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