#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 ! 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 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 ! 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 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