#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