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poisson.f90
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!################################################################################
!This file is part of Incompact3d.
!
!Incompact3d
!Copyright (c) 2012 Eric Lamballais and Sylvain Laizet
!
! Incompact3d is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation.
!
! Incompact3d is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with the code. If not, see <http://www.gnu.org/licenses/>.
!-------------------------------------------------------------------------------
!-------------------------------------------------------------------------------
! We kindly request that you cite Incompact3d in your publications and
! presentations. The following citations are suggested:
!
! 1-Laizet S. & Lamballais E., 2009, High-order compact schemes for
! incompressible flows: a simple and efficient method with the quasi-spectral
! accuracy, J. Comp. Phys., vol 228 (15), pp 5989-6015
!
! 2-Laizet S. & Li N., 2011, Incompact3d: a powerful tool to tackle turbulence
! problems with up to 0(10^5) computational cores, Int. J. of Numerical
! Methods in Fluids, vol 67 (11), pp 1735-1757
!################################################################################
module decomp_2d_poisson
use decomp_2d
use decomp_2d_fft
use param
use variables
implicit none
private ! Make everything private unless declared public
! real(mytype), private, parameter :: PI = 3.14159265358979323846_mytype
#ifdef DOUBLE_PREC
real(mytype), parameter :: epsilon = 1.e-16
#else
real(mytype), parameter :: epsilon = 1.e-8
#endif
! boundary conditions
integer, save :: bcx, bcy, bcz
! decomposition object for physical space
TYPE(DECOMP_INFO), save :: ph
! decomposition object for spectral space
TYPE(DECOMP_INFO), save :: sp
! store sine/cosine factors
real(mytype), save, allocatable, dimension(:) :: az,bz
real(mytype), save, allocatable, dimension(:) :: ay,by
real(mytype), save, allocatable, dimension(:) :: ax,bx
! wave numbers
complex(mytype), save, allocatable, dimension(:,:,:) :: kxyz
!wave numbers for stretching in a pentadiagonal matrice
complex(mytype), save, allocatable, dimension(:,:,:,:) :: a,a2,a3
! work arrays,
! naming convention: cw (complex); rw (real);
! 1 = X-pencil; 2 = Y-pencil; 3 = Z-pencil
real(mytype), allocatable, dimension(:,:,:) :: rw1,rw1b,rw2,rw2b,rw3
complex(mytype), allocatable, dimension(:,:,:) :: cw1,cw1b,cw2,cw22,cw2b,cw2c
! underlying FFT library only needs to be initialised once
logical, save :: fft_initialised = .false.
public :: decomp_2d_poisson_stg, decomp_2d_poisson_init, &
decomp_2d_poisson_finalize
! For staggered mesh where main variables are defined in the centre of
! control volumes while boundary conditions are defined on interfaces
interface decomp_2d_poisson_stg
module procedure poisson
end interface
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Initialise Poisson solver for given boundary conditions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine decomp_2d_poisson_init(bcx1, bcy1, bcz1)
implicit none
integer, intent(IN) :: bcx1, bcy1, bcz1
integer :: nx, ny, nz, i
bcx = bcx1
bcy = bcy1
bcz = bcz1
nx = nx_global
ny = ny_global
nz = nz_global
! pressure-grid having 1 fewer point for non-periodic directions
if (bcx==1) nx=nx-1
if (bcy==1) ny=ny-1
if (bcz==1) nz=nz-1
allocate(ax(nx),bx(nx))
allocate(ay(ny),by(ny))
allocate(az(nz),bz(nz))
call abxyz(ax,ay,az,bx,by,bz,nx,ny,nz,bcx,bcy,bcz)
call decomp_info_init(nx, ny, nz, ph)
call decomp_info_init(nx, ny, nz/2+1, sp)
! allocate work space
if (bcx==0 .and. bcy==0 .and. bcz==0) then
allocate(cw1(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(kxyz(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(a(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a2(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a3(sp%yst(1):sp%yen(1),ny,sp%yst(3):sp%yen(3),5))
else if (bcx==1 .and. bcy==0 .and. bcz==0) then
allocate(cw1(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(cw1b(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(rw1(ph%xst(1):ph%xen(1),ph%xst(2):ph%xen(2), &
ph%xst(3):ph%xen(3)))
allocate(rw1b(ph%xst(1):ph%xen(1),ph%xst(2):ph%xen(2), &
ph%xst(3):ph%xen(3)))
allocate(rw2(ph%yst(1):ph%yen(1),ph%yst(2):ph%yen(2), &
ph%yst(3):ph%yen(3)))
allocate(kxyz(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(a(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a2(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a3(sp%yst(1):sp%yen(1),ny,sp%yst(3):sp%yen(3),5))
else if (bcx==0 .and. bcy==1 .and. bcz==0) then
allocate(rw2(ph%yst(1):ph%yen(1),ph%yst(2):ph%yen(2), &
ph%yst(3):ph%yen(3)))
allocate(rw2b(ph%yst(1):ph%yen(1),ph%yst(2):ph%yen(2), &
ph%yst(3):ph%yen(3)))
allocate(cw1(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(cw2(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw22(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw2b(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw2c(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(kxyz(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(a(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a2(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a3(sp%yst(1):sp%yen(1),ny,sp%yst(3):sp%yen(3),5))
else if (bcx==1 .and. bcy==1) then
allocate(cw1(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(cw1b(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(cw2(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw22(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw2b(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(cw2c(sp%yst(1):sp%yen(1),sp%yst(2):sp%yen(2), &
sp%yst(3):sp%yen(3)))
allocate(rw1(ph%xst(1):ph%xen(1),ph%xst(2):ph%xen(2), &
ph%xst(3):ph%xen(3)))
allocate(rw1b(ph%xst(1):ph%xen(1),ph%xst(2):ph%xen(2), &
ph%xst(3):ph%xen(3)))
allocate(rw2(ph%yst(1):ph%yen(1),ph%yst(2):ph%yen(2), &
ph%yst(3):ph%yen(3)))
allocate(rw2b(ph%yst(1):ph%yen(1),ph%yst(2):ph%yen(2), &
ph%yst(3):ph%yen(3)))
if (bcz==1) then
allocate(rw3(ph%zsz(1),ph%zsz(2),ph%zsz(3)))
end if
allocate(kxyz(sp%xst(1):sp%xen(1),sp%xst(2):sp%xen(2), &
sp%xst(3):sp%xen(3)))
allocate(a(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a2(sp%yst(1):sp%yen(1),ny/2,sp%yst(3):sp%yen(3),5))
allocate(a3(sp%yst(1):sp%yen(1),nym,sp%yst(3):sp%yen(3),5))
end if
call waves()
return
end subroutine decomp_2d_poisson_init
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Release memory used by Poisson solver
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine decomp_2d_poisson_finalize
implicit none
deallocate(ax,bx,ay,by,az,bz)
call decomp_info_finalize(ph)
call decomp_info_finalize(sp)
call decomp_2d_fft_finalize
fft_initialised = .false.
deallocate(kxyz)
if (bcx==0 .and. bcy==0 .and. bcz==0) then
deallocate(cw1)
else if (bcx==1 .and. bcy==0 .and. bcz==0) then
deallocate(cw1,cw1b,rw1,rw1b,rw2)
else if (bcx==0 .and. bcy==1 .and. bcz==0) then
deallocate(cw1,cw2,cw2b,rw2,rw2b)
else if (bcx==1 .and. bcy==1) then
deallocate(cw1,cw1b,cw2,cw2b,rw1,rw1b,rw2,rw2b)
if (bcz==1) then
deallocate(rw3)
end if
end if
return
end subroutine decomp_2d_poisson_finalize
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Top level wrapper
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine poisson(rhs, bcx, bcy, bcz)
implicit none
real(mytype), dimension(:,:,:), intent(INOUT) :: rhs
integer, intent(IN) :: bcx, bcy, bcz ! boundary conditions
integer :: i
if (bcx==0 .and. bcy==0 .and. bcz==0) then
call poisson_000(rhs)
else if (bcx==1 .and. bcy==0 .and. bcz==0) then
call poisson_100(rhs)
else if (bcx==0 .and. bcy==1 .and. bcz==0) then
call poisson_010(rhs)
else if (bcx==1 .and. bcy==1) then ! 110 & 111
call poisson_11x(rhs, bcz)
else
stop 'boundary condition not supported'
end if
return
end subroutine poisson
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Solving 3D Poisson equation with periodic B.C in all 3 dimensions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine poisson_000(rhs)
use derivX
use derivY
use derivZ
! right-hand-side of Poisson as input
! solution of Poisson as output
real(mytype), dimension(:,:,:), intent(INOUT) :: rhs
integer, dimension(3) :: fft_start, fft_end, fft_size
complex(mytype) :: xyzk
complex(mytype) :: ytt,xtt,ztt,yt1,xt1,yt2,xt2
complex(mytype) :: xtt1,ytt1,ztt1,zt1,zt2
real(mytype) :: tmp1, tmp2,x ,y, z
integer :: nx,ny,nz, i,j,k
nx = nx_global
ny = ny_global
nz = nz_global
if (.not. fft_initialised) then
call decomp_2d_fft_init(PHYSICAL_IN_Z)
fft_initialised = .true.
end if
! compute r2c transform
call decomp_2d_fft_3d(rhs,cw1)
! normalisation
cw1 = cw1 / real(nx, kind=mytype) /real(ny, kind=mytype) &
/ real(nz, kind=mytype)
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
! post-processing in spectral space
! POST PROCESSING IN Z
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)+tmp2*az(k), &
tmp2*bz(k)-tmp1*az(k), kind=mytype)
! POST PROCESSING IN Y
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*by(j)+tmp2*ay(j), &
tmp2*by(j)-tmp1*ay(j), kind=mytype)
if (j.gt.(ny/2+1)) cw1(i,j,k)=-cw1(i,j,k)
! POST PROCESSING IN X
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bx(i)+tmp2*ax(i), &
tmp2*bx(i)-tmp1*ax(i), kind=mytype)
if (i.gt.(nx/2+1)) cw1(i,j,k)=-cw1(i,j,k)
! Solve Poisson
tmp1=real(kxyz(i,j,k), kind=mytype)
tmp2=aimag(kxyz(i,j,k))
! CANNOT DO A DIVISION BY ZERO
if ((tmp1.lt.epsilon).or.(tmp2.lt.epsilon)) then
cw1(i,j,k)=0._mytype
! print *,'DIV 0',i,j,k,epsilon
else
cw1(i,j,k)=cmplx( real(cw1(i,j,k), kind=mytype) / (-tmp1), &
aimag(cw1(i,j,k))/(-tmp2), kind=mytype)
end if
!Print result in spectal space after Poisson
! if (abs(out(i,j,k)) > 1.0e-4) then
! write(*,*) 'AFTER',i,j,k,out(i,j,k),xyzk
! end if
! post-processing backward
! POST PROCESSING IN Z
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)-tmp2*az(k), &
-tmp2*bz(k)-tmp1*az(k), kind=mytype)
! POST PROCESSING IN Y
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*by(j)+tmp2*ay(j), &
tmp2*by(j)-tmp1*ay(j), kind=mytype)
if (j.gt.(ny/2+1)) cw1(i,j,k)=-cw1(i,j,k)
! POST PROCESSING IN X
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bx(i)+tmp2*ax(i), &
-tmp2*bx(i)+tmp1*ax(i), kind=mytype)
if (i.gt.(nx/2+1)) cw1(i,j,k)=-cw1(i,j,k)
end do
end do
end do
! compute c2r transform
call decomp_2d_fft_3d(cw1,rhs)
! call decomp_2d_fft_finalize
return
end subroutine poisson_000
subroutine poisson_100(rhs)
implicit none
real(mytype), dimension(:,:,:), intent(INOUT) :: rhs
complex(mytype) :: xyzk
real(mytype) :: tmp1, tmp2, tmp3, tmp4
real(mytype) :: xx1,xx2,xx3,xx4,xx5,xx6,xx7,xx8
integer :: nx,ny,nz, i,j,k, itmp
100 format(1x,a8,3I4,2F12.6)
nx = nx_global - 1
ny = ny_global
nz = nz_global
! rhs is in Z-pencil but requires global operations in X
call transpose_z_to_y(rhs,rw2,ph)
call transpose_y_to_x(rw2,rw1,ph)
do k=ph%xst(3),ph%xen(3)
do j=ph%xst(2),ph%xen(2)
do i=1,nx/2
rw1b(i,j,k)=rw1(2*(i-1)+1,j,k)
enddo
do i=nx/2+1,nx
rw1b(i,j,k)=rw1(2*nx-2*i+2,j,k)
enddo
enddo
end do
call transpose_x_to_y(rw1b,rw2,ph)
call transpose_y_to_z(rw2,rhs,ph)
if (.not. fft_initialised) then
call decomp_2d_fft_init(PHYSICAL_IN_Z,nx,ny,nz)
fft_initialised = .true.
end if
! compute r2c transform
call decomp_2d_fft_3d(rhs,cw1)
! normalisation
cw1 = cw1 / real(nx, kind=mytype) /real(ny, kind=mytype) &
/ real(nz, kind=mytype)
#ifdef DEBUG
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
if (abs(cw1(i,j,k)) > 1.0e-4) then
write(*,100) 'START',i,j,k,cw1(i,j,k)
end if
end do
end do
end do
#endif
! post-processing in spectral space
! POST PROCESSING IN Z
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)+tmp2*az(k), &
tmp2*bz(k)-tmp1*az(k), kind=mytype)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'after z',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN Y
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*by(j)+tmp2*ay(j), &
tmp2*by(j)-tmp1*ay(j), kind=mytype)
if (j.gt.(ny/2+1)) cw1(i,j,k)=-cw1(i,j,k)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'after y',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN X
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
cw1b(1,j,k)=cw1(1,j,k)
do i = 2,nx
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
tmp3 = real(cw1(nx-i+2,j,k), kind=mytype)
tmp4 = aimag(cw1(nx-i+2,j,k))
xx1=tmp1*bx(i)/2._mytype
xx2=tmp1*ax(i)/2._mytype
xx3=tmp2*bx(i)/2._mytype
xx4=tmp2*ax(i)/2._mytype
xx5=tmp3*bx(i)/2._mytype
xx6=tmp3*ax(i)/2._mytype
xx7=tmp4*bx(i)/2._mytype
xx8=tmp4*ax(i)/2._mytype
cw1b(i,j,k) = cmplx(xx1+xx4+xx5-xx8,-xx2+xx3+xx6+xx7, &
kind=mytype)
end do
end do
end do
#ifdef DEBUG
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
if (abs(cw1b(i,j,k)) > 1.0e-4) then
write(*,100) 'after x',i,j,k,cw1b(i,j,k)
end if
end do
end do
end do
#endif
! Solve Poisson
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
!tmp1=real(zk2(k)+yk2(j)+xk2(i), kind=mytype)
!tmp2=aimag(zk2(k)+yk2(j)+xk2(i))
tmp1=real(kxyz(i,j,k), kind=mytype)
tmp2=aimag(kxyz(i,j,k))
!xyzk=cmplx(tmp1,tmp2, kind=mytype)
! CANNOT DO A DIVISION BY ZERO
if ((abs(tmp1).lt.epsilon).and.(abs(tmp2).lt.epsilon)) then
cw1b(i,j,k)=cmplx(0._mytype,0._mytype, kind=mytype)
end if
if ((abs(tmp1).lt.epsilon).and.(abs(tmp2).ge.epsilon)) then
cw1b(i,j,k)=cmplx(0._mytype, &
aimag(cw1b(i,j,k))/(-tmp2), kind=mytype)
end if
if ((abs(tmp1).ge.epsilon).and.(abs(tmp2).lt.epsilon)) then
cw1b(i,j,k)=cmplx( real(cw1b(i,j,k), kind=mytype) &
/(-tmp1), 0._mytype, kind=mytype)
end if
if ((abs(tmp1).ge.epsilon).and.(abs(tmp2).ge.epsilon)) then
cw1b(i,j,k)=cmplx( real(cw1b(i,j,k), kind=mytype) &
/(-tmp1), &
aimag(cw1b(i,j,k))/(-tmp2), kind=mytype)
end if
#ifdef DEBUG
if (abs(cw1b(i,j,k)) > 1.0e-4) &
write(*,100) 'AFTER',i,j,k,cw1b(i,j,k)
#endif
end do
end do
end do
! post-processing backward
! POST PROCESSING IN X
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
cw1(1,j,k)=cw1b(1,j,k)
do i = 2,nx
tmp1 = real(cw1b(i,j,k), kind=mytype)
tmp2 = aimag(cw1b(i,j,k))
tmp3 = real(cw1b(nx-i+2,j,k), kind=mytype)
tmp4 = aimag(cw1b(nx-i+2,j,k))
xx1=tmp1*bx(i)
xx2=tmp1*ax(i)
xx3=tmp2*bx(i)
xx4=tmp2*ax(i)
xx5=tmp3*bx(i)
xx6=tmp3*ax(i)
xx7=tmp4*bx(i)
xx8=tmp4*ax(i)
cw1(i,j,k) = cmplx(xx1-xx4+xx6+xx7,-(-xx2-xx3+xx5-xx8), &
kind=mytype)
end do
end do
end do
#ifdef DEBUG
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
if (abs(cw1(i,j,k)) > 1.0e-4) then
write(*,100) 'AFTER X',i,j,k,cw1(i,j,k)
end if
end do
end do
end do
#endif
! POST PROCESSING IN Y
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*by(j)-tmp2*ay(j), &
tmp2*by(j)+tmp1*ay(j), kind=mytype)
if (j.gt.(ny/2+1)) cw1(i,j,k)=-cw1(i,j,k)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'AFTER Y',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN Z
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)-tmp2*az(k), &
tmp2*bz(k)+tmp1*az(k), kind=mytype)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'END',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! compute c2r transform
call decomp_2d_fft_3d(cw1,rhs)
! rhs is in Z-pencil but requires global operations in X
call transpose_z_to_y(rhs,rw2,ph)
call transpose_y_to_x(rw2,rw1,ph)
do k=ph%xst(3),ph%xen(3)
do j=ph%xst(2),ph%xen(2)
do i=1,nx/2
rw1b(2*i-1,j,k)=rw1(i,j,k)
enddo
do i=1,nx/2
rw1b(2*i,j,k)=rw1(nx-i+1,j,k)
enddo
enddo
end do
call transpose_x_to_y(rw1b,rw2,ph)
call transpose_y_to_z(rw2,rhs,ph)
! call decomp_2d_fft_finalize
return
end subroutine poisson_100
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Solving 3D Poisson equation: Neumann in Y; periodic in X & Z
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine poisson_010(rhs)
implicit none
real(mytype), dimension(:,:,:), intent(INOUT) :: rhs
complex(mytype) :: xyzk
real(mytype) :: tmp1, tmp2, tmp3, tmp4
real(mytype) :: xx1,xx2,xx3,xx4,xx5,xx6,xx7,xx8
integer :: nx,ny,nz, i,j,k
100 format(1x,a8,3I4,2F12.6)
nx = nx_global
ny = ny_global - 1
nz = nz_global
! rhs is in Z-pencil but requires global operations in Y
call transpose_z_to_y(rhs,rw2,ph)
do k=ph%yst(3),ph%yen(3)
do i=ph%yst(1),ph%yen(1)
do j=1,ny/2
rw2b(i,j,k)=rw2(i,2*(j-1)+1,k)
enddo
do j=ny/2+1,ny
rw2b(i,j,k)=rw2(i,2*ny-2*j+2,k)
enddo
enddo
end do
call transpose_y_to_z(rw2b,rhs,ph)
if (.not. fft_initialised) then
call decomp_2d_fft_init(PHYSICAL_IN_Z,nx,ny,nz)
fft_initialised = .true.
end if
! compute r2c transform
call decomp_2d_fft_3d(rhs,cw1)
! normalisation
cw1 = cw1 / real(nx, kind=mytype) /real(ny, kind=mytype) &
/ real(nz, kind=mytype)
#ifdef DEBUG
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
if (abs(cw1(i,j,k)) > 1.0e-4) then
write(*,100) 'START',i,j,k,cw1(i,j,k)
end if
end do
end do
end do
#endif
! post-processing in spectral space
! POST PROCESSING IN Z
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)+tmp2*az(k), &
tmp2*bz(k)-tmp1*az(k), kind=mytype)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'after z',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN X
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bx(i)+tmp2*ax(i), &
tmp2*bx(i)-tmp1*ax(i), kind=mytype)
if (i.gt.(nx/2+1)) cw1(i,j,k)=-cw1(i,j,k)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'after x',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN Y
! NEED TO BE IN Y PENCILS!!!!!!!!!!!!!!!
call transpose_x_to_y(cw1,cw2,sp)
do k = sp%yst(3), sp%yen(3)
do i = sp%yst(1), sp%yen(1)
cw2b(i,1,k)=cw2(i,1,k)
do j = 2,ny
tmp1 = real(cw2(i,j,k), kind=mytype)
tmp2 = aimag(cw2(i,j,k))
tmp3 = real(cw2(i,ny-j+2,k), kind=mytype)
tmp4 = aimag(cw2(i,ny-j+2,k))
xx1=tmp1*by(j)/2._mytype
xx2=tmp1*ay(j)/2._mytype
xx3=tmp2*by(j)/2._mytype
xx4=tmp2*ay(j)/2._mytype
xx5=tmp3*by(j)/2._mytype
xx6=tmp3*ay(j)/2._mytype
xx7=tmp4*by(j)/2._mytype
xx8=tmp4*ay(j)/2._mytype
cw2b(i,j,k) = cmplx(xx1+xx4+xx5-xx8,-xx2+xx3+xx6+xx7, &
kind=mytype)
end do
end do
end do
#ifdef DEBUG
do k = sp%yst(3), sp%yen(3)
do j = sp%yst(2), sp%yen(2)
do i = sp%yst(1), sp%yen(1)
if (abs(cw2b(i,j,k)) > 1.0e-4) then
write(*,100) 'after y',i,j,k,cw2b(i,j,k)
print *,kxyz(i,j,k)
end if
end do
end do
end do
#endif
if (istret==0) then
! Solve Poisson
! doing wave number division in Y-pencil
do k = sp%yst(3), sp%yen(3)
do j = sp%yst(2), sp%yen(2)
do i = sp%yst(1), sp%yen(1)
!tmp1=real(zk2(k)+yk2(j)+xk2(i), kind=mytype)
!tmp2=aimag(zk2(k)+yk2(j)+xk2(i))
tmp1=real(kxyz(i,j,k), kind=mytype)
tmp2=aimag(kxyz(i,j,k))
!xyzk=cmplx(tmp1,tmp2, kind=mytype)
!CANNOT DO A DIVISION BY ZERO
if ((abs(tmp1).lt.epsilon).and.(abs(tmp2).lt.epsilon)) then
cw2b(i,j,k)=cmplx(0._mytype,0._mytype, kind=mytype)
end if
if ((abs(tmp1).lt.epsilon).and.(abs(tmp2).ge.epsilon)) then
cw2b(i,j,k)=cmplx(0._mytype, &
aimag(cw2b(i,j,k))/(-tmp2), kind=mytype)
end if
if ((abs(tmp1).ge.epsilon).and.(abs(tmp2).lt.epsilon)) then
cw2b(i,j,k)=cmplx( real(cw2b(i,j,k), kind=mytype) &
/(-tmp1), 0._mytype, kind=mytype)
end if
if ((abs(tmp1).ge.epsilon).and.(abs(tmp2).ge.epsilon)) then
cw2b(i,j,k)=cmplx( real(cw2b(i,j,k), kind=mytype) &
/(-tmp1), &
aimag(cw2b(i,j,k))/(-tmp2), kind=mytype)
end if
end do
end do
end do
else
call matrice_refinement()
! do k = sp%yst(3), sp%yen(3)
! do j = 1,ny/2
! do i = sp%yst(1), sp%yen(1)
! print *,i,j,k,a(i,j,k,3)
!! if (nrank.le.1) print *,i,j,k,a(i,j,k,3)
!! if (nrank.gt.1) print *,i+4,j,k,a(i,j,k,3)
! enddo
! enddo
! enddo
if (istret.ne.3) then
cw2(:,:,:)=0.;cw2c(:,:,:)=0.
do k = sp%yst(3), sp%yen(3)
do j = 1,ny/2
do i = sp%yst(1), sp%yen(1)
cw2(i,j,k)=cw2b(i,2*j-1,k)
cw2c(i,j,k)=cw2b(i,2*j,k)
enddo
enddo
enddo
! do k = sp%yst(3), sp%yen(3)
! do j = 1,ny/2
! do i = sp%yst(1), sp%yen(1)
! if (abs(cw2(i,j,k)) > 1.0e-4) then
! write(*,*) 'before IN',i,j,k,cw2(i,j,k)!*2.
!! end if
! end do
! end do
! end do
call inversion5_v1(a,cw2,sp)
call inversion5_v1(a2,cw2c,sp)
! cw2(1,1,1)=cw2(1,1,1)*0.5
! do k = sp%yst(3), sp%yen(3)
! do j = 1,ny/2
! do i = sp%yst(1), sp%yen(1)
! if (abs(cw2c(i,j,k)) > 1.0e-4) then
! write(*,*) 'after IN',i,j,k,cw2c(i,j,k)!*2.
! end if
! end do
! end do
! end do
cw2b(:,:,:)=0.
do k=sp%yst(3), sp%yen(3)
do j=1,ny-1,2
do i=sp%yst(1), sp%yen(1)
cw2b(i,j,k)=cw2(i,(j+1)/2,k)
enddo
enddo
do j=2,ny,2
do i=sp%yst(1), sp%yen(1)
cw2b(i,j,k)=cw2c(i,j/2,k)
enddo
enddo
enddo
!do k=sp%yst(3), sp%yen(3)
!do i=sp%yst(1), sp%yen(1)
! if ((xkx(i)==0).and.(zkz(k)==0)) then
! ! cw2b(i,1,1)=0.
! ! cw2b(i,ny,1)=0.
! endif
!enddo
!enddo
else
do k = sp%yst(3), sp%yen(3)
do j = 1,ny
do i = sp%yst(1), sp%yen(1)
cw2(i,j,k)=cw2b(i,j,k)
enddo
enddo
enddo
call inversion5_v2(a3,cw2,sp)
do k = sp%yst(3), sp%yen(3)
do j = 1,ny
do i = sp%yst(1), sp%yen(1)
cw2b(i,j,k)=cw2(i,j,k)
enddo
enddo
enddo
endif
endif
! print *,nrank, sp%yst(3),sp%yen(3),sp%yst(1),sp%yen(1)
!we are in Y pencil
do k = sp%yst(3), sp%yen(3)
do i = sp%yst(1), sp%yen(1)
if ((i==nx/2+1).and.(k==nz/2+1)) then
cw2b(i,:,k)=0.
endif
enddo
enddo
#ifdef DEBUG
do k = sp%yst(3), sp%yen(3)
do j = sp%yst(2), sp%yen(2)
do i = sp%yst(1), sp%yen(1)
if (abs(cw2b(i,j,k)) > 1.0e-4) then
write(*,100) 'AFTER',i,j,k,cw2b(i,j,k)
print *,kxyz(i,j,k)
end if
end do
end do
end do
#endif
! post-processing backward
! POST PROCESSING IN Y
do k = sp%yst(3), sp%yen(3)
do i = sp%yst(1), sp%yen(1)
cw2(i,1,k)=cw2b(i,1,k)
do j = 2,ny
tmp1 = real(cw2b(i,j,k), kind=mytype)
tmp2 = aimag(cw2b(i,j,k))
tmp3 = real(cw2b(i,ny-j+2,k), kind=mytype)
tmp4 = aimag(cw2b(i,ny-j+2,k))
xx1=tmp1*by(j)
xx2=tmp1*ay(j)
xx3=tmp2*by(j)
xx4=tmp2*ay(j)
xx5=tmp3*by(j)
xx6=tmp3*ay(j)
xx7=tmp4*by(j)
xx8=tmp4*ay(j)
cw2(i,j,k) = cmplx(xx1-xx4+xx6+xx7,-(-xx2-xx3+xx5-xx8), &
kind=mytype)
end do
end do
end do
! Back to X-pencil
call transpose_y_to_x(cw2,cw1,sp)
#ifdef DEBUG
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
if (abs(cw1(i,j,k)) > 1.0e-4) then
write(*,100) 'AFTER Y',i,j,k,cw1(i,j,k)
end if
end do
end do
end do
#endif
! POST PROCESSING IN X
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bx(i)-tmp2*ax(i), &
tmp2*bx(i)+tmp1*ax(i), kind=mytype)
if (i.gt.(nx/2+1)) cw1(i,j,k)=-cw1(i,j,k)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'AFTER X',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! POST PROCESSING IN Z
do k = sp%xst(3),sp%xen(3)
do j = sp%xst(2),sp%xen(2)
do i = sp%xst(1),sp%xen(1)
tmp1 = real(cw1(i,j,k), kind=mytype)
tmp2 = aimag(cw1(i,j,k))
cw1(i,j,k) = cmplx(tmp1*bz(k)-tmp2*az(k), &
tmp2*bz(k)+tmp1*az(k), kind=mytype)
#ifdef DEBUG
if (abs(cw1(i,j,k)) > 1.0e-4) &
write(*,100) 'END',i,j,k,cw1(i,j,k)
#endif
end do
end do
end do
! compute c2r transform, back to physical space
call decomp_2d_fft_3d(cw1,rhs)
! rhs is in Z-pencil but requires global operations in Y
call transpose_z_to_y(rhs,rw2,ph)
do k=ph%yst(3),ph%yen(3)
do i=ph%yst(1),ph%yen(1)
do j=1,ny/2
rw2b(i,2*j-1,k)=rw2(i,j,k)
enddo
do j=1,ny/2