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AMSS-NCKU/AMSS_NCKU_source/diff_new.f90.backup
CGH0S7 039dce4d65 Add aggressive compiler optimizations and vectorization directives 
Changes:
1. Enhanced compiler flags in makefile.inc:
   - Added -march=native -mtune=native for CPU-specific optimizations
   - Added -funroll-loops for loop unrolling
   - Added -qopt-prefetch for aggressive prefetching
   - Added -qopt-report=5 for optimization analysis

2. Added Intel vectorization directives to diff_new.f90:
   - Added !DIR$ SIMD and !DIR$ IVDEP to critical loops
   - Targets fderivs and related finite difference functions
   - Forces compiler to vectorize inner loops

Expected improvement: 15-30% speedup in computation loops
Mathematical equivalence: Preserved (compiler optimizations only)
Precision: IEEE 754 maintained
2026-01-19 10:17:31 +08:00

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#include "macrodef.fh"
! we need only distinguish different finite difference order
! Vertex or Cell is distinguished in routine symmetry_bd which locates in
! file "fmisc.f90"
#if (ghost_width == 2)
! second order code
!-----------------------------------------------------------------------------------------------------------------
!
! General first derivatives of 2_nd oder accurate
!
! f(i+1) - f(i-1)
! fx(i) = -----------------------
! 2 dx
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx,fy,fz
real*8, intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
real*8, intent(in ):: SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d2dx,d2dy,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
fx = ZEO
fy = ZEO
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
! z direction
if(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fderivs
!-----------------------------------------------------------------------------
!
! single derivatives dx
!
!-----------------------------------------------------------------------------
subroutine fdx(ex,f,fx,X,SYM1,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx
real*8, intent(in ):: X(ex(1)),SYM1
!~~~~~~ other variables
real*8 :: dX
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d2dx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
SoA(1) = SYM1
! no use
SoA(2) = SYM1
SoA(3) = SYM1
call symmetry_bd(1,ex,f,fh,SoA)
d2dx = ONE/TWO/dX
fx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
enddo
enddo
enddo
return
end subroutine fdx
!-----------------------------------------------------------------------------
!
! single derivatives dy
!
!-----------------------------------------------------------------------------
subroutine fdy(ex,f,fy,Y,SYM2,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fy
real*8, intent(in ):: Y(ex(2)),SYM2
!~~~~~~ other variables
real*8 :: dY
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d2dy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dY = Y(2)-Y(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM2
SoA(2) = SYM2
SoA(3) = SYM2
call symmetry_bd(1,ex,f,fh,SoA)
d2dy = ONE/TWO/dY
fy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! y direction
if(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
enddo
enddo
enddo
return
end subroutine fdy
!-----------------------------------------------------------------------------
!
! single derivatives dz
!
!-----------------------------------------------------------------------------
subroutine fdz(ex,f,fz,Z,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fz
real*8, intent(in ):: Z(ex(3)),SYM3
!~~~~~~ other variables
real*8 :: dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
SoA(1) = SYM3
SoA(2) = SYM3
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
d2dz = ONE/TWO/dZ
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! z direction
if(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fdz
!-----------------------------------------------------------------------------------------------------------------
!
! General second derivatives of 2_nd oder accurate
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
!
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fdderivs(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Sdydy,Sdzdz
real*8 :: Sdxdy,Sdxdz,Sdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Sdydy = ONE /( dY * dY )
Sdzdz = ONE /( dZ * dZ )
Sdxdy = F1o4 /( dX * dY )
Sdxdz = F1o4 /( dX * dZ )
Sdydz = F1o4 /( dY * dZ )
fxx = ZEO
fyy = ZEO
fzz = ZEO
fxy = ZEO
fxz = ZEO
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+1 <= imax .and. i-1 >= imin)then
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
!~~~~~~ fyy
if(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
!~~~~~~ fzz
if(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
!~~~~~~ fxy
if(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
!~~~~~~ fxz
if(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
!~~~~~~ fyz
if(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fdderivs
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! only for compute_ricci.f90 usage
!-----------------------------------------------------------------------------
subroutine fddxx(ex,f,fxx,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
fxx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+1 <= imax .and. i-1 >= imin)then
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
enddo
enddo
enddo
return
end subroutine fddxx
subroutine fddyy(ex,f,fyy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdydy = ONE /( dY * dY )
fyy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyy
if(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
enddo
enddo
enddo
return
end subroutine fddyy
subroutine fddzz(ex,f,fzz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdzdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdzdz = ONE /( dZ * dZ )
fzz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fzz
if(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
enddo
enddo
enddo
return
end subroutine fddzz
subroutine fddxy(ex,f,fxy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdxdy = F1o4 /( dX * dY )
fxy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxy
if(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
enddo
enddo
enddo
return
end subroutine fddxy
subroutine fddxz(ex,f,fxz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdxdz = F1o4 /( dX * dZ )
fxz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxz
if(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddxz
subroutine fddyz(ex,f,fyz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdydz = F1o4 /( dY * dZ )
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyz
if(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddyz
!-----------------------------------------------------------------------------------------------------------------
!
! General second derivatives of 2_nd oder accurate
!
! f(i-2) - 2 f(i) + f(i+2)
! fxx(i) = --------------------------------
! 4 dx^2
!
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fdderivsdavid(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(0:ex(1),0:ex(2),0:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Sdydy,Sdzdz
real*8 :: Sdxdy,Sdxdz,Sdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = 0
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = 0
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = 0
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(1,ex,f,fh,SoA)
Sdxdx = F1o4 /( dX * dX )
Sdydy = F1o4 /( dY * dY )
Sdzdz = F1o4 /( dZ * dZ )
Sdxdy = F1o4 /( dX * dY )
Sdxdz = F1o4 /( dX * dZ )
Sdydz = F1o4 /( dY * dZ )
fxx = ZEO
fyy = ZEO
fzz = ZEO
fxy = ZEO
fxz = ZEO
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 2 f(i) + f(i+2)
! fxx(i) = --------------------------------
! 4 dx^2
fxx(i,j,k) = Sdxdx*(fh(i-2,j,k)-TWO*fh(i,j,k) &
+fh(i+2,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
fxx(i,j,k) = (fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )/dX/dX
endif
!~~~~~~ fyy
if(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-2,k)-TWO*fh(i,j,k) &
+fh(i,j+2,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = (fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )/dY/dY
endif
!~~~~~~ fzz
if(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-2)-TWO*fh(i,j,k) &
+fh(i,j,k+2) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = (fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )/dZ/dZ
endif
!~~~~~~ fxy
if(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
!~~~~~~ fxz
if(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
!~~~~~~ fyz
if(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fdderivsdavid
#elif (ghost_width == 3)
! fourth order code
!-----------------------------------------------------------------------------------------------------------------
!
! General first derivatives of 4_th oder accurate
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx,fy,fz
real*8, intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
real*8, intent(in ):: SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
fx = ZEO
fy = ZEO
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
#if 0
! x direction
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
! z direction
if(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
#elif 0
! x direction
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+3 <= imax .and. i-1 >= imin)then
fx(i,j,k)=d12dx*(-3.d0*fh(i-1,j,k)-1.d1*fh(i,j,k)+1.8d1*fh(i+1,j,k)-6.d0*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+1 <= imax .and. i-3 >= imin)then
fx(i,j,k)=d12dx*( 3.d0*fh(i+1,j,k)+1.d1*fh(i,j,k)-1.8d1*fh(i-1,j,k)+6.d0*fh(i-2,j,k)-fh(i-3,j,k))
! set imax and imin 0
endif
! y direction
if(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+3 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d12dy*(-3.d0*fh(i,j-1,k)-1.d1*fh(i,j,k)+1.8d1*fh(i,j+1,k)-6.d0*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+1 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d12dy*( 3.d0*fh(i,j+1,k)+1.d1*fh(i,j,k)-1.8d1*fh(i,j-1,k)+6.d0*fh(i,j-2,k)-fh(i,j-3,k))
! set jmax and jmin 0
endif
! z direction
if(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+3 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d12dz*(-3.d0*fh(i,j,k-1)-1.d1*fh(i,j,k)+1.8d1*fh(i,j,k+1)-6.d0*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+1 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d12dz*( 3.d0*fh(i,j,k+1)+1.d1*fh(i,j,k)-1.8d1*fh(i,j,k-1)+6.d0*fh(i,j,k-2)-fh(i,j,k-3))
! set kmax and kmin 0
endif
#else
! for bam comparison
if(i+2 <= imax .and. i-2 >= imin .and. &
j+2 <= jmax .and. j-2 >= jmin .and. &
k+2 <= kmax .and. k-2 >= kmin) then
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
endif
#endif
enddo
enddo
enddo
return
end subroutine fderivs
!-----------------------------------------------------------------------------
!
! single derivatives dx
!
!-----------------------------------------------------------------------------
subroutine fdx(ex,f,fx,X,SYM1,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx
real*8, intent(in ):: X(ex(1)),SYM1
!~~~~~~ other variables
real*8 :: dX
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d12dx,d2dx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
SoA(1) = SYM1
! no use
SoA(2) = SYM1
SoA(3) = SYM1
call symmetry_bd(2,ex,f,fh,SoA)
d12dx = ONE/F12/dX
d2dx = ONE/TWO/dX
fx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
enddo
enddo
enddo
return
end subroutine fdx
!-----------------------------------------------------------------------------
!
! single derivatives dy
!
!-----------------------------------------------------------------------------
subroutine fdy(ex,f,fy,Y,SYM2,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fy
real*8, intent(in ):: Y(ex(2)),SYM2
!~~~~~~ other variables
real*8 :: dY
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d12dy,d2dy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dY = Y(2)-Y(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM2
SoA(2) = SYM2
SoA(3) = SYM2
call symmetry_bd(2,ex,f,fh,SoA)
d12dy = ONE/F12/dY
d2dy = ONE/TWO/dY
fy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! y direction
if(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
enddo
enddo
enddo
return
end subroutine fdy
!-----------------------------------------------------------------------------
!
! single derivatives dz
!
!-----------------------------------------------------------------------------
subroutine fdz(ex,f,fz,Z,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fz
real*8, intent(in ):: Z(ex(3)),SYM3
!~~~~~~ other variables
real*8 :: dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d12dz,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
SoA(1) = SYM3
SoA(2) = SYM3
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
d12dz = ONE/F12/dZ
d2dz = ONE/TWO/dZ
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! z direction
if(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fdz
!-----------------------------------------------------------------------------------------------------------------
!
! General second derivatives of 4_th oder accurate
!
! - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
! fxx(i) = ----------------------------------------------------------
! 12 dx^2
!
! - ( - f(i+2,j+2) + 8 f(i+1,j+2) - 8 f(i-1,j+2) + f(i-2,j+2) )
! + 8 ( - f(i+2,j+1) + 8 f(i+1,j+1) - 8 f(i-1,j+1) + f(i-2,j+1) )
! - 8 ( - f(i+2,j-1) + 8 f(i+1,j-1) - 8 f(i-1,j-1) + f(i-2,j-1) )
! + ( - f(i+2,j-2) + 8 f(i+1,j-2) - 8 f(i-1,j-2) + f(i-2,j-2) )
! fxy(i,j) = ----------------------------------------------------------------
! 144 dx dy
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fdderivs(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz
real*8 :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Sdydy = ONE /( dY * dY )
Sdzdz = ONE /( dZ * dZ )
Fdxdx = F1o12 /( dX * dX )
Fdydy = F1o12 /( dY * dY )
Fdzdz = F1o12 /( dZ * dZ )
Sdxdy = F1o4 /( dX * dY )
Sdxdz = F1o4 /( dX * dZ )
Sdydz = F1o4 /( dY * dZ )
Fdxdy = F1o144 /( dX * dY )
Fdxdz = F1o144 /( dX * dZ )
Fdydz = F1o144 /( dY * dZ )
fxx = ZEO
fyy = ZEO
fzz = ZEO
fxy = ZEO
fxz = ZEO
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
#if 0
!~~~~~~ fxx
if(i+2 <= imax .and. i-2 >= imin)then
!
! - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
! fxx(i) = ----------------------------------------------------------
! 12 dx^2
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
!~~~~~~ fyy
if(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
!~~~~~~ fzz
if(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
!~~~~~~ fxy
if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
!
! ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
! - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
! + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
! - ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
! fxy(i,j) = ----------------------------------------------------------------
! 144 dx dy
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
!~~~~~~ fxz
if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
!~~~~~~ fyz
if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
#else
! for bam comparison
if(i+2 <= imax .and. i-2 >= imin .and. &
j+2 <= jmax .and. j-2 >= jmin .and. &
k+2 <= kmax .and. k-2 >= kmin) then
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. &
j+1 <= jmax .and. j-1 >= jmin .and. &
k+1 <= kmax .and. k-1 >= kmin) then
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
#endif
enddo
enddo
enddo
return
end subroutine fdderivs
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! only for compute_ricci.f90 usage
!-----------------------------------------------------------------------------
subroutine fddxx(ex,f,fxx,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Fdxdx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Fdxdx = F1o12 /( dX * dX )
fxx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+2 <= imax .and. i-2 >= imin)then
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
enddo
enddo
enddo
return
end subroutine fddxx
subroutine fddyy(ex,f,fyy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydy,Fdydy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdydy = ONE /( dY * dY )
Fdydy = F1o12 /( dY * dY )
fyy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyy
if(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
enddo
enddo
enddo
return
end subroutine fddyy
subroutine fddzz(ex,f,fzz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdzdz,Fdzdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdzdz = ONE /( dZ * dZ )
Fdzdz = F1o12 /( dZ * dZ )
fzz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fzz
if(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
enddo
enddo
enddo
return
end subroutine fddzz
subroutine fddxy(ex,f,fxy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdy,Fdxdy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdxdy = F1o4 /( dX * dY )
Fdxdy = F1o144 /( dX * dY )
fxy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxy
if(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
enddo
enddo
enddo
return
end subroutine fddxy
subroutine fddxz(ex,f,fxz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdz,Fdxdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdxdz = F1o4 /( dX * dZ )
Fdxdz = F1o144 /( dX * dZ )
fxz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxz
if(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddxz
subroutine fddyz(ex,f,fyz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-1:ex(1),-1:ex(2),-1:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydz,Fdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -1
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(2,ex,f,fh,SoA)
Sdydz = F1o4 /( dY * dZ )
Fdydz = F1o144 /( dY * dZ )
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyz
if(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddyz
#elif (ghost_width == 4)
! sixth order code
!-----------------------------------------------------------------------------------------------------------------
!
! General first derivatives of 6_th oder accurate
!
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx,fy,fz
real*8, intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
real*8, intent(in ):: SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
d60dx = ONE/F60/dX
d60dy = ONE/F60/dY
d60dz = ONE/F60/dZ
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
fx = ZEO
fy = ZEO
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+3 <= imax .and. i-3 >= imin)then
!
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
fx(i,j,k)=d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(j+3 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
! z direction
if(k+3 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fderivs
!-----------------------------------------------------------------------------
!
! single derivatives dx
!
!-----------------------------------------------------------------------------
subroutine fdx(ex,f,fx,X,SYM1,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx
real*8, intent(in ):: X(ex(1)),SYM1
!~~~~~~ other variables
real*8 :: dX
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d60dx,d12dx,d2dx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dX = X(2)-X(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
SoA(1) = SYM1
! no use
SoA(2) = SYM1
SoA(3) = SYM1
call symmetry_bd(3,ex,f,fh,SoA)
d60dx = ONE/F60/dX
d12dx = ONE/F12/dX
d2dx = ONE/TWO/dX
fx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+3 <= imax .and. i-3 >= imin)then
!
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
fx(i,j,k)=d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
enddo
enddo
enddo
return
end subroutine fdx
!-----------------------------------------------------------------------------
!
! single derivatives dy
!
!-----------------------------------------------------------------------------
subroutine fdy(ex,f,fy,Y,SYM2,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fy
real*8, intent(in ):: Y(ex(2)),SYM2
!~~~~~~ other variables
real*8 :: dY
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d60dy,d12dy,d2dy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dY = Y(2)-Y(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM2
SoA(2) = SYM2
SoA(3) = SYM2
call symmetry_bd(3,ex,f,fh,SoA)
d60dy = ONE/F60/dY
d12dy = ONE/F12/dY
d2dy = ONE/TWO/dY
fy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! y direction
if(j+3 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
enddo
enddo
enddo
return
end subroutine fdy
!-----------------------------------------------------------------------------
!
! single derivatives dz
!
!-----------------------------------------------------------------------------
subroutine fdz(ex,f,fz,Z,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fz
real*8, intent(in ):: Z(ex(3)),SYM3
!~~~~~~ other variables
real*8 :: dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d60dz,d12dz,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1
real*8, parameter :: TWO=2.d0,EIT=8.d0
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
SoA(1) = SYM3
SoA(2) = SYM3
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
d60dz = ONE/F60/dZ
d12dz = ONE/F12/dZ
d2dz = ONE/TWO/dZ
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! z direction
if(k+3 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fdz
!-----------------------------------------------------------------------------------------------------------------
!
! General second derivatives of 6_th oder accurate
!
! 2 f(i-3) - 27 f(i-2) + 270 f(i-1) - 490 f(i) + 270 f(i+1) - 27 f(i+2) + 2 f(i+3)
! fxx(i) = -----------------------------------------------------------------------------------
! 180 dx^2
!
! - ( - f(i-3,j-3) + 9 f(i-2,j-3) - 45 f(i-1,j-3) + 45 f(i+1,j-3) - 9 f(i+2,j-3) + f(i+3,j-3) )
! + 9 ( - f(i-3,j-2) + 9 f(i-2,j-2) - 45 f(i-1,j-2) + 45 f(i+1,j-2) - 9 f(i+2,j-2) + f(i+3,j-2) )
! - 45 ( - f(i-3,j-1) + 9 f(i-2,j-1) - 45 f(i-1,j-1) + 45 f(i+1,j-1) - 9 f(i+2,j-1) + f(i+3,j-1) )
! + 45 ( - f(i-3,j+1) + 9 f(i-2,j+1) - 45 f(i-1,j+1) + 45 f(i+1,j+1) - 9 f(i+2,j+1) + f(i+3,j+1) )
! - 9 ( - f(i-3,j+2) + 9 f(i-2,j+2) - 45 f(i-1,j+2) + 45 f(i+1,j+2) - 9 f(i+2,j+2) + f(i+3,j+2) )
! + ( - f(i-3,j+3) + 9 f(i-2,j+3) - 45 f(i-1,j+3) + 45 f(i+1,j+3) - 9 f(i+2,j+3) + f(i+3,j+3) )
! fxy(i,j) = ------------------------------------------------------------------------------------------------
! 3600 dx dy
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fdderivs(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz,Xdxdx,Xdydy,Xdzdz
real*8 :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz,Xdxdy,Xdxdz,Xdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Sdydy = ONE /( dY * dY )
Sdzdz = ONE /( dZ * dZ )
Fdxdx = F1o12 /( dX * dX )
Fdydy = F1o12 /( dY * dY )
Fdzdz = F1o12 /( dZ * dZ )
Xdxdx = F1o180 /( dX * dX )
Xdydy = F1o180 /( dY * dY )
Xdzdz = F1o180 /( dZ * dZ )
Sdxdy = F1o4 /( dX * dY )
Sdxdz = F1o4 /( dX * dZ )
Sdydz = F1o4 /( dY * dZ )
Fdxdy = F1o144 /( dX * dY )
Fdxdz = F1o144 /( dX * dZ )
Fdydz = F1o144 /( dY * dZ )
Xdxdy = F1o3600 /( dX * dY )
Xdxdz = F1o3600 /( dX * dZ )
Xdydz = F1o3600 /( dY * dZ )
fxx = ZEO
fyy = ZEO
fzz = ZEO
fxy = ZEO
fxz = ZEO
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+3 <= imax .and. i-3 >= imin)then
!
! 2 f(i-3) - 27 f(i-2) + 270 f(i-1) - 490 f(i) + 270 f(i+1) - 27 f(i+2) + 2 f(i+3)
! fxx(i) = -----------------------------------------------------------------------------------
! 180 dx^2
fxx(i,j,k) = Xdxdx*(TWO*fh(i-3,j,k)-F27*fh(i-2,j,k)+F270*fh(i-1,j,k)-F490*fh(i,j,k) &
+TWO*fh(i+3,j,k)-F27*fh(i+2,j,k)+F270*fh(i+1,j,k) )
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
! fxx(i) = ----------------------------------------------------------
! 12 dx^2
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
!~~~~~~ fyy
if(j+3 <= jmax .and. j-3 >= jmin)then
fyy(i,j,k) = Xdydy*(TWO*fh(i,j-3,k)-F27*fh(i,j-2,k)+F270*fh(i,j-1,k)-F490*fh(i,j,k) &
+TWO*fh(i,j+3,k)-F27*fh(i,j+2,k)+F270*fh(i,j+1,k) )
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
!~~~~~~ fzz
if(k+3 <= kmax .and. k-3 >= kmin)then
fzz(i,j,k) = Xdzdz*(TWO*fh(i,j,k-3)-F27*fh(i,j,k-2)+F270*fh(i,j,k-1)-F490*fh(i,j,k) &
+TWO*fh(i,j,k+3)-F27*fh(i,j,k+2)+F270*fh(i,j,k+1) )
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
!~~~~~~ fxy
if(i+3 <= imax .and. i-3 >= imin .and. j+3 <= jmax .and. j-3 >= jmin)then
!
! - ( - f(i-3,j-3) + 9 f(i-2,j-3) - 45 f(i-1,j-3) + 45 f(i+1,j-3) - 9 f(i+2,j-3) + f(i+3,j-3) )
! + 9 ( - f(i-3,j-2) + 9 f(i-2,j-2) - 45 f(i-1,j-2) + 45 f(i+1,j-2) - 9 f(i+2,j-2) + f(i+3,j-2) )
! - 45 ( - f(i-3,j-1) + 9 f(i-2,j-1) - 45 f(i-1,j-1) + 45 f(i+1,j-1) - 9 f(i+2,j-1) + f(i+3,j-1) )
! + 45 ( - f(i-3,j+1) + 9 f(i-2,j+1) - 45 f(i-1,j+1) + 45 f(i+1,j+1) - 9 f(i+2,j+1) + f(i+3,j+1) )
! - 9 ( - f(i-3,j+2) + 9 f(i-2,j+2) - 45 f(i-1,j+2) + 45 f(i+1,j+2) - 9 f(i+2,j+2) + f(i+3,j+2) )
! + ( - f(i-3,j+3) + 9 f(i-2,j+3) - 45 f(i-1,j+3) + 45 f(i+1,j+3) - 9 f(i+2,j+3) + f(i+3,j+3) )
! fxy(i,j) = ------------------------------------------------------------------------------------------------
! 3600 dx dy
fxy(i,j,k) = Xdxdy*(- (-fh(i-3,j-3,k)+F9*fh(i-2,j-3,k)-F45*fh(i-1,j-3,k)+F45*fh(i+1,j-3,k)-F9*fh(i+2,j-3,k)+fh(i+3,j-3,k)) &
+F9 *(-fh(i-3,j-2,k)+F9*fh(i-2,j-2,k)-F45*fh(i-1,j-2,k)+F45*fh(i+1,j-2,k)-F9*fh(i+2,j-2,k)+fh(i+3,j-2,k)) &
-F45*(-fh(i-3,j-1,k)+F9*fh(i-2,j-1,k)-F45*fh(i-1,j-1,k)+F45*fh(i+1,j-1,k)-F9*fh(i+2,j-1,k)+fh(i+3,j-1,k)) &
+F45*(-fh(i-3,j+1,k)+F9*fh(i-2,j+1,k)-F45*fh(i-1,j+1,k)+F45*fh(i+1,j+1,k)-F9*fh(i+2,j+1,k)+fh(i+3,j+1,k)) &
-F9 *(-fh(i-3,j+2,k)+F9*fh(i-2,j+2,k)-F45*fh(i-1,j+2,k)+F45*fh(i+1,j+2,k)-F9*fh(i+2,j+2,k)+fh(i+3,j+2,k)) &
+ (-fh(i-3,j+3,k)+F9*fh(i-2,j+3,k)-F45*fh(i-1,j+3,k)+F45*fh(i+1,j+3,k)-F9*fh(i+2,j+3,k)+fh(i+3,j+3,k)))
elseif(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
!
! ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
! - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
! + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
! - ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
! fxy(i,j) = ----------------------------------------------------------------
! 144 dx dy
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
!~~~~~~ fxz
if(i+3 <= imax .and. i-3 >= imin .and. k+3 <= kmax .and. k-3 >= kmin)then
fxz(i,j,k) = Xdxdz*(- (-fh(i-3,j,k-3)+F9*fh(i-2,j,k-3)-F45*fh(i-1,j,k-3)+F45*fh(i+1,j,k-3)-F9*fh(i+2,j,k-3)+fh(i+3,j,k-3)) &
+F9 *(-fh(i-3,j,k-2)+F9*fh(i-2,j,k-2)-F45*fh(i-1,j,k-2)+F45*fh(i+1,j,k-2)-F9*fh(i+2,j,k-2)+fh(i+3,j,k-2)) &
-F45*(-fh(i-3,j,k-1)+F9*fh(i-2,j,k-1)-F45*fh(i-1,j,k-1)+F45*fh(i+1,j,k-1)-F9*fh(i+2,j,k-1)+fh(i+3,j,k-1)) &
+F45*(-fh(i-3,j,k+1)+F9*fh(i-2,j,k+1)-F45*fh(i-1,j,k+1)+F45*fh(i+1,j,k+1)-F9*fh(i+2,j,k+1)+fh(i+3,j,k+1)) &
-F9 *(-fh(i-3,j,k+2)+F9*fh(i-2,j,k+2)-F45*fh(i-1,j,k+2)+F45*fh(i+1,j,k+2)-F9*fh(i+2,j,k+2)+fh(i+3,j,k+2)) &
+ (-fh(i-3,j,k+3)+F9*fh(i-2,j,k+3)-F45*fh(i-1,j,k+3)+F45*fh(i+1,j,k+3)-F9*fh(i+2,j,k+3)+fh(i+3,j,k+3)))
elseif(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
!~~~~~~ fyz
if(j+3 <= jmax .and. j-3 >= jmin .and. k+3 <= kmax .and. k-3 >= kmin)then
fyz(i,j,k) = Xdydz*(- (-fh(i,j-3,k-3)+F9*fh(i,j-2,k-3)-F45*fh(i,j-1,k-3)+F45*fh(i,j+1,k-3)-F9*fh(i,j+2,k-3)+fh(i,j+3,k-3)) &
+F9 *(-fh(i,j-3,k-2)+F9*fh(i,j-2,k-2)-F45*fh(i,j-1,k-2)+F45*fh(i,j+1,k-2)-F9*fh(i,j+2,k-2)+fh(i,j+3,k-2)) &
-F45*(-fh(i,j-3,k-1)+F9*fh(i,j-2,k-1)-F45*fh(i,j-1,k-1)+F45*fh(i,j+1,k-1)-F9*fh(i,j+2,k-1)+fh(i,j+3,k-1)) &
+F45*(-fh(i,j-3,k+1)+F9*fh(i,j-2,k+1)-F45*fh(i,j-1,k+1)+F45*fh(i,j+1,k+1)-F9*fh(i,j+2,k+1)+fh(i,j+3,k+1)) &
-F9 *(-fh(i,j-3,k+2)+F9*fh(i,j-2,k+2)-F45*fh(i,j-1,k+2)+F45*fh(i,j+1,k+2)-F9*fh(i,j+2,k+2)+fh(i,j+3,k+2)) &
+ (-fh(i,j-3,k+3)+F9*fh(i,j-2,k+3)-F45*fh(i,j-1,k+3)+F45*fh(i,j+1,k+3)-F9*fh(i,j+2,k+3)+fh(i,j+3,k+3)))
elseif(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fdderivs
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! only for compute_ricci.f90 usage
!-----------------------------------------------------------------------------
subroutine fddxx(ex,f,fxx,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Fdxdx,Xdxdx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Fdxdx = F1o12 /( dX * dX )
Xdxdx = F1o180 /( dX * dX )
fxx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+3 <= imax .and. i-3 >= imin)then
fxx(i,j,k) = Xdxdx*(TWO*fh(i-3,j,k)-F27*fh(i-2,j,k)+F270*fh(i-1,j,k)-F490*fh(i,j,k) &
+TWO*fh(i+3,j,k)-F27*fh(i+2,j,k)+F270*fh(i+1,j,k) )
elseif(i+2 <= imax .and. i-2 >= imin)then
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
enddo
enddo
enddo
return
end subroutine fddxx
subroutine fddyy(ex,f,fyy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydy,Fdydy,Xdydy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdydy = ONE /( dY * dY )
Fdydy = F1o12 /( dY * dY )
Xdydy = F1o180 /( dY * dY )
fyy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyy
if(j+3 <= jmax .and. j-3 >= jmin)then
fyy(i,j,k) = Xdydy*(TWO*fh(i,j-3,k)-F27*fh(i,j-2,k)+F270*fh(i,j-1,k)-F490*fh(i,j,k) &
+TWO*fh(i,j+3,k)-F27*fh(i,j+2,k)+F270*fh(i,j+1,k) )
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
enddo
enddo
enddo
return
end subroutine fddyy
subroutine fddzz(ex,f,fzz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdzdz,Fdzdz,Xdzdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdzdz = ONE /( dZ * dZ )
Fdzdz = F1o12 /( dZ * dZ )
Xdzdz = F1o180 /( dZ * dZ )
fzz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fzz
if(k+3 <= kmax .and. k-3 >= kmin)then
fzz(i,j,k) = Xdzdz*(TWO*fh(i,j,k-3)-F27*fh(i,j,k-2)+F270*fh(i,j,k-1)-F490*fh(i,j,k) &
+TWO*fh(i,j,k+3)-F27*fh(i,j,k+2)+F270*fh(i,j,k+1) )
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
enddo
enddo
enddo
return
end subroutine fddzz
subroutine fddxy(ex,f,fxy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdy,Fdxdy,Xdxdy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdxdy = F1o4 /( dX * dY )
Fdxdy = F1o144 /( dX * dY )
Xdxdy = F1o3600 /( dX * dY )
fxy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxy
if(i+3 <= imax .and. i-3 >= imin .and. j+3 <= jmax .and. j-3 >= jmin)then
fxy(i,j,k) = Xdxdy*(- (-fh(i-3,j-3,k)+F9*fh(i-2,j-3,k)-F45*fh(i-1,j-3,k)+F45*fh(i+1,j-3,k)-F9*fh(i+2,j-3,k)+fh(i+3,j-3,k)) &
+F9 *(-fh(i-3,j-2,k)+F9*fh(i-2,j-2,k)-F45*fh(i-1,j-2,k)+F45*fh(i+1,j-2,k)-F9*fh(i+2,j-2,k)+fh(i+3,j-2,k)) &
-F45*(-fh(i-3,j-1,k)+F9*fh(i-2,j-1,k)-F45*fh(i-1,j-1,k)+F45*fh(i+1,j-1,k)-F9*fh(i+2,j-1,k)+fh(i+3,j-1,k)) &
+F45*(-fh(i-3,j+1,k)+F9*fh(i-2,j+1,k)-F45*fh(i-1,j+1,k)+F45*fh(i+1,j+1,k)-F9*fh(i+2,j+1,k)+fh(i+3,j+1,k)) &
-F9 *(-fh(i-3,j+2,k)+F9*fh(i-2,j+2,k)-F45*fh(i-1,j+2,k)+F45*fh(i+1,j+2,k)-F9*fh(i+2,j+2,k)+fh(i+3,j+2,k)) &
+ (-fh(i-3,j+3,k)+F9*fh(i-2,j+3,k)-F45*fh(i-1,j+3,k)+F45*fh(i+1,j+3,k)-F9*fh(i+2,j+3,k)+fh(i+3,j+3,k)))
elseif(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
enddo
enddo
enddo
return
end subroutine fddxy
subroutine fddxz(ex,f,fxz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdz,Fdxdz,Xdxdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdxdz = F1o4 /( dX * dZ )
Fdxdz = F1o144 /( dX * dZ )
Xdxdz = F1o3600 /( dX * dZ )
fxz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxz
if(i+3 <= imax .and. i-3 >= imin .and. k+3 <= kmax .and. k-3 >= kmin)then
fxz(i,j,k) = Xdxdz*(- (-fh(i-3,j,k-3)+F9*fh(i-2,j,k-3)-F45*fh(i-1,j,k-3)+F45*fh(i+1,j,k-3)-F9*fh(i+2,j,k-3)+fh(i+3,j,k-3)) &
+F9 *(-fh(i-3,j,k-2)+F9*fh(i-2,j,k-2)-F45*fh(i-1,j,k-2)+F45*fh(i+1,j,k-2)-F9*fh(i+2,j,k-2)+fh(i+3,j,k-2)) &
-F45*(-fh(i-3,j,k-1)+F9*fh(i-2,j,k-1)-F45*fh(i-1,j,k-1)+F45*fh(i+1,j,k-1)-F9*fh(i+2,j,k-1)+fh(i+3,j,k-1)) &
+F45*(-fh(i-3,j,k+1)+F9*fh(i-2,j,k+1)-F45*fh(i-1,j,k+1)+F45*fh(i+1,j,k+1)-F9*fh(i+2,j,k+1)+fh(i+3,j,k+1)) &
-F9 *(-fh(i-3,j,k+2)+F9*fh(i-2,j,k+2)-F45*fh(i-1,j,k+2)+F45*fh(i+1,j,k+2)-F9*fh(i+2,j,k+2)+fh(i+3,j,k+2)) &
+ (-fh(i-3,j,k+3)+F9*fh(i-2,j,k+3)-F45*fh(i-1,j,k+3)+F45*fh(i+1,j,k+3)-F9*fh(i+2,j,k+3)+fh(i+3,j,k+3)))
elseif(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddxz
subroutine fddyz(ex,f,fyz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-2:ex(1),-2:ex(2),-2:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydz,Fdydz,Xdydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -2
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -2
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -2
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(3,ex,f,fh,SoA)
Sdydz = F1o4 /( dY * dZ )
Fdydz = F1o144 /( dY * dZ )
Xdydz = F1o3600 /( dY * dZ )
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyz
if(j+3 <= jmax .and. j-3 >= jmin .and. k+3 <= kmax .and. k-3 >= kmin)then
fyz(i,j,k) = Xdydz*(- (-fh(i,j-3,k-3)+F9*fh(i,j-2,k-3)-F45*fh(i,j-1,k-3)+F45*fh(i,j+1,k-3)-F9*fh(i,j+2,k-3)+fh(i,j+3,k-3)) &
+F9 *(-fh(i,j-3,k-2)+F9*fh(i,j-2,k-2)-F45*fh(i,j-1,k-2)+F45*fh(i,j+1,k-2)-F9*fh(i,j+2,k-2)+fh(i,j+3,k-2)) &
-F45*(-fh(i,j-3,k-1)+F9*fh(i,j-2,k-1)-F45*fh(i,j-1,k-1)+F45*fh(i,j+1,k-1)-F9*fh(i,j+2,k-1)+fh(i,j+3,k-1)) &
+F45*(-fh(i,j-3,k+1)+F9*fh(i,j-2,k+1)-F45*fh(i,j-1,k+1)+F45*fh(i,j+1,k+1)-F9*fh(i,j+2,k+1)+fh(i,j+3,k+1)) &
-F9 *(-fh(i,j-3,k+2)+F9*fh(i,j-2,k+2)-F45*fh(i,j-1,k+2)+F45*fh(i,j+1,k+2)-F9*fh(i,j+2,k+2)+fh(i,j+3,k+2)) &
+ (-fh(i,j-3,k+3)+F9*fh(i,j-2,k+3)-F45*fh(i,j-1,k+3)+F45*fh(i,j+1,k+3)-F9*fh(i,j+2,k+3)+fh(i,j+3,k+3)))
elseif(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddyz
#elif (ghost_width == 5)
! eighth order code
! PRD 77, 024034 (2008)
!-----------------------------------------------------------------------------------------------------------------
!
! General first derivatives of 8_th oder accurate
!
! 3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
! fx(i) = -------------------------------------------------------------------------------------------------
! 840 dx
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fderivs(ex,f,fx,fy,fz,X,Y,Z,SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx,fy,fz
real*8, intent(in) :: X(ex(1)),Y(ex(2)),Z(ex(3))
real*8, intent(in ):: SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d840dx,d840dy,d840dz
real*8 :: d60dx,d60dy,d60dz,d12dx,d12dy,d12dz,d2dx,d2dy,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1, F32 = 3.2d1
real*8, parameter :: TWO=2.d0,THR=3.d0, EIT=8.d0, F168=1.68d2
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1,F672=6.72d2
real*8, parameter :: F840=8.4d2
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
d840dx = ONE/F840/dX
d840dy = ONE/F840/dY
d840dz = ONE/F840/dZ
d60dx = ONE/F60/dX
d60dy = ONE/F60/dY
d60dz = ONE/F60/dZ
d12dx = ONE/F12/dX
d12dy = ONE/F12/dY
d12dz = ONE/F12/dZ
d2dx = ONE/TWO/dX
d2dy = ONE/TWO/dY
d2dz = ONE/TWO/dZ
fx = ZEO
fy = ZEO
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+4 <= imax .and. i-4 >= imin)then
! 3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
! fx(i) = -------------------------------------------------------------------------------------------------
! 840 dx
fx(i,j,k)=d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+ &
F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
elseif(i+3 <= imax .and. i-3 >= imin)then
!
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
fx(i,j,k)=d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
! y direction
if(j+4 <= jmax .and. j-4 >= jmin)then
fy(i,j,k)=d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+ &
F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
elseif(j+3 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
! z direction
if(k+4 <= kmax .and. k-4 >= kmin)then
fz(i,j,k)=d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+ &
F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
elseif(k+3 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fderivs
!-----------------------------------------------------------------------------
!
! single derivatives dx
!
!-----------------------------------------------------------------------------
subroutine fdx(ex,f,fx,X,SYM1,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fx
real*8, intent(in ):: X(ex(1)),SYM1
!~~~~~~ other variables
real*8 :: dX
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d840dx,d60dx,d12dx,d2dx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1, F32 = 3.2d1
real*8, parameter :: TWO=2.d0,THR=3.d0, EIT=8.d0, F168=1.68d2
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1,F672=6.72d2
real*8, parameter :: F840=8.4d2
dX = X(2)-X(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
SoA(1) = SYM1
! no use
SoA(2) = SYM1
SoA(3) = SYM1
call symmetry_bd(4,ex,f,fh,SoA)
d840dx = ONE/F840/dX
d60dx = ONE/F60/dX
d12dx = ONE/F12/dX
d2dx = ONE/TWO/dX
fx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! x direction
if(i+4 <= imax .and. i-4 >= imin)then
! 3 f(i-4) - 32 f(i-3) + 168 f(i-2) - 672 f(i-1) + 672 f(i+1) - 168 f(i+2) + 32 f(i+3) - 3 f(i+4)
! fx(i) = -------------------------------------------------------------------------------------------------
! 840 dx
fx(i,j,k)=d840dx*( THR*fh(i-4,j,k)-F32 *fh(i-3,j,k)+F168*fh(i-2,j,k)-F672*fh(i-1,j,k)+ &
F672*fh(i+1,j,k)-F168*fh(i+2,j,k)+F32 *fh(i+3,j,k)-THR *fh(i+4,j,k))
elseif(i+3 <= imax .and. i-3 >= imin)then
!
! - f(i-3) + 9 f(i-2) - 45 f(i-1) + 45 f(i+1) - 9 f(i+2) + f(i+3)
! fx(i) = -----------------------------------------------------------------
! 60 dx
fx(i,j,k)=d60dx*(-fh(i-3,j,k)+F9*fh(i-2,j,k)-F45*fh(i-1,j,k)+F45*fh(i+1,j,k)-F9*fh(i+2,j,k)+fh(i+3,j,k))
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! f(i-2) - 8 f(i-1) + 8 f(i+1) - f(i+2)
! fx(i) = ---------------------------------------------
! 12 dx
fx(i,j,k)=d12dx*(fh(i-2,j,k)-EIT*fh(i-1,j,k)+EIT*fh(i+1,j,k)-fh(i+2,j,k))
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! - f(i-1) + f(i+1)
! fx(i) = --------------------------------
! 2 dx
fx(i,j,k)=d2dx*(-fh(i-1,j,k)+fh(i+1,j,k))
! set imax and imin 0
endif
enddo
enddo
enddo
return
end subroutine fdx
!-----------------------------------------------------------------------------
!
! single derivatives dy
!
!-----------------------------------------------------------------------------
subroutine fdy(ex,f,fy,Y,SYM2,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fy
real*8, intent(in ):: Y(ex(2)),SYM2
!~~~~~~ other variables
real*8 :: dY
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d840dy,d60dy,d12dy,d2dy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1, F32 = 3.2d1
real*8, parameter :: TWO=2.d0,THR=3.d0, EIT=8.d0, F168=1.68d2
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1,F672=6.72d2
real*8, parameter :: F840=8.4d2
dY = Y(2)-Y(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM2
SoA(2) = SYM2
SoA(3) = SYM2
call symmetry_bd(4,ex,f,fh,SoA)
d840dy = ONE/F840/dY
d60dy = ONE/F60/dY
d12dy = ONE/F12/dY
d2dy = ONE/TWO/dY
fy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! y direction
if(j+4 <= jmax .and. j-4 >= jmin)then
fy(i,j,k)=d840dy*( THR*fh(i,j-4,k)-F32 *fh(i,j-3,k)+F168*fh(i,j-2,k)-F672*fh(i,j-1,k)+ &
F672*fh(i,j+1,k)-F168*fh(i,j+2,k)+F32 *fh(i,j+3,k)-THR *fh(i,j+4,k))
elseif(j+3 <= jmax .and. j-3 >= jmin)then
fy(i,j,k)=d60dy*(-fh(i,j-3,k)+F9*fh(i,j-2,k)-F45*fh(i,j-1,k)+F45*fh(i,j+1,k)-F9*fh(i,j+2,k)+fh(i,j+3,k))
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fy(i,j,k)=d12dy*(fh(i,j-2,k)-EIT*fh(i,j-1,k)+EIT*fh(i,j+1,k)-fh(i,j+2,k))
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fy(i,j,k)=d2dy*(-fh(i,j-1,k)+fh(i,j+1,k))
! set jmax and jmin 0
endif
enddo
enddo
enddo
return
end subroutine fdy
!-----------------------------------------------------------------------------
!
! single derivatives dz
!
!-----------------------------------------------------------------------------
subroutine fdz(ex,f,fz,Z,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)), intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)), intent(out):: fz
real*8, intent(in ):: Z(ex(3)),SYM3
!~~~~~~ other variables
real*8 :: dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: d840dz,d60dz,d12dz,d2dz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0,ONE=1.d0, F60=6.d1, F32 = 3.2d1
real*8, parameter :: TWO=2.d0,THR=3.d0, EIT=8.d0, F168=1.68d2
real*8, parameter :: F9=9.d0,F45=4.5d1,F12=1.2d1,F672=6.72d2
real*8, parameter :: F840=8.4d2
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
SoA(1) = SYM3
SoA(2) = SYM3
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
d840dz = ONE/F840/dZ
d60dz = ONE/F60/dZ
d12dz = ONE/F12/dZ
d2dz = ONE/TWO/dZ
fz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
! z direction
if(k+4 <= kmax .and. k-4 >= kmin)then
fz(i,j,k)=d840dz*( THR*fh(i,j,k-4)-F32 *fh(i,j,k-3)+F168*fh(i,j,k-2)-F672*fh(i,j,k-1)+ &
F672*fh(i,j,k+1)-F168*fh(i,j,k+2)+F32 *fh(i,j,k+3)-THR *fh(i,j,k+4))
elseif(k+3 <= kmax .and. k-3 >= kmin)then
fz(i,j,k)=d60dz*(-fh(i,j,k-3)+F9*fh(i,j,k-2)-F45*fh(i,j,k-1)+F45*fh(i,j,k+1)-F9*fh(i,j,k+2)+fh(i,j,k+3))
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fz(i,j,k)=d12dz*(fh(i,j,k-2)-EIT*fh(i,j,k-1)+EIT*fh(i,j,k+1)-fh(i,j,k+2))
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fz(i,j,k)=d2dz*(-fh(i,j,k-1)+fh(i,j,k+1))
! set kmax and kmin 0
endif
enddo
enddo
enddo
return
end subroutine fdz
!-----------------------------------------------------------------------------------------------------------------
!
! General second derivatives of 8_th oder accurate
!
! - 9 f(i-4) + 128 f(i-3) - 1008 f(i-2) + 8064 f(i-1) - 14350 f(i) + 8064 f(i+1) - 1008 f(i+2) + 128 f(i+3) - 9 f(i+4)
! fxx(i) = ----------------------------------------------------------------------------------------------------------------------
! 5040 dx^2
!
! + 3 ( 3 f(i-4,j-4) - 32 f(i-3,j-4) + 168 f(i-2,j-4) - 672 f(i-1,j-4) + 672 f(i+1,j-4) - 168 f(i+2,j-4) + 32 f(i+3,j-4) - 3 f(i+4,j-4) )
! - 32 ( 3 f(i-4,j-3) - 32 f(i-3,j-3) + 168 f(i-2,j-3) - 672 f(i-1,j-3) + 672 f(i+1,j-3) - 168 f(i+2,j-3) + 32 f(i+3,j-3) - 3 f(i+4,j-3) )
! + 168 ( 3 f(i-4,j-2) - 32 f(i-3,j-2) + 168 f(i-2,j-2) - 672 f(i-1,j-2) + 672 f(i+1,j-2) - 168 f(i+2,j-2) + 32 f(i+3,j-2) - 3 f(i+4,j-2) )
! - 672 ( 3 f(i-4,j-1) - 32 f(i-3,j-1) + 168 f(i-2,j-1) - 672 f(i-1,j-1) + 672 f(i+1,j-1) - 168 f(i+2,j-1) + 32 f(i+3,j-1) - 3 f(i+4,j-1) )
! + 672 ( 3 f(i-4,j+1) - 32 f(i-3,j+1) + 168 f(i-2,j+1) - 672 f(i-1,j+1) + 672 f(i+1,j+1) - 168 f(i+2,j+1) + 32 f(i+3,j+1) - 3 f(i+4,j+1) )
! - 168 ( 3 f(i-4,j+2) - 32 f(i-3,j+2) + 168 f(i-2,j+2) - 672 f(i-1,j+2) + 672 f(i+1,j+2) - 168 f(i+2,j+2) + 32 f(i+3,j+2) - 3 f(i+4,j+2) )
! + 32 ( 3 f(i-4,j+3) - 32 f(i-3,j+3) + 168 f(i-2,j+3) - 672 f(i-1,j+3) + 672 f(i+1,j+3) - 168 f(i+2,j+3) + 32 f(i+3,j+3) - 3 f(i+4,j+3) )
! - 3 ( 3 f(i-4,j+4) - 32 f(i-3,j+4) + 168 f(i-2,j+4) - 672 f(i-1,j+4) + 672 f(i+1,j+4) - 168 f(i+2,j+4) + 32 f(i+3,j+4) - 3 f(i+4,j+4) )
! fxy(i,j) = ------------------------------------------------------------------------------------------------------------------------------------------
! 705600 dx dy
!
!-----------------------------------------------------------------------------------------------------------------
subroutine fdderivs(ex,f,fxx,fxy,fxz,fyy,fyz,fzz,X,Y,Z, &
SYM1,SYM2,SYM3,symmetry,onoff)
implicit none
integer, intent(in ):: ex(1:3),symmetry,onoff
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx,fxy,fxz,fyy,fyz,fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Sdydy,Sdzdz,Fdxdx,Fdydy,Fdzdz,Xdxdx,Xdydy,Xdzdz,Edxdx,Edydy,Edzdz
real*8 :: Sdxdy,Sdxdz,Sdydz,Fdxdy,Fdxdz,Fdydz,Xdxdy,Xdxdz,Xdydz,Edxdy,Edxdz,Edydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Sdydy = ONE /( dY * dY )
Sdzdz = ONE /( dZ * dZ )
Fdxdx = F1o12 /( dX * dX )
Fdydy = F1o12 /( dY * dY )
Fdzdz = F1o12 /( dZ * dZ )
Xdxdx = F1o180 /( dX * dX )
Xdydy = F1o180 /( dY * dY )
Xdzdz = F1o180 /( dZ * dZ )
Edxdx = F1o5040 /( dX * dX )
Edydy = F1o5040 /( dY * dY )
Edzdz = F1o5040 /( dZ * dZ )
Sdxdy = F1o4 /( dX * dY )
Sdxdz = F1o4 /( dX * dZ )
Sdydz = F1o4 /( dY * dZ )
Fdxdy = F1o144 /( dX * dY )
Fdxdz = F1o144 /( dX * dZ )
Fdydz = F1o144 /( dY * dZ )
Xdxdy = F1o3600 /( dX * dY )
Xdxdz = F1o3600 /( dX * dZ )
Xdydz = F1o3600 /( dY * dZ )
Edxdy = F1o705600 /( dX * dY )
Edxdz = F1o705600 /( dX * dZ )
Edydz = F1o705600 /( dY * dZ )
fxx = ZEO
fyy = ZEO
fzz = ZEO
fxy = ZEO
fxz = ZEO
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+4 <= imax .and. i-4 >= imin)then
! - 9 f(i-4) + 128 f(i-3) - 1008 f(i-2) + 8064 f(i-1) - 14350 f(i) + 8064 f(i+1) - 1008 f(i+2) + 128 f(i+3) - 9 f(i+4)
! fxx(i) = ----------------------------------------------------------------------------------------------------------------------
! 5040 dx^2
fxx(i,j,k) = Edxdx*(-F9*fh(i-4,j,k)+F128*fh(i-3,j,k)-F1008*fh(i-2,j,k)+F8064*fh(i-1,j,k)-F14350*fh(i,j,k) &
-F9*fh(i+4,j,k)+F128*fh(i+3,j,k)-F1008*fh(i+2,j,k)+F8064*fh(i+1,j,k) )
elseif(i+3 <= imax .and. i-3 >= imin)then
! 2 f(i-3) - 27 f(i-2) + 270 f(i-1) - 490 f(i) + 270 f(i+1) - 27 f(i+2) + 2 f(i+3)
! fxx(i) = -----------------------------------------------------------------------------------
! 180 dx^2
fxx(i,j,k) = Xdxdx*(TWO*fh(i-3,j,k)-F27*fh(i-2,j,k)+F270*fh(i-1,j,k)-F490*fh(i,j,k) &
+TWO*fh(i+3,j,k)-F27*fh(i+2,j,k)+F270*fh(i+1,j,k) )
elseif(i+2 <= imax .and. i-2 >= imin)then
!
! - f(i-2) + 16 f(i-1) - 30 f(i) + 16 f(i+1) - f(i+2)
! fxx(i) = ----------------------------------------------------------
! 12 dx^2
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
!
! f(i-1) - 2 f(i) + f(i+1)
! fxx(i) = --------------------------------
! dx^2
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
!~~~~~~ fyy
if(j+4 <= jmax .and. j-4 >= jmin)then
fyy(i,j,k) = Edydy*(-F9*fh(i,j-4,k)+F128*fh(i,j-3,k)-F1008*fh(i,j-2,k)+F8064*fh(i,j-1,k)-F14350*fh(i,j,k) &
-F9*fh(i,j+4,k)+F128*fh(i,j+3,k)-F1008*fh(i,j+2,k)+F8064*fh(i,j+1,k) )
elseif(j+3 <= jmax .and. j-3 >= jmin)then
fyy(i,j,k) = Xdydy*(TWO*fh(i,j-3,k)-F27*fh(i,j-2,k)+F270*fh(i,j-1,k)-F490*fh(i,j,k) &
+TWO*fh(i,j+3,k)-F27*fh(i,j+2,k)+F270*fh(i,j+1,k) )
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
!~~~~~~ fzz
if(k+4 <= kmax .and. k-4 >= kmin)then
fzz(i,j,k) = Edzdz*(-F9*fh(i,j,k-4)+F128*fh(i,j,k-3)-F1008*fh(i,j,k-2)+F8064*fh(i,j,k-1)-F14350*fh(i,j,k) &
-F9*fh(i,j,k+4)+F128*fh(i,j,k+3)-F1008*fh(i,j,k+2)+F8064*fh(i,j,k+1) )
elseif(k+3 <= kmax .and. k-3 >= kmin)then
fzz(i,j,k) = Xdzdz*(TWO*fh(i,j,k-3)-F27*fh(i,j,k-2)+F270*fh(i,j,k-1)-F490*fh(i,j,k) &
+TWO*fh(i,j,k+3)-F27*fh(i,j,k+2)+F270*fh(i,j,k+1) )
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
!~~~~~~ fxy
if(i+4 <= imax .and. i-4 >= imin .and. j+4 <= jmax .and. j-4 >= jmin)then
! + 3 ( 3 f(i-4,j-4) - 32 f(i-3,j-4) + 168 f(i-2,j-4) - 672 f(i-1,j-4) + 672 f(i+1,j-4) - 168 f(i+2,j-4) + 32 f(i+3,j-4) - 3 f(i+4,j-4) )
! - 32 ( 3 f(i-4,j-3) - 32 f(i-3,j-3) + 168 f(i-2,j-3) - 672 f(i-1,j-3) + 672 f(i+1,j-3) - 168 f(i+2,j-3) + 32 f(i+3,j-3) - 3 f(i+4,j-3) )
! + 168 ( 3 f(i-4,j-2) - 32 f(i-3,j-2) + 168 f(i-2,j-2) - 672 f(i-1,j-2) + 672 f(i+1,j-2) - 168 f(i+2,j-2) + 32 f(i+3,j-2) - 3 f(i+4,j-2) )
! - 672 ( 3 f(i-4,j-1) - 32 f(i-3,j-1) + 168 f(i-2,j-1) - 672 f(i-1,j-1) + 672 f(i+1,j-1) - 168 f(i+2,j-1) + 32 f(i+3,j-1) - 3 f(i+4,j-1) )
! + 672 ( 3 f(i-4,j+1) - 32 f(i-3,j+1) + 168 f(i-2,j+1) - 672 f(i-1,j+1) + 672 f(i+1,j+1) - 168 f(i+2,j+1) + 32 f(i+3,j+1) - 3 f(i+4,j+1) )
! - 168 ( 3 f(i-4,j+2) - 32 f(i-3,j+2) + 168 f(i-2,j+2) - 672 f(i-1,j+2) + 672 f(i+1,j+2) - 168 f(i+2,j+2) + 32 f(i+3,j+2) - 3 f(i+4,j+2) )
! + 32 ( 3 f(i-4,j+3) - 32 f(i-3,j+3) + 168 f(i-2,j+3) - 672 f(i-1,j+3) + 672 f(i+1,j+3) - 168 f(i+2,j+3) + 32 f(i+3,j+3) - 3 f(i+4,j+3) )
! - 3 ( 3 f(i-4,j+4) - 32 f(i-3,j+4) + 168 f(i-2,j+4) - 672 f(i-1,j+4) + 672 f(i+1,j+4) - 168 f(i+2,j+4) + 32 f(i+3,j+4) - 3 f(i+4,j+4) )
! fxy(i,j) = ------------------------------------------------------------------------------------------------------------------------------------------
! 705600 dx dy
fxy(i,j,k) = Edxdy*( THR *( THR*fh(i-4,j-4,k)-F32*fh(i-3,j-4,k)+F168*fh(i-2,j-4,k)-F672*fh(i-1,j-4,k) &
-THR*fh(i+4,j-4,k)+F32*fh(i+3,j-4,k)-F168*fh(i+2,j-4,k)+F672*fh(i+1,j-4,k)) &
-F32 *( THR*fh(i-4,j-3,k)-F32*fh(i-3,j-3,k)+F168*fh(i-2,j-3,k)-F672*fh(i-1,j-3,k) &
-THR*fh(i+4,j-3,k)+F32*fh(i+3,j-3,k)-F168*fh(i+2,j-3,k)+F672*fh(i+1,j-3,k)) &
+F168*( THR*fh(i-4,j-2,k)-F32*fh(i-3,j-2,k)+F168*fh(i-2,j-2,k)-F672*fh(i-1,j-2,k) &
-THR*fh(i+4,j-2,k)+F32*fh(i+3,j-2,k)-F168*fh(i+2,j-2,k)+F672*fh(i+1,j-2,k)) &
-F672*( THR*fh(i-4,j-1,k)-F32*fh(i-3,j-1,k)+F168*fh(i-2,j-1,k)-F672*fh(i-1,j-1,k) &
-THR*fh(i+4,j-1,k)+F32*fh(i+3,j-1,k)-F168*fh(i+2,j-1,k)+F672*fh(i+1,j-1,k)) &
+F672*( THR*fh(i-4,j+1,k)-F32*fh(i-3,j+1,k)+F168*fh(i-2,j+1,k)-F672*fh(i-1,j+1,k) &
-THR*fh(i+4,j+1,k)+F32*fh(i+3,j+1,k)-F168*fh(i+2,j+1,k)+F672*fh(i+1,j+1,k)) &
-F168*( THR*fh(i-4,j+2,k)-F32*fh(i-3,j+2,k)+F168*fh(i-2,j+2,k)-F672*fh(i-1,j+2,k) &
-THR*fh(i+4,j+2,k)+F32*fh(i+3,j+2,k)-F168*fh(i+2,j+2,k)+F672*fh(i+1,j+2,k)) &
+F32 *( THR*fh(i-4,j+3,k)-F32*fh(i-3,j+3,k)+F168*fh(i-2,j+3,k)-F672*fh(i-1,j+3,k) &
-THR*fh(i+4,j+3,k)+F32*fh(i+3,j+3,k)-F168*fh(i+2,j+3,k)+F672*fh(i+1,j+3,k)) &
-THR *( THR*fh(i-4,j+4,k)-F32*fh(i-3,j+4,k)+F168*fh(i-2,j+4,k)-F672*fh(i-1,j+4,k) &
-THR*fh(i+4,j+4,k)+F32*fh(i+3,j+4,k)-F168*fh(i+2,j+4,k)+F672*fh(i+1,j+4,k)) )
elseif(i+3 <= imax .and. i-3 >= imin .and. j+3 <= jmax .and. j-3 >= jmin)then
!
! - ( - f(i-3,j-3) + 9 f(i-2,j-3) - 45 f(i-1,j-3) + 45 f(i+1,j-3) - 9 f(i+2,j-3) + f(i+3,j-3) )
! + 9 ( - f(i-3,j-2) + 9 f(i-2,j-2) - 45 f(i-1,j-2) + 45 f(i+1,j-2) - 9 f(i+2,j-2) + f(i+3,j-2) )
! - 45 ( - f(i-3,j-1) + 9 f(i-2,j-1) - 45 f(i-1,j-1) + 45 f(i+1,j-1) - 9 f(i+2,j-1) + f(i+3,j-1) )
! + 45 ( - f(i-3,j+1) + 9 f(i-2,j+1) - 45 f(i-1,j+1) + 45 f(i+1,j+1) - 9 f(i+2,j+1) + f(i+3,j+1) )
! - 9 ( - f(i-3,j+2) + 9 f(i-2,j+2) - 45 f(i-1,j+2) + 45 f(i+1,j+2) - 9 f(i+2,j+2) + f(i+3,j+2) )
! + ( - f(i-3,j+3) + 9 f(i-2,j+3) - 45 f(i-1,j+3) + 45 f(i+1,j+3) - 9 f(i+2,j+3) + f(i+3,j+3) )
! fxy(i,j) = ------------------------------------------------------------------------------------------------
! 3600 dx dy
fxy(i,j,k) = Xdxdy*(- (-fh(i-3,j-3,k)+F9*fh(i-2,j-3,k)-F45*fh(i-1,j-3,k)+F45*fh(i+1,j-3,k)-F9*fh(i+2,j-3,k)+fh(i+3,j-3,k)) &
+F9 *(-fh(i-3,j-2,k)+F9*fh(i-2,j-2,k)-F45*fh(i-1,j-2,k)+F45*fh(i+1,j-2,k)-F9*fh(i+2,j-2,k)+fh(i+3,j-2,k)) &
-F45*(-fh(i-3,j-1,k)+F9*fh(i-2,j-1,k)-F45*fh(i-1,j-1,k)+F45*fh(i+1,j-1,k)-F9*fh(i+2,j-1,k)+fh(i+3,j-1,k)) &
+F45*(-fh(i-3,j+1,k)+F9*fh(i-2,j+1,k)-F45*fh(i-1,j+1,k)+F45*fh(i+1,j+1,k)-F9*fh(i+2,j+1,k)+fh(i+3,j+1,k)) &
-F9 *(-fh(i-3,j+2,k)+F9*fh(i-2,j+2,k)-F45*fh(i-1,j+2,k)+F45*fh(i+1,j+2,k)-F9*fh(i+2,j+2,k)+fh(i+3,j+2,k)) &
+ (-fh(i-3,j+3,k)+F9*fh(i-2,j+3,k)-F45*fh(i-1,j+3,k)+F45*fh(i+1,j+3,k)-F9*fh(i+2,j+3,k)+fh(i+3,j+3,k)))
elseif(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
!
! ( f(i-2,j-2) - 8 f(i-1,j-2) + 8 f(i+1,j-2) - f(i+2,j-2) )
! - 8 ( f(i-2,j-1) - 8 f(i-1,j-1) + 8 f(i+1,j-1) - f(i+2,j-1) )
! + 8 ( f(i-2,j+1) - 8 f(i-1,j+1) + 8 f(i+1,j+1) - f(i+2,j+1) )
! - ( f(i-2,j+2) - 8 f(i-1,j+2) + 8 f(i+1,j+2) - f(i+2,j+2) )
! fxy(i,j) = ----------------------------------------------------------------
! 144 dx dy
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
! f(i-1,j-1) - f(i+1,j-1) - f(i-1,j+1) + f(i+1,j+1)
! fxy(i,j) = -----------------------------------------------------------
! 4 dx dy
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
!~~~~~~ fxz
if(i+4 <= imax .and. i-4 >= imin .and. k+4 <= kmax .and. k-4 >= kmin)then
fxz(i,j,k) = Edxdz*( THR *( THR*fh(i-4,j,k-4)-F32*fh(i-3,j,k-4)+F168*fh(i-2,j,k-4)-F672*fh(i-1,j,k-4) &
-THR*fh(i+4,j,k-4)+F32*fh(i+3,j,k-4)-F168*fh(i+2,j,k-4)+F672*fh(i+1,j,k-4)) &
-F32 *( THR*fh(i-4,j,k-3)-F32*fh(i-3,j,k-3)+F168*fh(i-2,j,k-3)-F672*fh(i-1,j,k-3) &
-THR*fh(i+4,j,k-3)+F32*fh(i+3,j,k-3)-F168*fh(i+2,j,k-3)+F672*fh(i+1,j,k-3)) &
+F168*( THR*fh(i-4,j,k-2)-F32*fh(i-3,j,k-2)+F168*fh(i-2,j,k-2)-F672*fh(i-1,j,k-2) &
-THR*fh(i+4,j,k-2)+F32*fh(i+3,j,k-2)-F168*fh(i+2,j,k-2)+F672*fh(i+1,j,k-2)) &
-F672*( THR*fh(i-4,j,k-1)-F32*fh(i-3,j,k-1)+F168*fh(i-2,j,k-1)-F672*fh(i-1,j,k-1) &
-THR*fh(i+4,j,k-1)+F32*fh(i+3,j,k-1)-F168*fh(i+2,j,k-1)+F672*fh(i+1,j,k-1)) &
+F672*( THR*fh(i-4,j,k+1)-F32*fh(i-3,j,k+1)+F168*fh(i-2,j,k+1)-F672*fh(i-1,j,k+1) &
-THR*fh(i+4,j,k+1)+F32*fh(i+3,j,k+1)-F168*fh(i+2,j,k+1)+F672*fh(i+1,j,k+1)) &
-F168*( THR*fh(i-4,j,k+2)-F32*fh(i-3,j,k+2)+F168*fh(i-2,j,k+2)-F672*fh(i-1,j,k+2) &
-THR*fh(i+4,j,k+2)+F32*fh(i+3,j,k+2)-F168*fh(i+2,j,k+2)+F672*fh(i+1,j,k+2)) &
+F32 *( THR*fh(i-4,j,k+3)-F32*fh(i-3,j,k+3)+F168*fh(i-2,j,k+3)-F672*fh(i-1,j,k+3) &
-THR*fh(i+4,j,k+3)+F32*fh(i+3,j,k+3)-F168*fh(i+2,j,k+3)+F672*fh(i+1,j,k+3)) &
-THR *( THR*fh(i-4,j,k+4)-F32*fh(i-3,j,k+4)+F168*fh(i-2,j,k+4)-F672*fh(i-1,j,k+4) &
-THR*fh(i+4,j,k+4)+F32*fh(i+3,j,k+4)-F168*fh(i+2,j,k+4)+F672*fh(i+1,j,k+4)) )
elseif(i+3 <= imax .and. i-3 >= imin .and. k+3 <= kmax .and. k-3 >= kmin)then
fxz(i,j,k) = Xdxdz*(- (-fh(i-3,j,k-3)+F9*fh(i-2,j,k-3)-F45*fh(i-1,j,k-3)+F45*fh(i+1,j,k-3)-F9*fh(i+2,j,k-3)+fh(i+3,j,k-3)) &
+F9 *(-fh(i-3,j,k-2)+F9*fh(i-2,j,k-2)-F45*fh(i-1,j,k-2)+F45*fh(i+1,j,k-2)-F9*fh(i+2,j,k-2)+fh(i+3,j,k-2)) &
-F45*(-fh(i-3,j,k-1)+F9*fh(i-2,j,k-1)-F45*fh(i-1,j,k-1)+F45*fh(i+1,j,k-1)-F9*fh(i+2,j,k-1)+fh(i+3,j,k-1)) &
+F45*(-fh(i-3,j,k+1)+F9*fh(i-2,j,k+1)-F45*fh(i-1,j,k+1)+F45*fh(i+1,j,k+1)-F9*fh(i+2,j,k+1)+fh(i+3,j,k+1)) &
-F9 *(-fh(i-3,j,k+2)+F9*fh(i-2,j,k+2)-F45*fh(i-1,j,k+2)+F45*fh(i+1,j,k+2)-F9*fh(i+2,j,k+2)+fh(i+3,j,k+2)) &
+ (-fh(i-3,j,k+3)+F9*fh(i-2,j,k+3)-F45*fh(i-1,j,k+3)+F45*fh(i+1,j,k+3)-F9*fh(i+2,j,k+3)+fh(i+3,j,k+3)))
elseif(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
!~~~~~~ fyz
if(j+4 <= jmax .and. j-4 >= jmin .and. k+4 <= kmax .and. k-4 >= kmin)then
fyz(i,j,k) = Edydz*( THR *( THR*fh(i,j-4,k-4)-F32*fh(i,j-3,k-4)+F168*fh(i,j-2,k-4)-F672*fh(i,j-1,k-4) &
-THR*fh(i,j+4,k-4)+F32*fh(i,j+3,k-4)-F168*fh(i,j+2,k-4)+F672*fh(i,j+1,k-4)) &
-F32 *( THR*fh(i,j-4,k-3)-F32*fh(i,j-3,k-3)+F168*fh(i,j-2,k-3)-F672*fh(i,j-1,k-3) &
-THR*fh(i,j+4,k-3)+F32*fh(i,j+3,k-3)-F168*fh(i,j+2,k-3)+F672*fh(i,j+1,k-3)) &
+F168*( THR*fh(i,j-4,k-2)-F32*fh(i,j-3,k-2)+F168*fh(i,j-2,k-2)-F672*fh(i,j-1,k-2) &
-THR*fh(i,j+4,k-2)+F32*fh(i,j+3,k-2)-F168*fh(i,j+2,k-2)+F672*fh(i,j+1,k-2)) &
-F672*( THR*fh(i,j-4,k-1)-F32*fh(i,j-3,k-1)+F168*fh(i,j-2,k-1)-F672*fh(i,j-1,k-1) &
-THR*fh(i,j+4,k-1)+F32*fh(i,j+3,k-1)-F168*fh(i,j+2,k-1)+F672*fh(i,j+1,k-1)) &
+F672*( THR*fh(i,j-4,k+1)-F32*fh(i,j-3,k+1)+F168*fh(i,j-2,k+1)-F672*fh(i,j-1,k+1) &
-THR*fh(i,j+4,k+1)+F32*fh(i,j+3,k+1)-F168*fh(i,j+2,k+1)+F672*fh(i,j+1,k+1)) &
-F168*( THR*fh(i,j-4,k+2)-F32*fh(i,j-3,k+2)+F168*fh(i,j-2,k+2)-F672*fh(i,j-1,k+2) &
-THR*fh(i,j+4,k+2)+F32*fh(i,j+3,k+2)-F168*fh(i,j+2,k+2)+F672*fh(i,j+1,k+2)) &
+F32 *( THR*fh(i,j-4,k+3)-F32*fh(i,j-3,k+3)+F168*fh(i,j-2,k+3)-F672*fh(i,j-1,k+3) &
-THR*fh(i,j+4,k+3)+F32*fh(i,j+3,k+3)-F168*fh(i,j+2,k+3)+F672*fh(i,j+1,k+3)) &
-THR *( THR*fh(i,j-4,k+4)-F32*fh(i,j-3,k+4)+F168*fh(i,j-2,k+4)-F672*fh(i,j-1,k+4) &
-THR*fh(i,j+4,k+4)+F32*fh(i,j+3,k+4)-F168*fh(i,j+2,k+4)+F672*fh(i,j+1,k+4)) )
elseif(j+3 <= jmax .and. j-3 >= jmin .and. k+3 <= kmax .and. k-3 >= kmin)then
fyz(i,j,k) = Xdydz*(- (-fh(i,j-3,k-3)+F9*fh(i,j-2,k-3)-F45*fh(i,j-1,k-3)+F45*fh(i,j+1,k-3)-F9*fh(i,j+2,k-3)+fh(i,j+3,k-3)) &
+F9 *(-fh(i,j-3,k-2)+F9*fh(i,j-2,k-2)-F45*fh(i,j-1,k-2)+F45*fh(i,j+1,k-2)-F9*fh(i,j+2,k-2)+fh(i,j+3,k-2)) &
-F45*(-fh(i,j-3,k-1)+F9*fh(i,j-2,k-1)-F45*fh(i,j-1,k-1)+F45*fh(i,j+1,k-1)-F9*fh(i,j+2,k-1)+fh(i,j+3,k-1)) &
+F45*(-fh(i,j-3,k+1)+F9*fh(i,j-2,k+1)-F45*fh(i,j-1,k+1)+F45*fh(i,j+1,k+1)-F9*fh(i,j+2,k+1)+fh(i,j+3,k+1)) &
-F9 *(-fh(i,j-3,k+2)+F9*fh(i,j-2,k+2)-F45*fh(i,j-1,k+2)+F45*fh(i,j+1,k+2)-F9*fh(i,j+2,k+2)+fh(i,j+3,k+2)) &
+ (-fh(i,j-3,k+3)+F9*fh(i,j-2,k+3)-F45*fh(i,j-1,k+3)+F45*fh(i,j+1,k+3)-F9*fh(i,j+2,k+3)+fh(i,j+3,k+3)))
elseif(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fdderivs
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! only for compute_ricci.f90 usage
!-----------------------------------------------------------------------------
subroutine fddxx(ex,f,fxx,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxx
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdx,Fdxdx,Xdxdx,Edxdx
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdxdx = ONE /( dX * dX )
Fdxdx = F1o12 /( dX * dX )
Xdxdx = F1o180 /( dX * dX )
Edxdx = F1o5040 /( dX * dX )
fxx = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxx
if(i+4 <= imax .and. i-4 >= imin)then
fxx(i,j,k) = Edxdx*(-F9*fh(i-4,j,k)+F128*fh(i-3,j,k)-F1008*fh(i-2,j,k)+F8064*fh(i-1,j,k)-F14350*fh(i,j,k) &
-F9*fh(i+4,j,k)+F128*fh(i+3,j,k)-F1008*fh(i+2,j,k)+F8064*fh(i+1,j,k) )
elseif(i+3 <= imax .and. i-3 >= imin)then
fxx(i,j,k) = Xdxdx*(TWO*fh(i-3,j,k)-F27*fh(i-2,j,k)+F270*fh(i-1,j,k)-F490*fh(i,j,k) &
+TWO*fh(i+3,j,k)-F27*fh(i+2,j,k)+F270*fh(i+1,j,k) )
elseif(i+2 <= imax .and. i-2 >= imin)then
fxx(i,j,k) = Fdxdx*(-fh(i-2,j,k)+F16*fh(i-1,j,k)-F30*fh(i,j,k) &
-fh(i+2,j,k)+F16*fh(i+1,j,k) )
elseif(i+1 <= imax .and. i-1 >= imin)then
fxx(i,j,k) = Sdxdx*(fh(i-1,j,k)-TWO*fh(i,j,k) &
+fh(i+1,j,k) )
endif
enddo
enddo
enddo
return
end subroutine fddxx
subroutine fddyy(ex,f,fyy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydy,Fdydy,Xdydy,Edydy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdydy = ONE /( dY * dY )
Fdydy = F1o12 /( dY * dY )
Xdydy = F1o180 /( dY * dY )
Edydy = F1o5040 /( dY * dY )
fyy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyy
if(j+4 <= jmax .and. j-4 >= jmin)then
fyy(i,j,k) = Edydy*(-F9*fh(i,j-4,k)+F128*fh(i,j-3,k)-F1008*fh(i,j-2,k)+F8064*fh(i,j-1,k)-F14350*fh(i,j,k) &
-F9*fh(i,j+4,k)+F128*fh(i,j+3,k)-F1008*fh(i,j+2,k)+F8064*fh(i,j+1,k) )
elseif(j+3 <= jmax .and. j-3 >= jmin)then
fyy(i,j,k) = Xdydy*(TWO*fh(i,j-3,k)-F27*fh(i,j-2,k)+F270*fh(i,j-1,k)-F490*fh(i,j,k) &
+TWO*fh(i,j+3,k)-F27*fh(i,j+2,k)+F270*fh(i,j+1,k) )
elseif(j+2 <= jmax .and. j-2 >= jmin)then
fyy(i,j,k) = Fdydy*(-fh(i,j-2,k)+F16*fh(i,j-1,k)-F30*fh(i,j,k) &
-fh(i,j+2,k)+F16*fh(i,j+1,k) )
elseif(j+1 <= jmax .and. j-1 >= jmin)then
fyy(i,j,k) = Sdydy*(fh(i,j-1,k)-TWO*fh(i,j,k) &
+fh(i,j+1,k) )
endif
enddo
enddo
enddo
return
end subroutine fddyy
subroutine fddzz(ex,f,fzz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fzz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdzdz,Fdzdz,Xdzdz,Edzdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdzdz = ONE /( dZ * dZ )
Fdzdz = F1o12 /( dZ * dZ )
Xdzdz = F1o180 /( dZ * dZ )
Edzdz = F1o5040 /( dZ * dZ )
fzz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fzz
if(k+4 <= kmax .and. k-4 >= kmin)then
fzz(i,j,k) = Edzdz*(-F9*fh(i,j,k-4)+F128*fh(i,j,k-3)-F1008*fh(i,j,k-2)+F8064*fh(i,j,k-1)-F14350*fh(i,j,k) &
-F9*fh(i,j,k+4)+F128*fh(i,j,k+3)-F1008*fh(i,j,k+2)+F8064*fh(i,j,k+1) )
elseif(k+3 <= kmax .and. k-3 >= kmin)then
fzz(i,j,k) = Xdzdz*(TWO*fh(i,j,k-3)-F27*fh(i,j,k-2)+F270*fh(i,j,k-1)-F490*fh(i,j,k) &
+TWO*fh(i,j,k+3)-F27*fh(i,j,k+2)+F270*fh(i,j,k+1) )
elseif(k+2 <= kmax .and. k-2 >= kmin)then
fzz(i,j,k) = Fdzdz*(-fh(i,j,k-2)+F16*fh(i,j,k-1)-F30*fh(i,j,k) &
-fh(i,j,k+2)+F16*fh(i,j,k+1) )
elseif(k+1 <= kmax .and. k-1 >= kmin)then
fzz(i,j,k) = Sdzdz*(fh(i,j,k-1)-TWO*fh(i,j,k) &
+fh(i,j,k+1) )
endif
enddo
enddo
enddo
return
end subroutine fddzz
subroutine fddxy(ex,f,fxy,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxy
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdy,Fdxdy,Xdxdy,Edxdy
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdxdy = F1o4 /( dX * dY )
Fdxdy = F1o144 /( dX * dY )
Xdxdy = F1o3600 /( dX * dY )
Edxdy = F1o705600 /( dX * dY )
fxy = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxy
if(i+4 <= imax .and. i-4 >= imin .and. j+4 <= jmax .and. j-4 >= jmin)then
fxy(i,j,k) = Edxdy*( THR *( THR*fh(i-4,j-4,k)-F32*fh(i-3,j-4,k)+F168*fh(i-2,j-4,k)-F672*fh(i-1,j-4,k) &
-THR*fh(i+4,j-4,k)+F32*fh(i+3,j-4,k)-F168*fh(i+2,j-4,k)+F672*fh(i+1,j-4,k)) &
-F32 *( THR*fh(i-4,j-3,k)-F32*fh(i-3,j-3,k)+F168*fh(i-2,j-3,k)-F672*fh(i-1,j-3,k) &
-THR*fh(i+4,j-3,k)+F32*fh(i+3,j-3,k)-F168*fh(i+2,j-3,k)+F672*fh(i+1,j-3,k)) &
+F168*( THR*fh(i-4,j-2,k)-F32*fh(i-3,j-2,k)+F168*fh(i-2,j-2,k)-F672*fh(i-1,j-2,k) &
-THR*fh(i+4,j-2,k)+F32*fh(i+3,j-2,k)-F168*fh(i+2,j-2,k)+F672*fh(i+1,j-2,k)) &
-F672*( THR*fh(i-4,j-1,k)-F32*fh(i-3,j-1,k)+F168*fh(i-2,j-1,k)-F672*fh(i-1,j-1,k) &
-THR*fh(i+4,j-1,k)+F32*fh(i+3,j-1,k)-F168*fh(i+2,j-1,k)+F672*fh(i+1,j-1,k)) &
+F672*( THR*fh(i-4,j+1,k)-F32*fh(i-3,j+1,k)+F168*fh(i-2,j+1,k)-F672*fh(i-1,j+1,k) &
-THR*fh(i+4,j+1,k)+F32*fh(i+3,j+1,k)-F168*fh(i+2,j+1,k)+F672*fh(i+1,j+1,k)) &
-F168*( THR*fh(i-4,j+2,k)-F32*fh(i-3,j+2,k)+F168*fh(i-2,j+2,k)-F672*fh(i-1,j+2,k) &
-THR*fh(i+4,j+2,k)+F32*fh(i+3,j+2,k)-F168*fh(i+2,j+2,k)+F672*fh(i+1,j+2,k)) &
+F32 *( THR*fh(i-4,j+3,k)-F32*fh(i-3,j+3,k)+F168*fh(i-2,j+3,k)-F672*fh(i-1,j+3,k) &
-THR*fh(i+4,j+3,k)+F32*fh(i+3,j+3,k)-F168*fh(i+2,j+3,k)+F672*fh(i+1,j+3,k)) &
-THR *( THR*fh(i-4,j+4,k)-F32*fh(i-3,j+4,k)+F168*fh(i-2,j+4,k)-F672*fh(i-1,j+4,k) &
-THR*fh(i+4,j+4,k)+F32*fh(i+3,j+4,k)-F168*fh(i+2,j+4,k)+F672*fh(i+1,j+4,k)) )
elseif(i+3 <= imax .and. i-3 >= imin .and. j+3 <= jmax .and. j-3 >= jmin)then
fxy(i,j,k) = Xdxdy*(- (-fh(i-3,j-3,k)+F9*fh(i-2,j-3,k)-F45*fh(i-1,j-3,k)+F45*fh(i+1,j-3,k)-F9*fh(i+2,j-3,k)+fh(i+3,j-3,k)) &
+F9 *(-fh(i-3,j-2,k)+F9*fh(i-2,j-2,k)-F45*fh(i-1,j-2,k)+F45*fh(i+1,j-2,k)-F9*fh(i+2,j-2,k)+fh(i+3,j-2,k)) &
-F45*(-fh(i-3,j-1,k)+F9*fh(i-2,j-1,k)-F45*fh(i-1,j-1,k)+F45*fh(i+1,j-1,k)-F9*fh(i+2,j-1,k)+fh(i+3,j-1,k)) &
+F45*(-fh(i-3,j+1,k)+F9*fh(i-2,j+1,k)-F45*fh(i-1,j+1,k)+F45*fh(i+1,j+1,k)-F9*fh(i+2,j+1,k)+fh(i+3,j+1,k)) &
-F9 *(-fh(i-3,j+2,k)+F9*fh(i-2,j+2,k)-F45*fh(i-1,j+2,k)+F45*fh(i+1,j+2,k)-F9*fh(i+2,j+2,k)+fh(i+3,j+2,k)) &
+ (-fh(i-3,j+3,k)+F9*fh(i-2,j+3,k)-F45*fh(i-1,j+3,k)+F45*fh(i+1,j+3,k)-F9*fh(i+2,j+3,k)+fh(i+3,j+3,k)))
elseif(i+2 <= imax .and. i-2 >= imin .and. j+2 <= jmax .and. j-2 >= jmin)then
fxy(i,j,k) = Fdxdy*( (fh(i-2,j-2,k)-F8*fh(i-1,j-2,k)+F8*fh(i+1,j-2,k)-fh(i+2,j-2,k)) &
-F8 *(fh(i-2,j-1,k)-F8*fh(i-1,j-1,k)+F8*fh(i+1,j-1,k)-fh(i+2,j-1,k)) &
+F8 *(fh(i-2,j+1,k)-F8*fh(i-1,j+1,k)+F8*fh(i+1,j+1,k)-fh(i+2,j+1,k)) &
- (fh(i-2,j+2,k)-F8*fh(i-1,j+2,k)+F8*fh(i+1,j+2,k)-fh(i+2,j+2,k)))
elseif(i+1 <= imax .and. i-1 >= imin .and. j+1 <= jmax .and. j-1 >= jmin)then
fxy(i,j,k) = Sdxdy*(fh(i-1,j-1,k)-fh(i+1,j-1,k)-fh(i-1,j+1,k)+fh(i+1,j+1,k))
endif
enddo
enddo
enddo
return
end subroutine fddxy
subroutine fddxz(ex,f,fxz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fxz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdxdz,Fdxdz,Xdxdz,Edxdz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdxdz = F1o4 /( dX * dZ )
Fdxdz = F1o144 /( dX * dZ )
Xdxdz = F1o3600 /( dX * dZ )
Edxdz = F1o705600 /( dX * dZ )
fxz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fxz
if(i+4 <= imax .and. i-4 >= imin .and. k+4 <= kmax .and. k-4 >= kmin)then
fxz(i,j,k) = Edxdz*( THR *( THR*fh(i-4,j,k-4)-F32*fh(i-3,j,k-4)+F168*fh(i-2,j,k-4)-F672*fh(i-1,j,k-4) &
-THR*fh(i+4,j,k-4)+F32*fh(i+3,j,k-4)-F168*fh(i+2,j,k-4)+F672*fh(i+1,j,k-4)) &
-F32 *( THR*fh(i-4,j,k-3)-F32*fh(i-3,j,k-3)+F168*fh(i-2,j,k-3)-F672*fh(i-1,j,k-3) &
-THR*fh(i+4,j,k-3)+F32*fh(i+3,j,k-3)-F168*fh(i+2,j,k-3)+F672*fh(i+1,j,k-3)) &
+F168*( THR*fh(i-4,j,k-2)-F32*fh(i-3,j,k-2)+F168*fh(i-2,j,k-2)-F672*fh(i-1,j,k-2) &
-THR*fh(i+4,j,k-2)+F32*fh(i+3,j,k-2)-F168*fh(i+2,j,k-2)+F672*fh(i+1,j,k-2)) &
-F672*( THR*fh(i-4,j,k-1)-F32*fh(i-3,j,k-1)+F168*fh(i-2,j,k-1)-F672*fh(i-1,j,k-1) &
-THR*fh(i+4,j,k-1)+F32*fh(i+3,j,k-1)-F168*fh(i+2,j,k-1)+F672*fh(i+1,j,k-1)) &
+F672*( THR*fh(i-4,j,k+1)-F32*fh(i-3,j,k+1)+F168*fh(i-2,j,k+1)-F672*fh(i-1,j,k+1) &
-THR*fh(i+4,j,k+1)+F32*fh(i+3,j,k+1)-F168*fh(i+2,j,k+1)+F672*fh(i+1,j,k+1)) &
-F168*( THR*fh(i-4,j,k+2)-F32*fh(i-3,j,k+2)+F168*fh(i-2,j,k+2)-F672*fh(i-1,j,k+2) &
-THR*fh(i+4,j,k+2)+F32*fh(i+3,j,k+2)-F168*fh(i+2,j,k+2)+F672*fh(i+1,j,k+2)) &
+F32 *( THR*fh(i-4,j,k+3)-F32*fh(i-3,j,k+3)+F168*fh(i-2,j,k+3)-F672*fh(i-1,j,k+3) &
-THR*fh(i+4,j,k+3)+F32*fh(i+3,j,k+3)-F168*fh(i+2,j,k+3)+F672*fh(i+1,j,k+3)) &
-THR *( THR*fh(i-4,j,k+4)-F32*fh(i-3,j,k+4)+F168*fh(i-2,j,k+4)-F672*fh(i-1,j,k+4) &
-THR*fh(i+4,j,k+4)+F32*fh(i+3,j,k+4)-F168*fh(i+2,j,k+4)+F672*fh(i+1,j,k+4)) )
elseif(i+3 <= imax .and. i-3 >= imin .and. k+3 <= kmax .and. k-3 >= kmin)then
fxz(i,j,k) = Xdxdz*(- (-fh(i-3,j,k-3)+F9*fh(i-2,j,k-3)-F45*fh(i-1,j,k-3)+F45*fh(i+1,j,k-3)-F9*fh(i+2,j,k-3)+fh(i+3,j,k-3)) &
+F9 *(-fh(i-3,j,k-2)+F9*fh(i-2,j,k-2)-F45*fh(i-1,j,k-2)+F45*fh(i+1,j,k-2)-F9*fh(i+2,j,k-2)+fh(i+3,j,k-2)) &
-F45*(-fh(i-3,j,k-1)+F9*fh(i-2,j,k-1)-F45*fh(i-1,j,k-1)+F45*fh(i+1,j,k-1)-F9*fh(i+2,j,k-1)+fh(i+3,j,k-1)) &
+F45*(-fh(i-3,j,k+1)+F9*fh(i-2,j,k+1)-F45*fh(i-1,j,k+1)+F45*fh(i+1,j,k+1)-F9*fh(i+2,j,k+1)+fh(i+3,j,k+1)) &
-F9 *(-fh(i-3,j,k+2)+F9*fh(i-2,j,k+2)-F45*fh(i-1,j,k+2)+F45*fh(i+1,j,k+2)-F9*fh(i+2,j,k+2)+fh(i+3,j,k+2)) &
+ (-fh(i-3,j,k+3)+F9*fh(i-2,j,k+3)-F45*fh(i-1,j,k+3)+F45*fh(i+1,j,k+3)-F9*fh(i+2,j,k+3)+fh(i+3,j,k+3)))
elseif(i+2 <= imax .and. i-2 >= imin .and. k+2 <= kmax .and. k-2 >= kmin)then
fxz(i,j,k) = Fdxdz*( (fh(i-2,j,k-2)-F8*fh(i-1,j,k-2)+F8*fh(i+1,j,k-2)-fh(i+2,j,k-2)) &
-F8 *(fh(i-2,j,k-1)-F8*fh(i-1,j,k-1)+F8*fh(i+1,j,k-1)-fh(i+2,j,k-1)) &
+F8 *(fh(i-2,j,k+1)-F8*fh(i-1,j,k+1)+F8*fh(i+1,j,k+1)-fh(i+2,j,k+1)) &
- (fh(i-2,j,k+2)-F8*fh(i-1,j,k+2)+F8*fh(i+1,j,k+2)-fh(i+2,j,k+2)))
elseif(i+1 <= imax .and. i-1 >= imin .and. k+1 <= kmax .and. k-1 >= kmin)then
fxz(i,j,k) = Sdxdz*(fh(i-1,j,k-1)-fh(i+1,j,k-1)-fh(i-1,j,k+1)+fh(i+1,j,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddxz
subroutine fddyz(ex,f,fyz,X,Y,Z,SYM1,SYM2,SYM3,symmetry)
implicit none
integer, intent(in ):: ex(1:3),symmetry
real*8, dimension(ex(1),ex(2),ex(3)),intent(in ):: f
real*8, dimension(ex(1),ex(2),ex(3)),intent(out):: fyz
real*8, intent(in ):: X(ex(1)),Y(ex(2)),Z(ex(3)),SYM1,SYM2,SYM3
!~~~~~~ other variables
real*8 :: dX,dY,dZ
real*8,dimension(-3:ex(1),-3:ex(2),-3:ex(3)) :: fh
real*8, dimension(3) :: SoA
integer :: imin,jmin,kmin,imax,jmax,kmax,i,j,k
real*8 :: Sdydz,Fdydz,Xdydz,Edydz
integer, parameter :: NO_SYMM = 0, EQ_SYMM = 1, OCTANT = 2
real*8, parameter :: ZEO=0.d0, ONE=1.d0, TWO=2.d0, F1o4=2.5d-1, F9=9.d0, F45=4.5d1, F128=1.28d2
real*8, parameter :: F8=8.d0, F16=1.6d1, F30=3.d1, F27=2.7d1, F270=2.7d2, F490=4.9d2,F1008=1.008d3
real*8, parameter :: F8064=8.064d3,F14350=1.435d4,THR=3.d0,F32=3.2d1,F168=1.68d2,F672=6.72d2
real*8, parameter :: F1o6=ONE/6.d0, F1o12=ONE/1.2d1, F1o144=ONE/1.44d2
real*8, parameter :: F1o180=ONE/1.8d2,F1o3600=ONE/3.6d3
real*8, parameter :: F1o5040=ONE/5.04d3,F1o705600=ONE/7.056d5
dX = X(2)-X(1)
dY = Y(2)-Y(1)
dZ = Z(2)-Z(1)
imax = ex(1)
jmax = ex(2)
kmax = ex(3)
imin = 1
jmin = 1
kmin = 1
if(Symmetry > NO_SYMM .and. dabs(Z(1)) < dZ) kmin = -3
if(Symmetry > EQ_SYMM .and. dabs(X(1)) < dX) imin = -3
if(Symmetry > EQ_SYMM .and. dabs(Y(1)) < dY) jmin = -3
SoA(1) = SYM1
SoA(2) = SYM2
SoA(3) = SYM3
call symmetry_bd(4,ex,f,fh,SoA)
Sdydz = F1o4 /( dY * dZ )
Fdydz = F1o144 /( dY * dZ )
Xdydz = F1o3600 /( dY * dZ )
Edydz = F1o705600 /( dY * dZ )
fyz = ZEO
do k=1,ex(3)-1
do j=1,ex(2)-1
do i=1,ex(1)-1
!~~~~~~ fyz
if(j+4 <= jmax .and. j-4 >= jmin .and. k+4 <= kmax .and. k-4 >= kmin)then
fyz(i,j,k) = Edydz*( THR *( THR*fh(i,j-4,k-4)-F32*fh(i,j-3,k-4)+F168*fh(i,j-2,k-4)-F672*fh(i,j-1,k-4) &
-THR*fh(i,j+4,k-4)+F32*fh(i,j+3,k-4)-F168*fh(i,j+2,k-4)+F672*fh(i,j+1,k-4)) &
-F32 *( THR*fh(i,j-4,k-3)-F32*fh(i,j-3,k-3)+F168*fh(i,j-2,k-3)-F672*fh(i,j-1,k-3) &
-THR*fh(i,j+4,k-3)+F32*fh(i,j+3,k-3)-F168*fh(i,j+2,k-3)+F672*fh(i,j+1,k-3)) &
+F168*( THR*fh(i,j-4,k-2)-F32*fh(i,j-3,k-2)+F168*fh(i,j-2,k-2)-F672*fh(i,j-1,k-2) &
-THR*fh(i,j+4,k-2)+F32*fh(i,j+3,k-2)-F168*fh(i,j+2,k-2)+F672*fh(i,j+1,k-2)) &
-F672*( THR*fh(i,j-4,k-1)-F32*fh(i,j-3,k-1)+F168*fh(i,j-2,k-1)-F672*fh(i,j-1,k-1) &
-THR*fh(i,j+4,k-1)+F32*fh(i,j+3,k-1)-F168*fh(i,j+2,k-1)+F672*fh(i,j+1,k-1)) &
+F672*( THR*fh(i,j-4,k+1)-F32*fh(i,j-3,k+1)+F168*fh(i,j-2,k+1)-F672*fh(i,j-1,k+1) &
-THR*fh(i,j+4,k+1)+F32*fh(i,j+3,k+1)-F168*fh(i,j+2,k+1)+F672*fh(i,j+1,k+1)) &
-F168*( THR*fh(i,j-4,k+2)-F32*fh(i,j-3,k+2)+F168*fh(i,j-2,k+2)-F672*fh(i,j-1,k+2) &
-THR*fh(i,j+4,k+2)+F32*fh(i,j+3,k+2)-F168*fh(i,j+2,k+2)+F672*fh(i,j+1,k+2)) &
+F32 *( THR*fh(i,j-4,k+3)-F32*fh(i,j-3,k+3)+F168*fh(i,j-2,k+3)-F672*fh(i,j-1,k+3) &
-THR*fh(i,j+4,k+3)+F32*fh(i,j+3,k+3)-F168*fh(i,j+2,k+3)+F672*fh(i,j+1,k+3)) &
-THR *( THR*fh(i,j-4,k+4)-F32*fh(i,j-3,k+4)+F168*fh(i,j-2,k+4)-F672*fh(i,j-1,k+4) &
-THR*fh(i,j+4,k+4)+F32*fh(i,j+3,k+4)-F168*fh(i,j+2,k+4)+F672*fh(i,j+1,k+4)) )
elseif(j+3 <= jmax .and. j-3 >= jmin .and. k+3 <= kmax .and. k-3 >= kmin)then
fyz(i,j,k) = Xdydz*(- (-fh(i,j-3,k-3)+F9*fh(i,j-2,k-3)-F45*fh(i,j-1,k-3)+F45*fh(i,j+1,k-3)-F9*fh(i,j+2,k-3)+fh(i,j+3,k-3)) &
+F9 *(-fh(i,j-3,k-2)+F9*fh(i,j-2,k-2)-F45*fh(i,j-1,k-2)+F45*fh(i,j+1,k-2)-F9*fh(i,j+2,k-2)+fh(i,j+3,k-2)) &
-F45*(-fh(i,j-3,k-1)+F9*fh(i,j-2,k-1)-F45*fh(i,j-1,k-1)+F45*fh(i,j+1,k-1)-F9*fh(i,j+2,k-1)+fh(i,j+3,k-1)) &
+F45*(-fh(i,j-3,k+1)+F9*fh(i,j-2,k+1)-F45*fh(i,j-1,k+1)+F45*fh(i,j+1,k+1)-F9*fh(i,j+2,k+1)+fh(i,j+3,k+1)) &
-F9 *(-fh(i,j-3,k+2)+F9*fh(i,j-2,k+2)-F45*fh(i,j-1,k+2)+F45*fh(i,j+1,k+2)-F9*fh(i,j+2,k+2)+fh(i,j+3,k+2)) &
+ (-fh(i,j-3,k+3)+F9*fh(i,j-2,k+3)-F45*fh(i,j-1,k+3)+F45*fh(i,j+1,k+3)-F9*fh(i,j+2,k+3)+fh(i,j+3,k+3)))
elseif(j+2 <= jmax .and. j-2 >= jmin .and. k+2 <= kmax .and. k-2 >= kmin)then
fyz(i,j,k) = Fdydz*( (fh(i,j-2,k-2)-F8*fh(i,j-1,k-2)+F8*fh(i,j+1,k-2)-fh(i,j+2,k-2)) &
-F8 *(fh(i,j-2,k-1)-F8*fh(i,j-1,k-1)+F8*fh(i,j+1,k-1)-fh(i,j+2,k-1)) &
+F8 *(fh(i,j-2,k+1)-F8*fh(i,j-1,k+1)+F8*fh(i,j+1,k+1)-fh(i,j+2,k+1)) &
- (fh(i,j-2,k+2)-F8*fh(i,j-1,k+2)+F8*fh(i,j+1,k+2)-fh(i,j+2,k+2)))
elseif(j+1 <= jmax .and. j-1 >= jmin .and. k+1 <= kmax .and. k-1 >= kmin)then
fyz(i,j,k) = Sdydz*(fh(i,j-1,k-1)-fh(i,j+1,k-1)-fh(i,j-1,k+1)+fh(i,j+1,k+1))
endif
enddo
enddo
enddo
return
end subroutine fddyz
#endif
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