! old code
#if 0
! Because of overlap determination, source region is always larger than target region
#include "microdef.fh"
#ifdef Vertex
#ifdef Cell
#error Both Cell and Vertex are defined
#endif
!--------------------------------------------------------------------------------------
!
! Restrict from finner grids to coarser grids ignore the boundary point
! this routine is valid for all orders finite difference
!
! 1 2 3 4
! *---*---*---*
! ^
! COPY directly!
!--------------------------------------------------------------------------------------
subroutine restrict3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbr,uubr,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbr,uubr
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(inout):: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(in):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbr,ubr,lbrf,ubrf
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k
real*8, dimension(4,4,4) :: ya
real*8, dimension(4,4) :: tmp2
real*8, dimension(4) :: tmp1
real*8, parameter :: C1=-1.d0/1.6d1,C2=9.d0/1.6d1
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
! it's possible a iolated point for target but not for source
FD = (uubf-llbf)/(extf-1)
CD = 2*FD
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)+1
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)+1
lbr = idint((llbr-base)/CD+0.4)+1
lbrf = idint((llbr-base)/FD+0.4)+1
ubr = idint((uubr-base)/CD+0.4)+1
ubrf = idint((uubr-base)/FD+0.4)+1
!sanity check
imino=lbr(1)-lbc(1) + 1
imaxo=ubr(1)-lbc(1) + 1
jmino=lbr(2)-lbc(2) + 1
jmaxo=ubr(2)-lbc(2) + 1
kmino=lbr(3)-lbc(3) + 1
kmaxo=ubr(3)-lbc(3) + 1
imini=lbrf(1)-lbf(1) + 1
imaxi=ubrf(1)-lbf(1) + 1
jmini=lbrf(2)-lbf(2) + 1
jmaxi=ubrf(2)-lbf(2) + 1
kmini=lbrf(3)-lbf(3) + 1
kmaxi=ubrf(3)-lbf(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extc(1).or.jmaxo.gt.extc(2).or.kmaxo.gt.extc(3).or.&
imaxi.gt.extf(1).or.jmaxi.gt.extf(2).or.kmaxi.gt.extf(3))then
write(*,*)"error in restrict for"
write(*,*)"mino = ",imino,jmino,kmino
write(*,*)"maxo = ",imaxo,jmaxo,kmaxo
write(*,*)"extc = ",extc
write(*,*)"CD = ",CD
write(*,*)"mini = ",imini,jmini,kmini
write(*,*)"maxi = ",imaxi,jmaxi,kmaxi
write(*,*)"extf = ",extf
write(*,*)"FD = ",FD
write(*,*)"from"
write(*,*)lbf,ubf,extf
write(*,*)"to"
write(*,*)lbc,ubc,extc
write(*,*)"want"
write(*,*)lbr,ubr,lbrf,ubrf
write(*,*)"llbf = ",llbf
write(*,*)"uubf = ",uubf
write(*,*)"llbc = ",llbc
write(*,*)"uubc = ",uubc
write(*,*)"llbr = ",llbr
write(*,*)"uubr = ",uubr
stop
endif
!~~~~~~> restriction start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to fine level reference
!|*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*|
!|x===============x===============x===============x========|
cxI = 2*(cxI+lbc-1) - 1
! change to array index
cxI = cxI - lbf + 1
func(i,j,k)= funf(cxI(1),cxI(2),cxI(3))
enddo
enddo
enddo
return
end subroutine restrict3
#endif
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! for different finite difference order usage
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
#if (ghost_width == 2)
! second order code
#ifdef Vertex
#ifdef Cell
#error Both Cell and Vertex are defined
#endif
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 4 points, 3rd order interpolation
! 1 2 3 4
! *---*---*---*
! ^
! f=-1/16*f_1 + 9/16*f_2
! -1/16*f_4 + 9/16*f_3
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(4,4,4) :: ya
real*8, dimension(4,4) :: tmp2
real*8, dimension(4) :: tmp1
real*8, parameter :: C1=-1.d0/16,C2=9.d0/16
real*8, parameter :: C4=C1,C3=C2
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
! it's possible a iolated point for target but not for source
CD = (uubc-llbc)/(extc-1)
FD = CD/2
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)+1
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)+1
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)+1
ubpc = idint((uubp-base)/CD+0.4)+1
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-1.or.jmaxi.gt.extc(2)-1.or.kmaxi.gt.extc(3)-1)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
if(imini.lt.1) write(*,*)"imini = ",imini
if(jmini.lt.1) write(*,*)"jmini = ",jmini
if(kmini.lt.1) write(*,*)"kmini = ",kmini
if(imino.lt.1) write(*,*)"imino = ",imino
if(jmino.lt.1) write(*,*)"jmino = ",jmino
if(kmino.lt.1) write(*,*)"kmino = ",kmino
if(imaxi.gt.extc(1)) write(*,*)"imaxi = ",imaxi,"extc(1) = ",extc(1)
if(jmaxi.gt.extc(2)) write(*,*)"jmaxi = ",jmaxi,"extc(2) = ",extc(2)
if(kmaxi.gt.extc(3)) write(*,*)"kmaxi = ",kmaxi,"extc(3) = ",extc(3)
if(imaxo.gt.extf(1)) write(*,*)"imaxo = ",imaxo,"extf(1) = ",extf(1)
if(jmaxo.gt.extf(2)) write(*,*)"jmaxo = ",jmaxo,"extf(2) = ",extf(2)
if(kmaxo.gt.extf(3)) write(*,*)"kmaxo = ",kmaxo,"extf(3) = ",extf(3)
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
! change to coarse level reference
!|*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*|
!|x===============x===============x===============x========|
! if(i/2*2 == i)then
! cxI(1) = (i+lbf(1)-1)/2
! else
! cxI(1) = (i+lbf(1)-1)/2+1
! endif
! if(j/2*2 == j)then
! cxI(2) = (j+lbf(2)-1)/2
! else
! cxI(2) = (j+lbf(2)-1)/2+1
! endif
! if(k/2*2 == k)then
! cxI(3) = (k+lbf(3)-1)/2
! else
! cxI(3) = (k+lbf(3)-1)/2+1
! endif
! above code segment is equivalent to
cxI(1) = i
cxI(2) = j
cxI(3) = k
cxI = (cxI+lbf)/2
! change to array index
cxI = cxI - lbc + 1
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(any(cxI+2 > extc)) write(*,*)"error in prolong"
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3))
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,2)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= tmp2(:,2)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3))
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,2)
endif
tmp1= tmp2(:,2)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= tmp1(2)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3))
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,2)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= tmp1(2)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= tmp2(:,2)
funf(i,j,k)= tmp1(2)
else
funf(i,j,k)= func(cxI(1),cxI(2),cxI(3))
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#ifdef Cell
!--------------------------------------------------------------------------------------
!
! Restrict from finner grids to coarser grids ignore the boundary point
!
! 4 points, 3rd order interpolation
! 1 2 3 4
! *---*---*---*
! ^
! f=-1/16*(f_1+f_4) + 9/16*(f_2+f_3)
!--------------------------------------------------------------------------------------
subroutine restrict3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbr,uubr,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in)::wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbr,uubr
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(inout):: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(in):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbr,ubr,lbrf,ubrf
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k
real*8, dimension(4,4,4) :: ya
real*8, dimension(4,4) :: tmp2
real*8, dimension(4) :: tmp1
real*8, parameter :: C1=-1.d0/1.6d1,C2=9.d0/1.6d1
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
! note say base = 0, llbf = 0, uubf = 2
! llbf->1 and uubf->2
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbr = idint((llbr-base)/CD+0.4)+1
lbrf = idint((llbr-base)/FD+0.4)+1
ubr = idint((uubr-base)/CD+0.4)
ubrf = idint((uubr-base)/FD+0.4)
!sanity check
imino=lbr(1)-lbc(1) + 1
imaxo=ubr(1)-lbc(1) + 1
jmino=lbr(2)-lbc(2) + 1
jmaxo=ubr(2)-lbc(2) + 1
kmino=lbr(3)-lbc(3) + 1
kmaxo=ubr(3)-lbc(3) + 1
imini=lbrf(1)-lbf(1) + 1
imaxi=ubrf(1)-lbf(1) + 1
jmini=lbrf(2)-lbf(2) + 1
jmaxi=ubrf(2)-lbf(2) + 1
kmini=lbrf(3)-lbf(3) + 1
kmaxi=ubrf(3)-lbf(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extc(1).or.jmaxo.gt.extc(2).or.kmaxo.gt.extc(3).or.&
imaxi.gt.extf(1)-1.or.jmaxi.gt.extf(2)-1.or.kmaxi.gt.extf(3)-1)then
write(*,*)"error in restrict for"
write(*,*)"from"
write(*,*)lbf,ubf
write(*,*)"to"
write(*,*)lbc,ubc
write(*,*)"want"
write(*,*)lbr,ubr,lbrf,ubrf
write(*,*)"llbf = ",llbf
write(*,*)"uubf = ",uubf
write(*,*)"llbc = ",llbc
write(*,*)"uubc = ",uubc
write(*,*)"llbr = ",llbr
write(*,*)"uubr = ",uubr
write(*,*)"base = ",base
stop
endif
!~~~~~~> restriction start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to fine level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = 2*(cxI+lbc-1) - 1
! change to array index
cxI = cxI - lbf + 1
if(any(cxI+2 > extf)) write(*,*)"error in restrict"
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*(funf(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+funf(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2))&
+C2*(funf(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+funf(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1))
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extf,funf,funf,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"restrict3 position index: ",i+lbc(1)-1,j+lbc(2)-1,k+lbc(3)-1
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,4))+C2*(ya(:,:,2)+ya(:,:,3))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,4))+C2*(tmp2(:,2)+tmp2(:,3))
func(i,j,k)= C1*(tmp1(1)+tmp1(4))+C2*(tmp1(2)+tmp1(3))
enddo
enddo
enddo
return
end subroutine restrict3
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 4 points, 3rd order interpolation
! 1 2 3 4
! *---*---*---*
! ^
! f=-7/128*f_1 + 105/128*f_2
! -5/128*f_4 + 35/128*f_3
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(4,4,4) :: ya
real*8, dimension(4,4) :: tmp2
real*8, dimension(4) :: tmp1
real*8, parameter :: C1=-7.d0/1.28d2,C2=1.05d2/1.28d2
real*8, parameter :: C4=-5.d0/1.28d2,C3= 3.5d1/1.28d2
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)
ubpc = idint((uubp-base)/CD+0.4)
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-1.or.jmaxi.gt.extc(2)-1.or.kmaxi.gt.extc(3)-1)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(any(cxI+2 > extc)) write(*,*)"error in prolong"
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C4*ya(:,:,1)+C3*ya(:,:,2)+C2*ya(:,:,3)+C1*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C4*tmp2(:,1)+C3*tmp2(:,2)+C2*tmp2(:,3)+C1*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C4*ya(:,:,1)+C3*ya(:,:,2)+C2*ya(:,:,3)+C1*ya(:,:,4)
endif
tmp1= C4*tmp2(:,1)+C3*tmp2(:,2)+C2*tmp2(:,3)+C1*tmp2(:,4)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C4*tmp1(1)+C3*tmp1(2)+C2*tmp1(3)+C1*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C4*ya(:,:,1)+C3*ya(:,:,2)+C2*ya(:,:,3)+C1*ya(:,:,4)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)
funf(i,j,k)= C4*tmp1(1)+C3*tmp1(2)+C2*tmp1(3)+C1*tmp1(4)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)
endif
tmp1= C4*tmp2(:,1)+C3*tmp2(:,2)+C2*tmp2(:,3)+C1*tmp2(:,4)
funf(i,j,k)= C4*tmp1(1)+C3*tmp1(2)+C2*tmp1(3)+C1*tmp1(4)
else
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= C4*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
C3*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
C2*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
C1*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C4*ya(:,:,1)+C3*ya(:,:,2)+C2*ya(:,:,3)+C1*ya(:,:,4)
endif
tmp1= C4*tmp2(:,1)+C3*tmp2(:,2)+C2*tmp2(:,3)+C1*tmp2(:,4)
funf(i,j,k)= C4*tmp1(1)+C3*tmp1(2)+C2*tmp1(3)+C1*tmp1(4)
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
subroutine prolong3new(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(4,4,4) :: ya
real*8, dimension(4,4) :: tmp2
real*8, dimension(4) :: tmp1
real*8, parameter :: C1=-7.d0/1.28d2,C2=1.05d2/1.28d2
real*8, parameter :: C4=-5.d0/1.28d2,C3= 3.5d1/1.28d2
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
real*8,dimension(3,4) :: CC
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)
ubpc = idint((uubp-base)/CD+0.4)
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-2.or.jmaxi.gt.extc(2)-2.or.kmaxi.gt.extc(3)-2)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
return
endif
!~~~~~~> prolongation start...
do i=1,3
if(lbp(i)/2*2 == lbp(i))then
CC(i,1) = C1
CC(i,2) = C2
CC(i,3) = C3
CC(i,4) = C4
else
CC(i,1) = C4
CC(i,2) = C3
CC(i,3) = C2
CC(i,4) = C1
endif
enddo
do k = kmino,kmaxo,2
do j = jmino,jmaxo,2
do i = imino,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,1)*ya(:,:,1)+CC(3,2)*ya(:,:,2)+CC(3,3)*ya(:,:,3)+CC(3,4)*ya(:,:,4)
endif
tmp1= CC(2,1)*tmp2(:,1)+CC(2,2)*tmp2(:,2)+CC(2,3)*tmp2(:,3)+CC(2,4)*tmp2(:,4)
funf(i,j,k)= CC(1,1)*tmp1(1)+CC(1,2)*tmp1(2)+CC(1,3)*tmp1(3)+CC(1,4)*tmp1(4)
enddo
enddo
enddo
do k = kmino+1,kmaxo,2
do j = jmino,jmaxo,2
do i = imino,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,4)*ya(:,:,1)+CC(3,3)*ya(:,:,2)+CC(3,2)*ya(:,:,3)+CC(3,1)*ya(:,:,4)
endif
tmp1= CC(2,1)*tmp2(:,1)+CC(2,2)*tmp2(:,2)+CC(2,3)*tmp2(:,3)+CC(2,4)*tmp2(:,4)
funf(i,j,k)= CC(1,1)*tmp1(1)+CC(1,2)*tmp1(2)+CC(1,3)*tmp1(3)+CC(1,4)*tmp1(4)
enddo
enddo
enddo
do k = kmino,kmaxo,2
do j = jmino+1,jmaxo,2
do i = imino,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,1)*ya(:,:,1)+CC(3,2)*ya(:,:,2)+CC(3,3)*ya(:,:,3)+CC(3,4)*ya(:,:,4)
endif
tmp1= CC(2,4)*tmp2(:,1)+CC(2,3)*tmp2(:,2)+CC(2,2)*tmp2(:,3)+CC(2,1)*tmp2(:,4)
funf(i,j,k)= CC(1,1)*tmp1(1)+CC(1,2)*tmp1(2)+CC(1,3)*tmp1(3)+CC(1,4)*tmp1(4)
enddo
enddo
enddo
do k = kmino+1,kmaxo,2
do j = jmino+1,jmaxo,2
do i = imino,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,4)*ya(:,:,1)+CC(3,3)*ya(:,:,2)+CC(3,2)*ya(:,:,3)+CC(3,1)*ya(:,:,4)
endif
tmp1= CC(2,4)*tmp2(:,1)+CC(2,3)*tmp2(:,2)+CC(2,2)*tmp2(:,3)+CC(2,1)*tmp2(:,4)
funf(i,j,k)= CC(1,1)*tmp1(1)+CC(1,2)*tmp1(2)+CC(1,3)*tmp1(3)+CC(1,4)*tmp1(4)
enddo
enddo
enddo
do k = kmino,kmaxo,2
do j = jmino,jmaxo,2
do i = imino+1,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,1)*ya(:,:,1)+CC(3,2)*ya(:,:,2)+CC(3,3)*ya(:,:,3)+CC(3,4)*ya(:,:,4)
endif
tmp1= CC(2,1)*tmp2(:,1)+CC(2,2)*tmp2(:,2)+CC(2,3)*tmp2(:,3)+CC(2,4)*tmp2(:,4)
funf(i,j,k)= CC(1,4)*tmp1(1)+CC(1,3)*tmp1(2)+CC(1,2)*tmp1(3)+CC(1,1)*tmp1(4)
enddo
enddo
enddo
do k = kmino+1,kmaxo,2
do j = jmino,jmaxo,2
do i = imino+1,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,4)*ya(:,:,1)+CC(3,3)*ya(:,:,2)+CC(3,2)*ya(:,:,3)+CC(3,1)*ya(:,:,4)
endif
tmp1= CC(2,1)*tmp2(:,1)+CC(2,2)*tmp2(:,2)+CC(2,3)*tmp2(:,3)+CC(2,4)*tmp2(:,4)
funf(i,j,k)= CC(1,4)*tmp1(1)+CC(1,3)*tmp1(2)+CC(1,2)*tmp1(3)+CC(1,1)*tmp1(4)
enddo
enddo
enddo
do k = kmino,kmaxo,2
do j = jmino+1,jmaxo,2
do i = imino+1,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,1)*ya(:,:,1)+CC(3,2)*ya(:,:,2)+CC(3,3)*ya(:,:,3)+CC(3,4)*ya(:,:,4)
endif
tmp1= CC(2,4)*tmp2(:,1)+CC(2,3)*tmp2(:,2)+CC(2,2)*tmp2(:,3)+CC(2,1)*tmp2(:,4)
funf(i,j,k)= CC(1,4)*tmp1(1)+CC(1,3)*tmp1(2)+CC(1,2)*tmp1(3)+CC(1,1)*tmp1(4)
enddo
enddo
enddo
do k = kmino+1,kmaxo,2
do j = jmino+1,jmaxo,2
do i = imino+1,imaxo,2
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>1.and.cxI(2)>1.and.cxI(3)>1)then
tmp2= CC(3,4)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)-1)+&
CC(3,3)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3) )+&
CC(3,2)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+1)+&
CC(3,1)*func(cxI(1)-1:cxI(1)+2,cxI(2)-1:cxI(2)+2,cxI(3)+2)
else
cxB=cxI-1
cxT=cxI+2
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,4,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= CC(3,4)*ya(:,:,1)+CC(3,3)*ya(:,:,2)+CC(3,2)*ya(:,:,3)+CC(3,1)*ya(:,:,4)
endif
tmp1= CC(2,4)*tmp2(:,1)+CC(2,3)*tmp2(:,2)+CC(2,2)*tmp2(:,3)+CC(2,1)*tmp2(:,4)
funf(i,j,k)= CC(1,4)*tmp1(1)+CC(1,3)*tmp1(2)+CC(1,2)*tmp1(3)+CC(1,1)*tmp1(4)
enddo
enddo
enddo
return
end subroutine prolong3new
#else
#error Not define Vertex nor Cell
#endif
#endif
#elif (ghost_width == 3)
! fourth order code
#ifdef Vertex
#ifdef Cell
#error Both Cell and Vertex are defined
#endif
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 6 points, 5th order interpolation
! 1 2 3 4 5 6
! *---*---*---*---*---*
! ^
! f=3/256*(f_1+f_6) - 25/256*(f_2+f_5) + 75/128*(f_3+f_4)
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(6,6) :: tmp2
real*8, dimension(6) :: tmp1
real*8, parameter :: C1=3.d0/2.56d2,C2=-2.5d1/2.56d2,C3=7.5d1/1.28d2
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
real*8, dimension(-1:extc(1),-1:extc(2),-1:extc(3)) :: funcc
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
! it's possible a iolated point for target but not for source
CD = (uubc-llbc)/(extc-1)
FD = CD/2
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)+1
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)+1
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)+1
ubpc = idint((uubp-base)/CD+0.4)+1
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-2.or.jmaxi.gt.extc(2)-2.or.kmaxi.gt.extc(3)-2)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
if(imini.lt.1) write(*,*)"imini = ",imini
if(jmini.lt.1) write(*,*)"jmini = ",jmini
if(kmini.lt.1) write(*,*)"kmini = ",kmini
if(imino.lt.1) write(*,*)"imino = ",imino
if(jmino.lt.1) write(*,*)"jmino = ",jmino
if(kmino.lt.1) write(*,*)"kmino = ",kmino
if(imaxi.gt.extc(1)) write(*,*)"imaxi = ",imaxi,"extc(1) = ",extc(1)
if(jmaxi.gt.extc(2)) write(*,*)"jmaxi = ",jmaxi,"extc(2) = ",extc(2)
if(kmaxi.gt.extc(3)) write(*,*)"kmaxi = ",kmaxi,"extc(3) = ",extc(3)
if(imaxo.gt.extf(1)) write(*,*)"imaxo = ",imaxo,"extf(1) = ",extf(1)
if(jmaxo.gt.extf(2)) write(*,*)"jmaxo = ",jmaxo,"extf(2) = ",extf(2)
if(kmaxo.gt.extf(3)) write(*,*)"kmaxo = ",kmaxo,"extf(3) = ",extf(3)
return
endif
call symmetry_bd(2,extc,func,funcc,SoA)
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
! change to coarse level reference v
!|*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*|
!|x===============x===============x===============x===============x===============x|
cxI(1) = i
cxI(2) = j
cxI(3) = k
cxI = (cxI+lbf)/2
! change to array index
cxI = cxI - lbc + 1
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(any(cxI+3 > extc)) write(*,*)"error in prolong"
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
tmp2= C1*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3))&
+C2*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2))&
+C3*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1))
tmp1= C1*(tmp2(:,1)+tmp2(:,6))+C2*(tmp2(:,2)+tmp2(:,5))+C3*(tmp2(:,3)+tmp2(:,4))
funf(i,j,k)= C1*(tmp1(1)+tmp1(6))+C2*(tmp1(2)+tmp1(5))+C3*(tmp1(3)+tmp1(4))
else
tmp2= funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3))
tmp1= C1*(tmp2(:,1)+tmp2(:,6))+C2*(tmp2(:,2)+tmp2(:,5))+C3*(tmp2(:,3)+tmp2(:,4))
funf(i,j,k)= C1*(tmp1(1)+tmp1(6))+C2*(tmp1(2)+tmp1(5))+C3*(tmp1(3)+tmp1(4))
endif
else
if(kk/2*2==kk)then
tmp2= C1*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3))&
+C2*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2))&
+C3*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1))
tmp1= tmp2(:,3)
funf(i,j,k)= C1*(tmp1(1)+tmp1(6))+C2*(tmp1(2)+tmp1(5))+C3*(tmp1(3)+tmp1(4))
else
tmp2= funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3))
tmp1= tmp2(:,3)
funf(i,j,k)= C1*(tmp1(1)+tmp1(6))+C2*(tmp1(2)+tmp1(5))+C3*(tmp1(3)+tmp1(4))
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
tmp2= C1*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3))&
+C2*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2))&
+C3*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1))
tmp1= C1*(tmp2(:,1)+tmp2(:,6))+C2*(tmp2(:,2)+tmp2(:,5))+C3*(tmp2(:,3)+tmp2(:,4))
funf(i,j,k)= tmp1(3)
else
tmp2= funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3))
tmp1= C1*(tmp2(:,1)+tmp2(:,6))+C2*(tmp2(:,2)+tmp2(:,5))+C3*(tmp2(:,3)+tmp2(:,4))
funf(i,j,k)= tmp1(3)
endif
else
if(kk/2*2==kk)then
tmp2= C1*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3))&
+C2*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2))&
+C3*(funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1))
tmp1= tmp2(:,3)
funf(i,j,k)= tmp1(3)
else
funf(i,j,k)= funcc(cxI(1),cxI(2),cxI(3))
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#ifdef Cell
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 6 points, 5th order interpolation
! 1 2 3 4 5 6
! *---*---*---*---*---*
! ^
! f=77/8192*f_1 - 693/8192*f_2 + 3465/4096*f_3 +
! 63/8192*f_6 - 495/8192*f_5 + 1155/4096*f_4
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
! when if=1 -> ic=0, this is different to vertex center grid
real*8, dimension(-2:extc(1),-2:extc(2),-2:extc(3)) :: funcc
integer,dimension(3) :: cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(6,6) :: tmp2
real*8, dimension(6) :: tmp1
real*8, parameter :: C1=7.7d1/8.192d3,C2=-6.93d2/8.192d3,C3=3.465d3/4.096d3
real*8, parameter :: C6=6.3d1/8.192d3,C5=-4.95d2/8.192d3,C4=1.155d3/4.096d3
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)
ubpc = idint((uubp-base)/CD+0.4)
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-2.or.jmaxi.gt.extc(2)-2.or.kmaxi.gt.extc(3)-2)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
return
endif
call symmetry_bd(3,extc,func,funcc,SoA)
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
if(any(cxI+3 > extc)) write(*,*)"error in prolong"
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
else
tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
endif
else
if(kk/2*2==kk)then
tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
else
tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5*tmp1(5)+C6*tmp1(6)
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
else
tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5*tmp2(:,5)+C6*tmp2(:,6)
funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
endif
else
if(kk/2*2==kk)then
tmp2= C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
else
tmp2= C6*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+&
C5*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+&
C4*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+&
C3*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1)+&
C2*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2)+&
C1*funcc(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3)
tmp1= C6*tmp2(:,1)+C5*tmp2(:,2)+C4*tmp2(:,3)+C3*tmp2(:,4)+C2*tmp2(:,5)+C1*tmp2(:,6)
funf(i,j,k)= C6*tmp1(1)+C5*tmp1(2)+C4*tmp1(3)+C3*tmp1(4)+C2*tmp1(5)+C1*tmp1(6)
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
!--------------------------------------------------------------------------
!
! Restrict from finner grids to coarser grids ignore the boundary point
!
! 6 points, 5th order interpolation
! 1 2 3 4 5 6
! *---*---*---*---*---*
! ^
! f=3/256*(f_1+f_6) - 25/256*(f_2+f_5) + 75/128*(f_3+f_4)
!--------------------------------------------------------------------------
subroutine restrict3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbr,uubr,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in)::wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbr,uubr
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(inout):: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(in):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbr,ubr,lbrf,ubrf
real*8, dimension(-1:extf(1),-1:extf(2),-1:extf(3)):: funff
integer,dimension(3) :: cxI
integer :: i,j,k
real*8, dimension(6,6) :: tmp2
real*8, dimension(6) :: tmp1
real*8, parameter :: C1=3.d0/2.56d2,C2=-2.5d1/2.56d2,C3=7.5d1/1.28d2
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
! note say base = 0, llbf = 0, uubf = 2
! llbf->1 and uubf->2
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbr = idint((llbr-base)/CD+0.4)+1
lbrf = idint((llbr-base)/FD+0.4)+1
ubr = idint((uubr-base)/CD+0.4)
ubrf = idint((uubr-base)/FD+0.4)
!sanity check
imino=lbr(1)-lbc(1) + 1
imaxo=ubr(1)-lbc(1) + 1
jmino=lbr(2)-lbc(2) + 1
jmaxo=ubr(2)-lbc(2) + 1
kmino=lbr(3)-lbc(3) + 1
kmaxo=ubr(3)-lbc(3) + 1
imini=lbrf(1)-lbf(1) + 1
imaxi=ubrf(1)-lbf(1) + 1
jmini=lbrf(2)-lbf(2) + 1
jmaxi=ubrf(2)-lbf(2) + 1
kmini=lbrf(3)-lbf(3) + 1
kmaxi=ubrf(3)-lbf(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extc(1).or.jmaxo.gt.extc(2).or.kmaxo.gt.extc(3).or.&
imaxi.gt.extf(1)-2.or.jmaxi.gt.extf(2)-2.or.kmaxi.gt.extf(3)-2)then
write(*,*)"error in restrict for"
write(*,*)"from"
write(*,*)lbf,ubf
write(*,*)"to"
write(*,*)lbc,ubc
write(*,*)"want"
write(*,*)lbr,ubr,lbrf,ubrf
write(*,*)"llbf = ",llbf
write(*,*)"uubf = ",uubf
write(*,*)"llbc = ",llbc
write(*,*)"uubc = ",uubc
write(*,*)"llbr = ",llbr
write(*,*)"uubr = ",uubr
write(*,*)"base = ",base
stop
endif
call symmetry_bd(2,extf,funf,funff,SoA)
!~~~~~~> restriction start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to fine level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = 2*(cxI+lbc-1) - 1
! change to array index
cxI = cxI - lbf + 1
if(any(cxI+3 > extf)) write(*,*)"error in restrict"
tmp2= C1*(funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-2)+funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+3))&
+C2*(funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)-1)+funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+2))&
+C3*(funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3) )+funff(cxI(1)-2:cxI(1)+3,cxI(2)-2:cxI(2)+3,cxI(3)+1))
tmp1= C1*(tmp2(:,1)+tmp2(:,6))+C2*(tmp2(:,2)+tmp2(:,5))+C3*(tmp2(:,3)+tmp2(:,4))
func(i,j,k)= C1*(tmp1(1)+tmp1(6))+C2*(tmp1(2)+tmp1(5))+C3*(tmp1(3)+tmp1(4))
enddo
enddo
enddo
return
end subroutine restrict3
#else
#error Not define Vertex nor Cell
#endif
#endif
#elif (ghost_width == 4)
! sixth order code
#ifdef Vertex
#ifdef Cell
#error Both Cell and Vertex are defined
#endif
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 8 points, 7th order interpolation
! 1 2 3 4 5 6 7 8
! *---*---*---*---*---*---*---*
! ^
! f=-5/2048*(f_1+f_8) + 49/2048*(f_2+f_7) - 245/2048*(f_3+f_6) + 1225/2048*(f_4+f_5)
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(8,8,8) :: ya
real*8, dimension(8,8) :: tmp2
real*8, dimension(8) :: tmp1
real*8, parameter :: C1=-5.d0/2.048d3,C2=4.9d1/2.048d3,C3=-2.45d2/2.048d3,C4=1.225d3/2.048d3
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
! it's possible a iolated point for target but not for source
CD = (uubc-llbc)/(extc-1)
FD = CD/2
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)+1
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)+1
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)+1
ubpc = idint((uubp-base)/CD+0.4)+1
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-3.or.jmaxi.gt.extc(2)-3.or.kmaxi.gt.extc(3)-3)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
if(imini.lt.1) write(*,*)"imini = ",imini
if(jmini.lt.1) write(*,*)"jmini = ",jmini
if(kmini.lt.1) write(*,*)"kmini = ",kmini
if(imino.lt.1) write(*,*)"imino = ",imino
if(jmino.lt.1) write(*,*)"jmino = ",jmino
if(kmino.lt.1) write(*,*)"kmino = ",kmino
if(imaxi.gt.extc(1)) write(*,*)"imaxi = ",imaxi,"extc(1) = ",extc(1)
if(jmaxi.gt.extc(2)) write(*,*)"jmaxi = ",jmaxi,"extc(2) = ",extc(2)
if(kmaxi.gt.extc(3)) write(*,*)"kmaxi = ",kmaxi,"extc(3) = ",extc(3)
if(imaxo.gt.extf(1)) write(*,*)"imaxo = ",imaxo,"extf(1) = ",extf(1)
if(jmaxo.gt.extf(2)) write(*,*)"jmaxo = ",jmaxo,"extf(2) = ",extf(2)
if(kmaxo.gt.extf(3)) write(*,*)"kmaxo = ",kmaxo,"extf(3) = ",extf(3)
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
! change to coarse level reference v
!|*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*|
!|x===============x===============x===============x===============x===============x===============x===============x|
cxI(1) = i
cxI(2) = j
cxI(3) = k
cxI = (cxI+lbf)/2
! change to array index
cxI = cxI - lbc + 1
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(any(cxI+4 > extc)) write(*,*)"error in prolong"
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4))&
+C2*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3))&
+C3*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2))&
+C4*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,8))+C2*(ya(:,:,2)+ya(:,:,7))+C3*(ya(:,:,3)+ya(:,:,6))+C4*(ya(:,:,4)+ya(:,:,5))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,8))+C2*(tmp2(:,2)+tmp2(:,7))+C3*(tmp2(:,3)+tmp2(:,6))+C4*(tmp2(:,4)+tmp2(:,5))
funf(i,j,k)= C1*(tmp1(1)+tmp1(8))+C2*(tmp1(2)+tmp1(7))+C3*(tmp1(3)+tmp1(6))+C4*(tmp1(4)+tmp1(5))
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= ya(:,:,4)
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,8))+C2*(tmp2(:,2)+tmp2(:,7))+C3*(tmp2(:,3)+tmp2(:,6))+C4*(tmp2(:,4)+tmp2(:,5))
funf(i,j,k)= C1*(tmp1(1)+tmp1(8))+C2*(tmp1(2)+tmp1(7))+C3*(tmp1(3)+tmp1(6))+C4*(tmp1(4)+tmp1(5))
endif
else
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4))&
+C2*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3))&
+C3*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2))&
+C4*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,8))+C2*(ya(:,:,2)+ya(:,:,7))+C3*(ya(:,:,3)+ya(:,:,6))+C4*(ya(:,:,4)+ya(:,:,5))
endif
tmp1= tmp2(:,4)
funf(i,j,k)= C1*(tmp1(1)+tmp1(8))+C2*(tmp1(2)+tmp1(7))+C3*(tmp1(3)+tmp1(6))+C4*(tmp1(4)+tmp1(5))
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= ya(:,:,4)
endif
tmp1= tmp2(:,4)
funf(i,j,k)= C1*(tmp1(1)+tmp1(8))+C2*(tmp1(2)+tmp1(7))+C3*(tmp1(3)+tmp1(6))+C4*(tmp1(4)+tmp1(5))
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4))&
+C2*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3))&
+C3*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2))&
+C4*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,8))+C2*(ya(:,:,2)+ya(:,:,7))+C3*(ya(:,:,3)+ya(:,:,6))+C4*(ya(:,:,4)+ya(:,:,5))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,8))+C2*(tmp2(:,2)+tmp2(:,7))+C3*(tmp2(:,3)+tmp2(:,6))+C4*(tmp2(:,4)+tmp2(:,5))
funf(i,j,k)= tmp1(4)
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= ya(:,:,4)
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,8))+C2*(tmp2(:,2)+tmp2(:,7))+C3*(tmp2(:,3)+tmp2(:,6))+C4*(tmp2(:,4)+tmp2(:,5))
funf(i,j,k)= tmp1(4)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4))&
+C2*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3))&
+C3*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2))&
+C4*(func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-1)*FD(1),llbf(2)+(j-1)*FD(2),llbf(3)+(k-1)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,8))+C2*(ya(:,:,2)+ya(:,:,7))+C3*(ya(:,:,3)+ya(:,:,6))+C4*(ya(:,:,4)+ya(:,:,5))
endif
tmp1= tmp2(:,4)
funf(i,j,k)= tmp1(4)
else
funf(i,j,k)= func(cxI(1),cxI(2),cxI(3))
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#ifdef Cell
!--------------------------------------------------------------------------------------
!
! Restrict from finner grids to coarser grids ignore the boundary point
!
! 8 points, 7th order interpolation
! 1 2 3 4 5 6 7 8
! *---*---*---*---*---*---*---*
! ^
! f=-5/2048*(f_1+f_8) + 49/2048*(f_2+f_7) - 245/2048*(f_3+f_6) + 1225/2048*(f_4+f_5)
!--------------------------------------------------------------------------------------
subroutine restrict3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbr,uubr,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in)::wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbr,uubr
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(inout):: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(in):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbr,ubr,lbrf,ubrf
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k
real*8, dimension(8,8,8) :: ya
real*8, dimension(8,8) :: tmp2
real*8, dimension(8) :: tmp1
real*8, parameter :: C1=-5.d0/2.048d3,C2=4.9d1/2.048d3,C3=-2.45d2/2.048d3,C4=1.225d3/2.048d3
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
! note say base = 0, llbf = 0, uubf = 2
! llbf->1 and uubf->2
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbr = idint((llbr-base)/CD+0.4)+1
lbrf = idint((llbr-base)/FD+0.4)+1
ubr = idint((uubr-base)/CD+0.4)
ubrf = idint((uubr-base)/FD+0.4)
!sanity check
imino=lbr(1)-lbc(1) + 1
imaxo=ubr(1)-lbc(1) + 1
jmino=lbr(2)-lbc(2) + 1
jmaxo=ubr(2)-lbc(2) + 1
kmino=lbr(3)-lbc(3) + 1
kmaxo=ubr(3)-lbc(3) + 1
imini=lbrf(1)-lbf(1) + 1
imaxi=ubrf(1)-lbf(1) + 1
jmini=lbrf(2)-lbf(2) + 1
jmaxi=ubrf(2)-lbf(2) + 1
kmini=lbrf(3)-lbf(3) + 1
kmaxi=ubrf(3)-lbf(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extc(1).or.jmaxo.gt.extc(2).or.kmaxo.gt.extc(3).or.&
imaxi.gt.extf(1)-3.or.jmaxi.gt.extf(2)-3.or.kmaxi.gt.extf(3)-3)then
!-3 is because
!|-x---x-|-x---x-|-x---
!|- -*- -|
write(*,*)"error in restrict for"
write(*,*)"from"
write(*,*)lbf,ubf
write(*,*)"to"
write(*,*)lbc,ubc
write(*,*)"want"
write(*,*)lbr,ubr,lbrf,ubrf
write(*,*)"llbf = ",llbf
write(*,*)"uubf = ",uubf
write(*,*)"llbc = ",llbc
write(*,*)"uubc = ",uubc
write(*,*)"llbr = ",llbr
write(*,*)"uubr = ",uubr
write(*,*)"base = ",base
stop
endif
!~~~~~~> restriction start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to fine level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = 2*(cxI+lbc-1) - 1
! change to array index
cxI = cxI - lbf + 1
if(any(cxI+4 > extf)) write(*,*)"error in restrict"
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*(funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4))&
+C2*(funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3))&
+C3*(funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2))&
+C4*(funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+funf(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1))
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extf,funf,funf,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"restrict3 position index: ",i+lbc(1)-1,j+lbc(2)-1,k+lbc(3)-1
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,8))+C2*(ya(:,:,2)+ya(:,:,7))+C3*(ya(:,:,3)+ya(:,:,6))+C4*(ya(:,:,4)+ya(:,:,5))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,8))+C2*(tmp2(:,2)+tmp2(:,7))+C3*(tmp2(:,3)+tmp2(:,6))+C4*(tmp2(:,4)+tmp2(:,5))
func(i,j,k)= C1*(tmp1(1)+tmp1(8))+C2*(tmp1(2)+tmp1(7))+C3*(tmp1(3)+tmp1(6))+C4*(tmp1(4)+tmp1(5))
enddo
enddo
enddo
return
end subroutine restrict3
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 8 points, 7th order interpolation
! 1 2 3 4 5 6 7 8
! *---*---*---*---*---*---*---*
! ^
! f=-495/262144*f_1 + 5005/262144*f_2 - 27027/262144*f_3 + 225225/262144*f_4
! -429/262144*f_8 + 4095/262144*f_7 - 19305/262144*f_6 + 75075/262144*f_5
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(8,8,8) :: ya
real*8, dimension(8,8) :: tmp2
real*8, dimension(8) :: tmp1
real*8, parameter :: C1=-4.95d2/2.62144d5,C2=5.005d3/2.62144d5,C3=-2.7027d4/2.62144d5,C4=2.25225d5/2.62144d5
real*8, parameter :: C8=-4.29d2/2.62144d5,C7=4.095d3/2.62144d5,C6=-1.9305d4/2.62144d5,C5=7.5075d4/2.62144d5
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)
ubpc = idint((uubp-base)/CD+0.4)
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-3.or.jmaxi.gt.extc(2)-3.or.kmaxi.gt.extc(3)-3)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
if(any(cxI+4 > extc)) write(*,*)"error in prolong"
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+&
C5*ya(:,:,5)+C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+&
C5*tmp2(:,5)+C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+&
C5*tmp1(5)+C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C8*ya(:,:,1)+C7*ya(:,:,2)+C6*ya(:,:,3)+C5*ya(:,:,4)+&
C4*ya(:,:,5)+C3*ya(:,:,6)+C2*ya(:,:,7)+C1*ya(:,:,8)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+&
C5*tmp2(:,5)+C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+&
C5*tmp1(5)+C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+&
C5*ya(:,:,5)+C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)
endif
tmp1= C8*tmp2(:,1)+C7*tmp2(:,2)+C6*tmp2(:,3)+C5*tmp2(:,4)+&
C4*tmp2(:,5)+C3*tmp2(:,6)+C2*tmp2(:,7)+C1*tmp2(:,8)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+&
C5*tmp1(5)+C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C8*ya(:,:,1)+C7*ya(:,:,2)+C6*ya(:,:,3)+C5*ya(:,:,4)+&
C4*ya(:,:,5)+C3*ya(:,:,6)+C2*ya(:,:,7)+C1*ya(:,:,8)
endif
tmp1= C8*tmp2(:,1)+C7*tmp2(:,2)+C6*tmp2(:,3)+C5*tmp2(:,4)+&
C4*tmp2(:,5)+C3*tmp2(:,6)+C2*tmp2(:,7)+C1*tmp2(:,8)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+&
C5*tmp1(5)+C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+&
C5*ya(:,:,5)+C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+&
C5*tmp2(:,5)+C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)
funf(i,j,k)= C8*tmp1(1)+C7*tmp1(2)+C6*tmp1(3)+C5*tmp1(4)+&
C4*tmp1(5)+C3*tmp1(6)+C2*tmp1(7)+C1*tmp1(8)
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C8*ya(:,:,1)+C7*ya(:,:,2)+C6*ya(:,:,3)+C5*ya(:,:,4)+&
C4*ya(:,:,5)+C3*ya(:,:,6)+C2*ya(:,:,7)+C1*ya(:,:,8)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+&
C5*tmp2(:,5)+C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)
funf(i,j,k)= C8*tmp1(1)+C7*tmp1(2)+C6*tmp1(3)+C5*tmp1(4)+&
C4*tmp1(5)+C3*tmp1(6)+C2*tmp1(7)+C1*tmp1(8)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+&
C5*ya(:,:,5)+C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)
endif
tmp1= C8*tmp2(:,1)+C7*tmp2(:,2)+C6*tmp2(:,3)+C5*tmp2(:,4)+&
C4*tmp2(:,5)+C3*tmp2(:,6)+C2*tmp2(:,7)+C1*tmp2(:,8)
funf(i,j,k)= C8*tmp1(1)+C7*tmp1(2)+C6*tmp1(3)+C5*tmp1(4)+&
C4*tmp1(5)+C3*tmp1(6)+C2*tmp1(7)+C1*tmp1(8)
else
if(cxI(1)>3.and.cxI(2)>3.and.cxI(3)>3)then
tmp2= C8*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-3)+&
C7*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-2)+&
C6*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)-1)+&
C5*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3) )+&
C4*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+1)+&
C3*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+2)+&
C2*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+3)+&
C1*func(cxI(1)-3:cxI(1)+4,cxI(2)-3:cxI(2)+4,cxI(3)+4)
else
cxB=cxI-3
cxT=cxI+4
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,8,Symmetry))then
write(*,*)"prolong3 position: "
write(*,*)llbf(1)+(i-0.5)*FD(1),llbf(2)+(j-0.5)*FD(2),llbf(3)+(k-0.5)*FD(3)
write(*,*)"llbf = ",llbf
stop
endif
tmp2= C8*ya(:,:,1)+C7*ya(:,:,2)+C6*ya(:,:,3)+C5*ya(:,:,4)+&
C4*ya(:,:,5)+C3*ya(:,:,6)+C2*ya(:,:,7)+C1*ya(:,:,8)
endif
tmp1= C8*tmp2(:,1)+C7*tmp2(:,2)+C6*tmp2(:,3)+C5*tmp2(:,4)+&
C4*tmp2(:,5)+C3*tmp2(:,6)+C2*tmp2(:,7)+C1*tmp2(:,8)
funf(i,j,k)= C8*tmp1(1)+C7*tmp1(2)+C6*tmp1(3)+C5*tmp1(4)+&
C4*tmp1(5)+C3*tmp1(6)+C2*tmp1(7)+C1*tmp1(8)
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#error Not define Vertex nor Cell
#endif
#endif
#elif (ghost_width == 5)
! eighth order code
#ifdef Vertex
#ifdef Cell
#error Both Cell and Vertex are defined
#endif
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 10 points, 9th order interpolation
! 1 2 3 4 5 6 7 8 9 10
! *---*---*---*---*---*---*---*---*---*
! ^
! f=35/65536(f_1+f_10)-405/65536*(f_2+f_9) + 567/16384*(f_3+f_8) - 2205/16384*(f_4+f_7) + 19845/32768*(f_5+f_6)
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(10,10,10) :: ya
real*8, dimension(10,10) :: tmp2
real*8, dimension(10) :: tmp1
real*8, parameter :: C1=3.5d1/6.5536d4,C2=-4.05d2/6.5536d4,C3=5.67d2/1.6384d4
real*8, parameter :: C4=-2.205d3/1.6384d4,C5=1.9845d4/3.2768d4
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
! it's possible a iolated point for target but not for source
CD = (uubc-llbc)/(extc-1)
FD = CD/2
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)+1
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)+1
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)+1
ubpc = idint((uubp-base)/CD+0.4)+1
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-4.or.jmaxi.gt.extc(2)-4.or.kmaxi.gt.extc(3)-4)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
if(imini.lt.1) write(*,*)"imini = ",imini
if(jmini.lt.1) write(*,*)"jmini = ",jmini
if(kmini.lt.1) write(*,*)"kmini = ",kmini
if(imino.lt.1) write(*,*)"imino = ",imino
if(jmino.lt.1) write(*,*)"jmino = ",jmino
if(kmino.lt.1) write(*,*)"kmino = ",kmino
if(imaxi.gt.extc(1)) write(*,*)"imaxi = ",imaxi,"extc(1) = ",extc(1)
if(jmaxi.gt.extc(2)) write(*,*)"jmaxi = ",jmaxi,"extc(2) = ",extc(2)
if(kmaxi.gt.extc(3)) write(*,*)"kmaxi = ",kmaxi,"extc(3) = ",extc(3)
if(imaxo.gt.extf(1)) write(*,*)"imaxo = ",imaxo,"extf(1) = ",extf(1)
if(jmaxo.gt.extf(2)) write(*,*)"jmaxo = ",jmaxo,"extf(2) = ",extf(2)
if(kmaxo.gt.extf(3)) write(*,*)"kmaxo = ",kmaxo,"extf(3) = ",extf(3)
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
! change to coarse level reference
!|*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*|
!|x===============x===============x===============x========|
cxI(1) = i
cxI(2) = j
cxI(3) = k
cxI = (cxI+lbf)/2
! change to array index
cxI = cxI - lbc + 1
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(any(cxI+5 > extc)) write(*,*)"error in prolong"
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5))&
+C2*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4))&
+C3*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3))&
+C4*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2))&
+C5*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,10))+C2*(ya(:,:,2)+ya(:,:,9))+C3*(ya(:,:,3)+ya(:,:,8)) &
+C4*(ya(:,:,4)+ya(:,:, 7))+C5*(ya(:,:,5)+ya(:,:,6))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,10))+C2*(tmp2(:,2)+tmp2(:,9))+C3*(tmp2(:,3)+tmp2(:,8)) &
+C4*(tmp2(:,4)+tmp2(:, 7))+C5*(tmp2(:,5)+tmp2(:,6))
funf(i,j,k)= C1*(tmp1(1)+tmp1(10))+C2*(tmp1(2)+tmp1(9))+C3*(tmp1(3)+tmp1(8)) &
+C4*(tmp1(4)+tmp1( 7))+C5*(tmp1(5)+tmp1(6))
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,5)
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,10))+C2*(tmp2(:,2)+tmp2(:,9))+C3*(tmp2(:,3)+tmp2(:,8)) &
+C4*(tmp2(:,4)+tmp2(:, 7))+C5*(tmp2(:,5)+tmp2(:,6))
funf(i,j,k)= C1*(tmp1(1)+tmp1(10))+C2*(tmp1(2)+tmp1(9))+C3*(tmp1(3)+tmp1(8)) &
+C4*(tmp1(4)+tmp1( 7))+C5*(tmp1(5)+tmp1(6))
endif
else
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5))&
+C2*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4))&
+C3*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3))&
+C4*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2))&
+C5*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,10))+C2*(ya(:,:,2)+ya(:,:,9))+C3*(ya(:,:,3)+ya(:,:,8)) &
+C4*(ya(:,:,4)+ya(:,:, 7))+C5*(ya(:,:,5)+ya(:,:,6))
endif
tmp1= tmp2(:,5)
funf(i,j,k)= C1*(tmp1(1)+tmp1(10))+C2*(tmp1(2)+tmp1(9))+C3*(tmp1(3)+tmp1(8)) &
+C4*(tmp1(4)+tmp1( 7))+C5*(tmp1(5)+tmp1(6))
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,5)
endif
tmp1= tmp2(:,5)
funf(i,j,k)= C1*(tmp1(1)+tmp1(10))+C2*(tmp1(2)+tmp1(9))+C3*(tmp1(3)+tmp1(8)) &
+C4*(tmp1(4)+tmp1( 7))+C5*(tmp1(5)+tmp1(6))
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5))&
+C2*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4))&
+C3*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3))&
+C4*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2))&
+C5*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,10))+C2*(ya(:,:,2)+ya(:,:,9))+C3*(ya(:,:,3)+ya(:,:,8)) &
+C4*(ya(:,:,4)+ya(:,:, 7))+C5*(ya(:,:,5)+ya(:,:,6))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,10))+C2*(tmp2(:,2)+tmp2(:,9))+C3*(tmp2(:,3)+tmp2(:,8)) &
+C4*(tmp2(:,4)+tmp2(:, 7))+C5*(tmp2(:,5)+tmp2(:,6))
funf(i,j,k)= tmp1(5)
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= ya(:,:,5)
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,10))+C2*(tmp2(:,2)+tmp2(:,9))+C3*(tmp2(:,3)+tmp2(:,8)) &
+C4*(tmp2(:,4)+tmp2(:, 7))+C5*(tmp2(:,5)+tmp2(:,6))
funf(i,j,k)= tmp1(5)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5))&
+C2*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4))&
+C3*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3))&
+C4*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2))&
+C5*(func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,10))+C2*(ya(:,:,2)+ya(:,:,9))+C3*(ya(:,:,3)+ya(:,:,8)) &
+C4*(ya(:,:,4)+ya(:,:, 7))+C5*(ya(:,:,5)+ya(:,:,6))
endif
tmp1= tmp2(:,5)
funf(i,j,k)= tmp1(5)
else
funf(i,j,k)= func(cxI(1),cxI(2),cxI(3))
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#ifdef Cell
!---------------------------------------------------------------------------------------------------------------
!
! Restrict from finner grids to coarser grids ignore the boundary point
!
! 10 points, 9th order interpolation
! 1 2 3 4 5 6 7 8 9 10
! *---*---*---*---*---*---*---*---*---*
! ^
! f=35/65536(f_1+f_10)-405/65536*(f_2+f_9) + 567/16384*(f_3+f_8) - 2205/16384*(f_4+f_7) + 19845/32768*(f_5+f_6)
!---------------------------------------------------------------------------------------------------------------
subroutine restrict3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbr,uubr,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in)::wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbr,uubr
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(inout):: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(in):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbr,ubr,lbrf,ubrf
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k
real*8, dimension(10,10,10) :: ya
real*8, dimension(10,10) :: tmp2
real*8, dimension(10) :: tmp1
real*8, parameter :: C1=3.5d1/6.5536d4,C2=-4.05d2/6.5536d4,C3=5.67d2/1.6384d4
real*8, parameter :: C4=-2.205d3/1.6384d4,C5=1.9845d4/3.2768d4
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::restrict3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
! note say base = 0, llbf = 0, uubf = 2
! llbf->1 and uubf->2
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbr = idint((llbr-base)/CD+0.4)+1
lbrf = idint((llbr-base)/FD+0.4)+1
ubr = idint((uubr-base)/CD+0.4)
ubrf = idint((uubr-base)/FD+0.4)
!sanity check
imino=lbr(1)-lbc(1) + 1
imaxo=ubr(1)-lbc(1) + 1
jmino=lbr(2)-lbc(2) + 1
jmaxo=ubr(2)-lbc(2) + 1
kmino=lbr(3)-lbc(3) + 1
kmaxo=ubr(3)-lbc(3) + 1
imini=lbrf(1)-lbf(1) + 1
imaxi=ubrf(1)-lbf(1) + 1
jmini=lbrf(2)-lbf(2) + 1
jmaxi=ubrf(2)-lbf(2) + 1
kmini=lbrf(3)-lbf(3) + 1
kmaxi=ubrf(3)-lbf(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extc(1).or.jmaxo.gt.extc(2).or.kmaxo.gt.extc(3).or.&
imaxi.gt.extf(1)-4.or.jmaxi.gt.extf(2)-4.or.kmaxi.gt.extf(3)-4)then
write(*,*)"error in restrict for"
write(*,*)"from"
write(*,*)lbf,ubf
write(*,*)"to"
write(*,*)lbc,ubc
write(*,*)"want"
write(*,*)lbr,ubr,lbrf,ubrf
write(*,*)"llbf = ",llbf
write(*,*)"uubf = ",uubf
write(*,*)"llbc = ",llbc
write(*,*)"uubc = ",uubc
write(*,*)"llbr = ",llbr
write(*,*)"uubr = ",uubr
write(*,*)"base = ",base
stop
endif
!~~~~~~> restriction start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to fine level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = 2*(cxI+lbc-1) - 1
! change to array index
cxI = cxI - lbf + 1
if(any(cxI+5 > extf)) write(*,*)"error in restrict"
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1*(funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5))&
+C2*(funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4))&
+C3*(funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3))&
+C4*(funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2))&
+C5*(funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+funf(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1))
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extf,funf,funf,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"restrict3 position index: ",i+lbc(1)-1,j+lbc(2)-1,k+lbc(3)-1
stop
endif
tmp2=C1*(ya(:,:,1)+ya(:,:,10))+C2*(ya(:,:,2)+ya(:,:,9))+C3*(ya(:,:,3)+ya(:,:,8)) &
+C4*(ya(:,:,4)+ya(:,:, 7))+C5*(ya(:,:,5)+ya(:,:,6))
endif
tmp1= C1*(tmp2(:,1)+tmp2(:,10))+C2*(tmp2(:,2)+tmp2(:,9))+C3*(tmp2(:,3)+tmp2(:,8)) &
+C4*(tmp2(:,4)+tmp2(:, 7))+C5*(tmp2(:,5)+tmp2(:,6))
func(i,j,k)= C1*(tmp1(1)+tmp1(10))+C2*(tmp1(2)+tmp1(9))+C3*(tmp1(3)+tmp1(8)) &
+C4*(tmp1(4)+tmp1( 7))+C5*(tmp1(5)+tmp1(6))
enddo
enddo
enddo
return
end subroutine restrict3
!--------------------------------------------------------------------------
!
! Prolongation from coarser grids to finer grids
! 10 points, 9th order interpolation
! 1 2 3 4 5 6 7 8 9 10
! *---*---*---*---*---*---*---*---*---*
! ^
!f= 13585/33554432*f_1-159885/33554432*f_2+230945/8388608*f_3- 969969/8388608*f_4+14549535/16777216*f_5
! +4849845/16777216*f_6- 692835/8388608*f_7+188955/8388608*f_8-138567/33554432*f_9+ 12155/33554432*f_10
!--------------------------------------------------------------------------
subroutine prolong3(wei,llbc,uubc,extc,func,&
llbf,uubf,extf,funf,&
llbp,uubp,SoA,Symmetry)
implicit none
!~~~~~~> input arguments
integer,intent(in) :: wei
! coarse fine coarse
real*8,dimension(3), intent(in) :: llbc,uubc,llbf,uubf,llbp,uubp
integer,dimension(3), intent(in) :: extc,extf
real*8, dimension(extc(1),extc(2),extc(3)),intent(in) :: func
real*8, dimension(extf(1),extf(2),extf(3)),intent(inout):: funf
real*8, dimension(1:3), intent(in) :: SoA
integer,intent(in)::Symmetry
!~~~~~~> local variables
real*8, dimension(1:3) :: base
integer,dimension(3) :: lbc,ubc,lbf,ubf,lbp,ubp,lbpc,ubpc
integer,dimension(3) :: cxB,cxT,cxI
integer :: i,j,k,ii,jj,kk
real*8, dimension(10,10,10) :: ya
real*8, dimension(10,10) :: tmp2
real*8, dimension(10) :: tmp1
real*8, parameter :: C1=1.3585d4/3.3554432d7,C2=-1.59885d5/3.3554432d7,C3=2.30945d5/8.388608d6
real*8, parameter :: C4=-9.69969d5/8.388608d6,C5=1.4549535d7/1.6777216d7,C6=4.849845d6/1.6777216d7
real*8, parameter :: C7=-6.92835d5/8.388608d6,C8=1.88955d5/8.388608d6,C9=-1.38567d5/3.3554432d7
real*8, parameter :: C10=1.2155d4/3.3554432d7
integer::imini,imaxi,jmini,jmaxi,kmini,kmaxi
integer::imino,imaxo,jmino,jmaxo,kmino,kmaxo
logical::decide3d
real*8,dimension(3) :: CD,FD
if(wei.ne.3)then
write(*,*)"prolongrestrict.f90::prolong3: this routine only surport 3 dimension"
write(*,*)"dim = ",wei
stop
endif
CD = (uubc-llbc)/extc
FD = (uubf-llbf)/extf
!take care the mismatch of the two segments of grid
do i=1,3
if(llbc(i) <= llbf(i))then
base(i) = llbc(i)
else
j=idint((llbc(i)-llbf(i))/FD(i)+0.4)
if(j/2*2 == j)then
base(i) = llbf(i)
else
base(i) = llbf(i) - CD(i)/2
endif
endif
enddo
!!! function idint:
!If A is of type REAL and |A| < 1, INT(A) equals 0. If |A| \geq 1,
!then INT(A) equals the largest integer that does not exceed the range of A
!and whose sign is the same as the sign of A.
lbf = idint((llbf-base)/FD+0.4)+1
ubf = idint((uubf-base)/FD+0.4)
lbc = idint((llbc-base)/CD+0.4)+1
ubc = idint((uubc-base)/CD+0.4)
lbp = idint((llbp-base)/FD+0.4)+1
lbpc = idint((llbp-base)/CD+0.4)+1
ubp = idint((uubp-base)/FD+0.4)
ubpc = idint((uubp-base)/CD+0.4)
!sanity check
imino=lbp(1)-lbf(1) + 1
imaxo=ubp(1)-lbf(1) + 1
jmino=lbp(2)-lbf(2) + 1
jmaxo=ubp(2)-lbf(2) + 1
kmino=lbp(3)-lbf(3) + 1
kmaxo=ubp(3)-lbf(3) + 1
imini=lbpc(1)-lbc(1) + 1
imaxi=ubpc(1)-lbc(1) + 1
jmini=lbpc(2)-lbc(2) + 1
jmaxi=ubpc(2)-lbc(2) + 1
kmini=lbpc(3)-lbc(3) + 1
kmaxi=ubpc(3)-lbc(3) + 1
if(imino.lt.1.or.jmino.lt.1.or.kmino.lt.1.or.&
imini.lt.1.or.jmini.lt.1.or.kmini.lt.1.or.&
imaxo.gt.extf(1).or.jmaxo.gt.extf(2).or.kmaxo.gt.extf(3).or.&
imaxi.gt.extc(1)-4.or.jmaxi.gt.extc(2)-4.or.kmaxi.gt.extc(3)-4)then
write(*,*)"error in prolongation for"
write(*,*)"from"
write(*,*)llbc,uubc
write(*,*)lbc,ubc
write(*,*)"to"
write(*,*)llbf,uubf
write(*,*)lbf,ubf
write(*,*)"want"
write(*,*)llbp,uubp
write(*,*)lbp,ubp,lbpc,ubpc
return
endif
!~~~~~~> prolongation start...
do k = kmino,kmaxo
do j = jmino,jmaxo
do i = imino,imaxo
cxI(1) = i
cxI(2) = j
cxI(3) = k
! change to coarse level reference
!|---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*--- ---*---|
!|=======x===============x===============x===============x=======|
cxI = (cxI+lbf-1)/2
! change to array index
cxI = cxI - lbc + 1
if(any(cxI+5 > extc)) write(*,*)"error in prolong"
ii=i+lbf(1)-1
jj=j+lbf(2)-1
kk=k+lbf(3)-1
if(ii/2*2==ii)then
if(jj/2*2==jj)then
if(kk/2*2==kk)then
! due to ghost zone, we can deal with symmetry boundary like this
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+C5 *ya(:,:, 5)+&
C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)+C9*ya(:,:,9)+C10*ya(:,:,10)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5 *tmp2(:, 5)+&
C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)+C9*tmp2(:,9)+C10*tmp2(:,10)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+ C5*tmp1( 5)+&
C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)+C9*tmp1(9)+C10*tmp1(10)
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C10*ya(:,:,1)+C9*ya(:,:,2)+C8*ya(:,:,3)+C7*ya(:,:,4)+C6*ya(:,:, 5)+&
C5 *ya(:,:,6)+C4*ya(:,:,7)+C3*ya(:,:,8)+C2*ya(:,:,9)+C1*ya(:,:,10)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5 *tmp2(:, 5)+&
C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)+C9*tmp2(:,9)+C10*tmp2(:,10)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5 *tmp1( 5)+&
C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)+C9*tmp1(9)+C10*tmp1(10)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+C5 *ya(:,:, 5)+&
C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)+C9*ya(:,:,9)+C10*ya(:,:,10)
endif
tmp1= C10*tmp2(:,1)+C9*tmp2(:,2)+C8*tmp2(:,3)+C7*tmp2(:,4)+C6*tmp2(:, 5)+&
C5 *tmp2(:,6)+C4*tmp2(:,7)+C3*tmp2(:,8)+C2*tmp2(:,9)+C1*tmp2(:,10)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5 *tmp1( 5)+&
C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)+C9*tmp1(9)+C10*tmp1(10)
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C10*ya(:,:,1)+C9*ya(:,:,2)+C8*ya(:,:,3)+C7*ya(:,:,4)+C6*ya(:,:, 5)+&
C5 *ya(:,:,6)+C4*ya(:,:,7)+C3*ya(:,:,8)+C2*ya(:,:,9)+C1*ya(:,:,10)
endif
tmp1= C10*tmp2(:,1)+C9*tmp2(:,2)+C8*tmp2(:,3)+C7*tmp2(:,4)+C6*tmp2(:, 5)+&
C5 *tmp2(:,6)+C4*tmp2(:,7)+C3*tmp2(:,8)+C2*tmp2(:,9)+C1*tmp2(:,10)
funf(i,j,k)= C1*tmp1(1)+C2*tmp1(2)+C3*tmp1(3)+C4*tmp1(4)+C5 *tmp1( 5)+&
C6*tmp1(6)+C7*tmp1(7)+C8*tmp1(8)+C9*tmp1(9)+C10*tmp1(10)
endif
endif
else
if(jj/2*2==jj)then
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+C5 *ya(:,:, 5)+&
C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)+C9*ya(:,:,9)+C10*ya(:,:,10)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5 *tmp2(:, 5)+&
C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)+C9*tmp2(:,9)+C10*tmp2(:,10)
funf(i,j,k)= C10*tmp1(1)+C9*tmp1(2)+C8*tmp1(3)+C7*tmp1(4)+C6*tmp1( 5)+&
C5 *tmp1(6)+C4*tmp1(7)+C3*tmp1(8)+C2*tmp1(9)+C1*tmp1(10)
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C10*ya(:,:,1)+C9*ya(:,:,2)+C8*ya(:,:,3)+C7*ya(:,:,4)+C6*ya(:,:, 5)+&
C5 *ya(:,:,6)+C4*ya(:,:,7)+C3*ya(:,:,8)+C2*ya(:,:,9)+C1*ya(:,:,10)
endif
tmp1= C1*tmp2(:,1)+C2*tmp2(:,2)+C3*tmp2(:,3)+C4*tmp2(:,4)+C5 *tmp2(:, 5)+&
C6*tmp2(:,6)+C7*tmp2(:,7)+C8*tmp2(:,8)+C9*tmp2(:,9)+C10*tmp2(:,10)
funf(i,j,k)= C10*tmp1(1)+C9*tmp1(2)+C8*tmp1(3)+C7*tmp1(4)+C6*tmp1( 5)+&
C5 *tmp1(6)+C4*tmp1(7)+C3*tmp1(8)+C2*tmp1(9)+C1*tmp1(10)
endif
else
if(kk/2*2==kk)then
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C1*ya(:,:,1)+C2*ya(:,:,2)+C3*ya(:,:,3)+C4*ya(:,:,4)+C5 *ya(:,:, 5)+&
C6*ya(:,:,6)+C7*ya(:,:,7)+C8*ya(:,:,8)+C9*ya(:,:,9)+C10*ya(:,:,10)
endif
tmp1= C10*tmp2(:,1)+C9*tmp2(:,2)+C8*tmp2(:,3)+C7*tmp2(:,4)+C6*tmp2(:, 5)+&
C5 *tmp2(:,6)+C4*tmp2(:,7)+C3*tmp2(:,8)+C2*tmp2(:,9)+C1*tmp2(:,10)
funf(i,j,k)= C10*tmp1(1)+C9*tmp1(2)+C8*tmp1(3)+C7*tmp1(4)+C6*tmp1( 5)+&
C5 *tmp1(6)+C4*tmp1(7)+C3*tmp1(8)+C2*tmp1(9)+C1*tmp1(10)
else
if(cxI(1)>4.and.cxI(2)>4.and.cxI(3)>4)then
tmp2= C10*func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-4)+&
C9 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-3)+&
C8 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-2)+&
C7 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)-1)+&
C6 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3) )+&
C5 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+1)+&
C4 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+2)+&
C3 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+3)+&
C2 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+4)+&
C1 *func(cxI(1)-4:cxI(1)+5,cxI(2)-4:cxI(2)+5,cxI(3)+5)
else
cxB=cxI-4
cxT=cxI+5
if(decide3d(extc,func,func,cxB,cxT,SoA,ya,10,Symmetry))then
write(*,*)"prolong3 position index: ",i+lbf(1)-1,j+lbf(2)-1,k+lbf(3)-1
return
endif
tmp2= C10*ya(:,:,1)+C9*ya(:,:,2)+C8*ya(:,:,3)+C7*ya(:,:,4)+C6*ya(:,:, 5)+&
C5 *ya(:,:,6)+C4*ya(:,:,7)+C3*ya(:,:,8)+C2*ya(:,:,9)+C1*ya(:,:,10)
endif
tmp1= C10*tmp2(:,1)+C9*tmp2(:,2)+C8*tmp2(:,3)+C7*tmp2(:,4)+C6*tmp2(:, 5)+&
C5 *tmp2(:,6)+C4*tmp2(:,7)+C3*tmp2(:,8)+C2*tmp2(:,9)+C1*tmp2(:,10)
funf(i,j,k)= C10*tmp1(1)+C9*tmp1(2)+C8*tmp1(3)+C7*tmp1(4)+C6*tmp1( 5)+&
C5 *tmp1(6)+C4*tmp1(7)+C3*tmp1(8)+C2*tmp1(9)+C1*tmp1(10)
endif
endif
endif
enddo
enddo
enddo
return
end subroutine prolong3
#else
#error Not define Vertex nor Cell
#endif
#endif
#endif
#endif