex,Azz,gzzx,gzzy,gzzz,crho,sigma,R, SYM, SYM,SYM,Symmetry,Lev,sst, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz)
gxxx = gxxx - ( Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz &
+ Gamxxx * Axx + Gamyxx * Axy + Gamzxx * Axz) - chix*Axx/chin1
gxyx = gxyx - ( Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz &
+ Gamxxx * Axy + Gamyxx * Ayy + Gamzxx * Ayz) - chix*Axy/chin1
gxzx = gxzx - ( Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz &
+ Gamxxx * Axz + Gamyxx * Ayz + Gamzxx * Azz) - chix*Axz/chin1
gyyx = gyyx - ( Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz &
+ Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chix*Ayy/chin1
gyzx = gyzx - ( Gamxxz * Axy + Gamyxz * Ayy + Gamzxz * Ayz &
+ Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chix*Ayz/chin1
gzzx = gzzx - ( Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz &
+ Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chix*Azz/chin1
gxxy = gxxy - ( Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz &
+ Gamxxy * Axx + Gamyxy * Axy + Gamzxy * Axz) - chiy*Axx/chin1
gxyy = gxyy - ( Gamxyy * Axx + Gamyyy * Axy + Gamzyy * Axz &
+ Gamxxy * Axy + Gamyxy * Ayy + Gamzxy * Ayz) - chiy*Axy/chin1
gxzy = gxzy - ( Gamxyz * Axx + Gamyyz * Axy + Gamzyz * Axz &
+ Gamxxy * Axz + Gamyxy * Ayz + Gamzxy * Azz) - chiy*Axz/chin1
gyyy = gyyy - ( Gamxyy * Axy + Gamyyy * Ayy + Gamzyy * Ayz &
+ Gamxyy * Axy + Gamyyy * Ayy + Gamzyy * Ayz) - chiy*Ayy/chin1
gyzy = gyzy - ( Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz &
+ Gamxyy * Axz + Gamyyy * Ayz + Gamzyy * Azz) - chiy*Ayz/chin1
gzzy = gzzy - ( Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz &
+ Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiy*Azz/chin1
gxxz = gxxz - ( Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz &
+ Gamxxz * Axx + Gamyxz * Axy + Gamzxz * Axz) - chiz*Axx/chin1
gxyz = gxyz - ( Gamxyz * Axx + Gamyyz * Axy + Gamzyz * Axz &
+ Gamxxz * Axy + Gamyxz * Ayy + Gamzxz * Ayz) - chiz*Axy/chin1
gxzz = gxzz - ( Gamxzz * Axx + Gamyzz * Axy + Gamzzz * Axz &
+ Gamxxz * Axz + Gamyxz * Ayz + Gamzxz * Azz) - chiz*Axz/chin1
gyyz = gyyz - ( Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz &
+ Gamxyz * Axy + Gamyyz * Ayy + Gamzyz * Ayz) - chiz*Ayy/chin1
gyzz = gyzz - ( Gamxzz * Axy + Gamyzz * Ayy + Gamzzz * Ayz &
+ Gamxyz * Axz + Gamyyz * Ayz + Gamzyz * Azz) - chiz*Ayz/chin1
gzzz = gzzz - ( Gamxzz * Axz + Gamyzz * Ayz + Gamzzz * Azz &
+ Gamxzz * Axz + Gamyzz * Ayz + Gamzzz * Azz) - chiz*Azz/chin1
movx_Res = gupxx*gxxx + gupyy*gxyy + gupzz*gxzz &
+gupxy*gxyx + gupxz*gxzx + gupyz*gxzy &
+gupxy*gxxy + gupxz*gxxz + gupyz*gxyz
movy_Res = gupxx*gxyx + gupyy*gyyy + gupzz*gyzz &
+gupxy*gyyx + gupxz*gyzx + gupyz*gyzy &
+gupxy*gxyy + gupxz*gxyz + gupyz*gyyz
movz_Res = gupxx*gxzx + gupyy*gyzy + gupzz*gzzz &
+gupxy*gyzx + gupxz*gzzx + gupyz*gzzy &
+gupxy*gxzy + gupxz*gxzz + gupyz*gyzz
movx_Res = movx_Res - F2o3*Kx - F8*PI*sx
movy_Res = movy_Res - F2o3*Ky - F8*PI*sy
movz_Res = movz_Res - F2o3*Kz - F8*PI*sz
endif
#if (ABV == 1)
call ricci_gamma_ss(ex,crho,sigma,R,X, Y, Z, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz, &
chi, &
dxx , gxy , gxz , dyy , gyz , dzz,&
Gamx , Gamy , Gamz , &
Gamxxx,Gamxxy,Gamxxz,Gamxyy,Gamxyz,Gamxzz,&
Gamyxx,Gamyxy,Gamyxz,Gamyyy,Gamyyz,Gamyzz,&
Gamzxx,Gamzxy,Gamzxz,Gamzyy,Gamzyz,Gamzzz,&
Rxx,Rxy,Rxz,Ryy,Ryz,Rzz,&
Symmetry,Lev,sst)
call constraint_bssn_ss(ex,crho,sigma,R,X, Y, Z, &
drhodx, drhody, drhodz, &
dsigmadx,dsigmady,dsigmadz, &
dRdx,dRdy,dRdz, &
drhodxx,drhodxy,drhodxz,drhodyy,drhodyz,drhodzz, &
dsigmadxx,dsigmadxy,dsigmadxz,dsigmadyy,dsigmadyz,dsigmadzz, &
dRdxx,dRdxy,dRdxz,dRdyy,dRdyz,dRdzz, &
chi,trK, &
dxx,gxy,gxz,dyy,gyz,dzz, &
Axx,Axy,Axz,Ayy,Ayz,Azz, &
Gamx,Gamy,Gamz,&
Lap,betax,betay,betaz,rho,Sx,Sy,Sz,&
Gamxxx, Gamxxy, Gamxxz,Gamxyy, Gamxyz, Gamxzz, &
Gamyxx, Gamyxy, Gamyxz,Gamyyy, Gamyyz, Gamyzz, &
Gamzxx, Gamzxy, Gamzxz,Gamzyy, Gamzyz, Gamzzz, &
Rxx,Rxy,Rxz,Ryy,Ryz,Rzz, &
ham_Res,movx_Res,movy_Res,movz_Res,Gmx_Res,Gmy_Res,Gmz_Res, &
Symmetry,Lev,sst)
#endif
gont = 0
return
end function compute_rhs_bssn_ss