/
poisson.f90
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/
poisson.f90
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!Copyright (c) 2012-2022, Xcompact3d
!This file is part of Xcompact3d (xcompact3d.com)
!SPDX-License-Identifier: BSD 3-Clause
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_mytype
#else
real(mytype), parameter :: epsilon = 1.e-8_mytype
#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.
abstract interface
subroutine poisson_xxx(rhs)
use decomp_2d, only : mytype
real(mytype), dimension(:,:,:), intent(inout) :: rhs
end subroutine poisson_xxx
end interface
procedure (poisson_xxx), pointer :: poisson
public :: decomp_2d_poisson_init,decomp_2d_poisson_finalize,poisson
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Initialise Poisson solver for given boundary conditions
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine decomp_2d_poisson_init()
implicit none
integer :: nx, ny, nz, i
real(mytype) :: rl, iy
external rl, iy
if (nclx) then
bcx=0
else
bcx=1
endif
if (ncly) then
bcy=0
else
bcy=1
endif
if (nclz) then
bcz=0
else
bcz=1
endif
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Top level wrapper
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (bcx==0 .and. bcy==0 .and. bcz==0) then
poisson => poisson_000
else if (bcx==1 .and. bcy==0 .and. bcz==0) then
poisson => poisson_100
else if (bcx==0 .and. bcy==1 .and. bcz==0) then
poisson => poisson_010
else if (bcx==1 .and. bcy==1) then ! 110 & 111
poisson => poisson_11x
else
stop 'boundary condition not supported'
end if
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
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# decomp_2d_poisson_init start'
#endif
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)
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# decomp_2d_poisson_init decomp_info_init'
#endif
call decomp_info_init(nx, ny, nz, ph)
call decomp_info_init(nx, ny, nz/2+1, sp)
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# decomp_2d_poisson_init decomp_info_init ok'
#endif
! 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
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# decomp_2d_poisson_init before waves'
#endif
call waves()
if (bcy == 1 .and. istret /= 0) call matrice_refinement()
!write(*,*) 'POinit ii1 arl ', rl(a(1,1,1,1)),rl(a(1,1,1,2)),rl(a(1,1,1,3)),&
! rl(a(1,1,1,4)),rl(a(1,1,1,5))
!write(*,*) 'POinit ii1 aiy ', iy(a(1,1,1,1)),iy(a(1,1,1,2)),iy(a(1,1,1,3)),&
! iy(a(1,1,1,4)),iy(a(1,1,1,5))
!!
!write(*,*) 'POinit ii5 arl ', rl(a(5,5,5,1)),rl(a(5,5,5,2)),rl(a(5,5,5,3)),&
! rl(a(5,5,5,4)),rl(a(5,5,5,5))
!write(*,*) 'POinit ii5 aiy ', iy(a(5,5,5,1)),iy(a(5,5,5,2)),iy(a(5,5,5,3)),&
! iy(a(5,5,5,4)),iy(a(5,5,5,5))
!!!
!write(*,*) 'POinit ii1 a2rl ', rl(a2(1,1,1,1)),rl(a2(1,1,1,2)),rl(a2(1,1,1,3)),&
! rl(a2(1,1,1,4)),rl(a2(1,1,1,5))
!write(*,*) 'POinit ii1 a2iy ', iy(a2(1,1,1,1)),iy(a2(1,1,1,2)),iy(a2(1,1,1,3)),&
! iy(a2(1,1,1,4)),iy(a2(1,1,1,5))
!!
!write(*,*) 'POinit ii5 a2rl ', rl(a2(5,5,5,1)),rl(a2(5,5,5,2)),rl(a2(5,5,5,3)),&
! rl(a2(5,5,5,4)),rl(a2(5,5,5,5))
!write(*,*) 'POinit ii5 a2iy ', iy(a2(5,5,5,1)),iy(a2(5,5,5,2)),iy(a2(5,5,5,3)),&
! iy(a2(5,5,5,4)),iy(a2(5,5,5,5))
!!!
!write(*,*) 'POinit ii1 a3rl ', rl(a3(1,1,1,1)),rl(a3(1,1,1,2)),rl(a3(1,1,1,3)),&
! rl(a3(1,1,1,4)),rl(a3(1,1,1,5))
!write(*,*) 'POinit ii1 a3iy ', iy(a3(1,1,1,1)),iy(a3(1,1,1,2)),iy(a3(1,1,1,3)),&
! iy(a3(1,1,1,4)),iy(a3(1,1,1,5))
!!
!write(*,*) 'POinit ii5 a3rl ', rl(a3(5,5,5,1)),rl(a3(5,5,5,2)),rl(a3(5,5,5,3)),&
! rl(a3(5,5,5,4)),rl(a3(5,5,5,5))
!write(*,*) 'POinit ii5 a3iy ', iy(a3(5,5,5,1)),iy(a3(5,5,5,2)),iy(a3(5,5,5,3)),&
! iy(a3(5,5,5,4)),iy(a3(5,5,5,5))
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# decomp_2d_poisson_init end'
#endif
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)
deallocate(a,a2,a3)
else if (bcx==1 .and. bcy==0 .and. bcz==0) then
deallocate(cw1,cw1b,rw1,rw1b,rw2)
deallocate(a,a2,a3)
else if (bcx==0 .and. bcy==1 .and. bcz==0) then
deallocate(cw1,cw2,cw2b,rw2,rw2b)
deallocate(a,a2,a3)
else if (bcx==1 .and. bcy==1) then
deallocate(cw1,cw1b,cw2,cw2b,rw1,rw1b,rw2,rw2b)
deallocate(a,a2,a3)
if (bcz==1) then
deallocate(rw3)
end if
end if
return
end subroutine decomp_2d_poisson_finalize
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! 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
complex(mytype) :: cx
real(mytype) :: rl, iy
external cx, rl, iy
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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) + tmp2 * az(k), &
tmp2 * bz(k) - tmp1 * az(k))
! POST PROCESSING IN Y
tmp1 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * by(j) + tmp2 * ay(j), &
tmp2 * by(j) - tmp1 * ay(j))
if (j > (ny/2+1)) cw1(i,j,k) = -cw1(i,j,k)
! POST PROCESSING IN X
tmp1 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bx(i) + tmp2 * ax(i), &
tmp2 * bx(i) - tmp1 * ax(i))
if (i > (nx/2+1)) cw1(i,j,k) = -cw1(i,j,k)
! Solve Poisson
tmp1 = rl(kxyz(i,j,k))
tmp2 = iy(kxyz(i,j,k))
! CANNOT DO A DIVISION BY ZERO
if ((tmp1 < epsilon).or.(tmp2 < epsilon)) then
cw1(i,j,k) = zero
else
cw1(i,j,k) = cx(rl(cw1(i,j,k)) / (-tmp1), &
iy(cw1(i,j,k)) / (-tmp2))
end if
!Print result in spectal space after Poisson
! if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) - tmp2 * az(k), &
-tmp2 * bz(k) - tmp1 * az(k))
! POST PROCESSING IN Y
tmp1 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * by(j) + tmp2 * ay(j), &
tmp2 * by(j) - tmp1 * ay(j))
if (j > (ny/2 + 1)) cw1(i,j,k) = -cw1(i,j,k)
! POST PROCESSING IN X
tmp1 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bx(i) + tmp2 * ax(i), &
-tmp2 * bx(i) + tmp1 * ax(i))
if (i > (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)
use dbg_schemes, only: abs_prec
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
complex(mytype) :: cx
real(mytype) :: rl, iy
external cx, rl, iy
100 format(1x,a8,3I4,2F12.6)
nx = nx_global - 1
ny = ny_global
nz = nz_global
!write(*,*) 'Poisson_100'
! 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_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) + tmp2 * az(k), &
tmp2 * bz(k) - tmp1 * az(k))
#ifdef DEBUG
if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * by(j) + tmp2 * ay(j), &
tmp2 * by(j) - tmp1 * ay(j))
if (j > (ny/2+1)) cw1(i,j,k) = -cw1(i,j,k)
#ifdef DEBUG
if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
tmp3 = rl(cw1(nx-i+2,j,k))
tmp4 = iy(cw1(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)
cw1b(i,j,k) = half * cx(xx1 + xx4 + xx5 - xx8, &
-xx2 + xx3 + xx6 + xx7)
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_prec(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 = rl(kxyz(i,j,k))
tmp2 = iy(kxyz(i,j,k))
! CANNOT DO A DIVISION BY ZERO
if ((abs_prec(tmp1) < epsilon).and.(abs_prec(tmp2) < epsilon)) then
cw1b(i,j,k)=cx(zero, zero)
end if
if ((abs_prec(tmp1) < epsilon).and.(abs_prec(tmp2) >= epsilon)) then
cw1b(i,j,k)=cx(zero, iy(cw1b(i,j,k)) / (-tmp2))
end if
if ((abs_prec(tmp1) >= epsilon).and.(abs_prec(tmp2) < epsilon)) then
cw1b(i,j,k)=cx(rl(cw1b(i,j,k)) / (-tmp1), zero)
end if
if ((abs_prec(tmp1) >= epsilon).and.(abs_prec(tmp2) >= epsilon)) then
cw1b(i,j,k)=cx(rl(cw1b(i,j,k)) / (-tmp1), iy(cw1b(i,j,k)) / (-tmp2))
end if
#ifdef DEBUG
if (abs_prec(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 = rl(cw1b(i,j,k))
tmp2 = iy(cw1b(i,j,k))
tmp3 = rl(cw1b(nx-i+2,j,k))
tmp4 = iy(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) = cx(xx1-xx4+xx6+xx7, &
-(-xx2-xx3+xx5-xx8))
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_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * by(j) - tmp2 * ay(j), &
tmp2 * by(j) + tmp1 * ay(j))
if (j > (ny/2+1)) cw1(i,j,k) = -cw1(i,j,k)
#ifdef DEBUG
if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) - tmp2 * az(k), &
tmp2 * bz(k) + tmp1 * az(k))
#ifdef DEBUG
if (abs_prec(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)
use dbg_schemes, only: abs_prec
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
complex(mytype) :: cx
real(mytype) :: rl, iy
external cx, rl, iy
100 format(1x,a8,3I4,2F12.6)
nx = nx_global
ny = ny_global - 1
nz = nz_global
#ifdef DEBG
if (nrank .eq. 0) write(*,*)'# Poisoon_010 Init'
#endif
! 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_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) + tmp2 * az(k), &
tmp2 * bz(k) - tmp1 * az(k))
#ifdef DEBUG
if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bx(i) + tmp2 * ax(i), &
tmp2 * bx(i) - tmp1 * ax(i))
if (i.gt.(nx/2+1)) cw1(i,j,k)=-cw1(i,j,k)
#ifdef DEBUG
if (abs_prec(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 = rl(cw2(i,j,k))
tmp2 = iy(cw2(i,j,k))
tmp3 = rl(cw2(i,ny-j+2,k))
tmp4 = iy(cw2(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)
cw2b(i,j,k) = half * cx(xx1+xx4+xx5-xx8, &
-xx2+xx3+xx6+xx7)
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_prec(cw2b(i,j,k)) > 1.0e-4) then
write(*,100) 'after y',i,j,k,cw2b(i,j,k)
write(*,*)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 = rl(kxyz(i,j,k))
tmp2 = iy(kxyz(i,j,k))
!CANNOT DO A DIVISION BY ZERO
if ((abs_prec(tmp1) < epsilon).and.(abs_prec(tmp2) < epsilon)) then
cw2b(i,j,k) = cx(zero, zero)
end if
if ((abs_prec(tmp1) < epsilon).and.(abs_prec(tmp2) >= epsilon)) then
cw2b(i,j,k) = cx(zero, iy(cw2b(i,j,k)) / (-tmp2))
end if
if ((abs_prec(tmp1) >= epsilon).and.(abs_prec(tmp2) < epsilon)) then
cw2b(i,j,k) = cx(rl(cw2b(i,j,k)) / (-tmp1), zero)
end if
if ((abs_prec(tmp1) >= epsilon).and.(abs_prec(tmp2) >= epsilon)) then
cw2b(i,j,k) = cx(rl(cw2b(i,j,k)) / (-tmp1), iy(cw2b(i,j,k)) / (-tmp2))
end if
end do
end do
end do
else
call matrice_refinement()
!write(*,*) 'PO_010 ii1 A rl ', rl(a(1,1,1,1)),rl(a(1,1,1,2)),rl(a(1,1,1,3)),&
! rl(a(1,1,1,4)),rl(a(1,1,1,5))
!write(*,*) 'PO_010 ii1 A iy ', iy(a(1,1,1,1)),iy(a(1,1,1,2)),iy(a(1,1,1,3)),&
! iy(a(1,1,1,4)),iy(a(1,1,1,5))
!!
!write(*,*) 'PO_010 ii5 A rl ', rl(a(5,5,5,1)),rl(a(5,5,5,2)),rl(a(5,5,5,3)),&
! rl(a(5,5,5,4)),rl(a(5,5,5,5))
!write(*,*) 'PO_010 ii5 A iy ', iy(a(5,5,5,1)),iy(a(5,5,5,2)),iy(a(5,5,5,3)),&
! iy(a(5,5,5,4)),iy(a(5,5,5,5))
!!
!write(*,*) 'PO_010 ii1 A2 rl ', rl(a2(1,1,1,1)),rl(a2(1,1,1,2)),rl(a2(1,1,1,3)),&
! rl(a2(1,1,1,4)),rl(a2(1,1,1,5))
!write(*,*) 'PO_010 ii1 A2 iy ', iy(a2(1,1,1,1)),iy(a2(1,1,1,2)),iy(a2(1,1,1,3)),&
! iy(a2(1,1,1,4)),iy(a2(1,1,1,5))
!!
!write(*,*) 'PO_010 ii5 A2 rl ', rl(a2(5,5,5,1)),rl(a2(5,5,5,2)),rl(a2(5,5,5,3)),&
! rl(a2(5,5,5,4)),rl(a2(5,5,5,5))
!write(*,*) 'PO_010 ii5 A2 iy ', iy(a2(5,5,5,1)),iy(a2(5,5,5,2)),iy(a2(5,5,5,3)),&
! iy(a2(5,5,5,4)),iy(a2(5,5,5,5))
!!!
!!!
!write(*,*) 'PO_010 ii1 A3 rl ', rl(a3(1,1,1,1)),rl(a3(1,1,1,2)),rl(a3(1,1,1,3)),&
! rl(a3(1,1,1,4)),rl(a3(1,1,1,5))
!write(*,*) 'PO_010 ii1 A3 iy ', iy(a3(1,1,1,1)),iy(a3(1,1,1,2)),iy(a3(1,1,1,3)),&
! iy(a3(1,1,1,4)),iy(a3(1,1,1,5))
!!
!write(*,*) 'PO_010 ii5 A3 rl ', rl(a3(5,5,5,1)),rl(a3(5,5,5,2)),rl(a3(5,5,5,3)),&
! rl(a3(5,5,5,4)),rl(a3(5,5,5,5))
!write(*,*) 'PO_010 ii5 A3 iy ', iy(a3(5,5,5,1)),iy(a3(5,5,5,2)),iy(a3(5,5,5,3)),&
! iy(a3(5,5,5,4)),iy(a3(5,5,5,5))
if (istret /= 3) then
cw2 = zero
cw2c = zero
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
call inversion5_v1(a,cw2,sp)
call inversion5_v1(a2,cw2c,sp)
cw2b = zero
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
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
!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) = zero
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_prec(cw2b(i,j,k)) > 1.0e-4) then
write(*,100) 'AFTER',i,j,k,cw2b(i,j,k)
write(*,*)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 = rl(cw2b(i,j,k))
tmp2 = iy(cw2b(i,j,k))
tmp3 = rl(cw2b(i,ny-j+2,k))
tmp4 = iy(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) = cx(xx1-xx4+xx6+xx7, &
-(-xx2-xx3+xx5-xx8))
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_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bx(i) - tmp2 * ax(i), &
tmp2 * bx(i) + tmp1 * ax(i))
if (i > (nx/2 + 1)) cw1(i,j,k) = -cw1(i,j,k)
#ifdef DEBUG
if (abs_prec(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 = rl(cw1(i,j,k))
tmp2 = iy(cw1(i,j,k))
cw1(i,j,k) = cx(tmp1 * bz(k) - tmp2 * az(k), &
tmp2 * bz(k) + tmp1 * az(k))
#ifdef DEBUG