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elliptic.f90
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MODULE elliptic
USE parameters
USE fft
USE mpi
IMPLICIT NONE
CONTAINS
SUBROUTINE helmholtzdouble(p,ft,b_bot,b_top)
double complex, dimension(iktx,ikty,n3h1), intent(out) :: p !Pressure in usual z-parallelization
double complex, dimension(iktx,n3d1, iktyp) :: pt !Transposed (ky-parallelization) pressure
double complex, dimension(iktx,n3, iktyp), intent(in) :: ft !Transposed (ky-parallelization) right-hand side
double complex, dimension(iktx,ikty), intent(in) :: b_bot,b_top !Top and bottom buoyancy terms
integer :: step1,step2 !Intermediate steps in calculation of indices
integer :: info ! Returns error for sgtsv
double precision :: d(n3),dl(n3-1),du(n3-1) !diagonal value
double precision :: br(n3), bi(n3) !real and imaginary parts of rhs
DO ikx=1,iktx
kx=kxa(ikx)
DO ikyp=1,iktyp
iky=ikyp+iktyp*mype
ky=kya(iky)
kh2=kx*kx + ky*ky
if(kh2/=0 .and. L(ikx,iky)==1 ) then
do iz=1,n3
br(iz)=dz*dz*DBLE( ft(ikx,iz,ikyp) )
bi(iz)=dz*dz*DIMAG( ft(ikx,iz,ikyp) )
end do
!--- For nonzero w* at the top/bot, we must add an extra to the RHS ---!
!----------------------------------------------------------------------!
iz=1
br(iz) = br(iz) + (a_helm(iz) - 0.5*b_helm(iz)*dz)* DBLE(b_bot(ikx,iky))*dz
bi(iz) = bi(iz) + (a_helm(iz) - 0.5*b_helm(iz)*dz)*DIMAG(b_bot(ikx,iky))*dz
iz=n3
br(iz) = br(iz) - (a_helm(iz) + 0.5*b_helm(iz)*dz)* DBLE(b_top(ikx,iky))*dz
bi(iz) = bi(iz) - (a_helm(iz) + 0.5*b_helm(iz)*dz)*DIMAG(b_top(ikx,iky))*dz
!----------------------------------------------------------------------!
do iz=1,n3
if(iz==1) then
d(iz) = -a_helm(iz)-0.5*b_helm(iz)*dz-kh2*dz*dz
du(iz) = a_helm(iz)+0.5*b_helm(iz)*dz
elseif(iz==n3) then
d(iz) = -a_helm(iz)+0.5*b_helm(iz)*dz-kh2*dz*dz
dl(iz-1) = a_helm(iz)-0.5*b_helm(iz)*dz
else !1<iz<n3
d(iz) = -2*a_helm(iz)-kh2*dz*dz
du(iz) = a_helm(iz)+0.5*b_helm(iz)*dz
dl(iz-1) = a_helm(iz)-0.5*b_helm(iz)*dz
end if
end do
call DGTSV( n3, 1, dl, d, du, br, n3, info )
if(info/=0) write(*,*) "problem in helmdouble", info
do iz=1,n3
if(iz==1) then
d(iz) = -a_helm(iz)-0.5*b_helm(iz)*dz-kh2*dz*dz
du(iz) = a_helm(iz)+0.5*b_helm(iz)*dz
elseif(iz==n3) then
d(iz) = -a_helm(iz)+0.5*b_helm(iz)*dz-kh2*dz*dz
dl(iz-1) = a_helm(iz)-0.5*b_helm(iz)*dz
else !1<iz<n3
d(iz) = -2*a_helm(iz)-kh2*dz*dz
du(iz) = a_helm(iz)+0.5*b_helm(iz)*dz
dl(iz-1) = a_helm(iz)-0.5*b_helm(iz)*dz
end if
end do
call DGTSV( n3, 1, dl, d, du, bi, n3, info )
if(info/=0) write(*,*) "problem in helmdouble (imag)", info
!*** Put the solution in pt ***!
do izth=1,n3d1
step1=(izth-1)/n3h1 !mype
step2=izth-n3h1*step1 !position in mype
iz=step1*n3h0+step2-1 !-1 factor since h1 fields
if(izth/=1 .and. izth/=n3d1) then
pt(ikx,izth,ikyp)=br(iz)+i*bi(iz)
else
pt(ikx,izth,ikyp)=(0.,0.)
end if
end do
else
!set kh=0 modes to zero...
DO izth=1,n3d1
pt(ikx,izth,ikyp)=(0.,0.)
END DO
end if
END DO
END DO
!*********** Transposition to z-parallelized p ***************!
call mpitranspose(pt,iktx,n3d1,iktyp,p,ikty,n3h1)
END SUBROUTINE HELMHOLTZDOUBLE
SUBROUTINE psi_solver(psik,qt)
! This subroutines solves the elliptic equation a_ell(z) d^2 psi/dz^2 + b_ell(z) d psi/dz - kh2 psi = q for the streamfunction psi.
double complex, dimension(iktx,ikty,n3h1), intent(out) :: psik !Pressure in usual z-parallelization
double complex, dimension(iktx,n3d1, iktyp) :: psit !Transposed (ky-parallelization) pressure
double complex, dimension(iktx,n3, iktyp), intent(in) :: qt !Transposed (ky-parallelization) right-hand side
integer :: step1,step2 !Intermediate steps in calculation of indices
integer :: info ! Returns error for sgtsv
double precision :: d(n3),dl(n3-1),du(n3-1) !diagonal value
double precision :: br(n3), bi(n3) !real and imaginary parts of rhs
DO ikx=1,iktx
kx=kxa(ikx)
DO ikyp=1,iktyp
iky=ikyp+iktyp*mype
ky=kya(iky)
kh2=kx*kx + ky*ky
if(kh2/=0 .and. L(ikx,iky)==1 ) then
do iz=1,n3
br(iz)=dz*dz*DBLE( qt(ikx,iz,ikyp) )
bi(iz)=dz*dz*DIMAG( qt(ikx,iz,ikyp) )
end do
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, br, n3, info )
if(info/=0) write(*,*) "problem in helmdouble", info
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, bi, n3, info )
if(info/=0) write(*,*) "problem in helmdouble (imag)", info
!*** Put the solution in pt ***!
do izth=1,n3d1
step1=(izth-1)/n3h1 !mype
step2=izth-n3h1*step1 !position in mype
iz=step1*n3h0+step2-1 !-1 factor since h1 fields
if(izth/=1 .and. izth/=n3d1) then
psit(ikx,izth,ikyp)=br(iz)+i*bi(iz)
else
psit(ikx,izth,ikyp)=(0.,0.)
end if
end do
else
!set kh=0 modes to zero...
DO izth=1,n3d1
psit(ikx,izth,ikyp)=(0.,0.)
END DO
end if
END DO
END DO
!*********** Transposition to z-parallelized p ***************!
call mpitranspose(psit,iktx,n3d1,iktyp,psik,ikty,n3h1)
END SUBROUTINE PSI_SOLVER
SUBROUTINE A_solver_ybj_plus_original(ak,bt)
! This subroutines solves the elliptic equation a_ell(z) d^2 psi/dz^2 + b_ell(z) d psi/dz - kh2 psi = q for the streamfunction psi.
double complex, dimension(iktx,ikty,n3h0), intent(out) :: ak !A in usual z-parallelization
double complex, dimension(iktx,n3, iktyp) :: at !Transposed (ky-parallelization) A
double complex, dimension(iktx,n3, iktyp), intent(in) :: bt !Transposed (ky-parallelization) right-hand side
integer :: info ! Returns error for sgtsv
double precision :: d(n3),dl(n3-1),du(n3-1) !diagonal value
double precision :: br(n3), bi(n3) !real and imaginary parts of rhs
DO ikx=1,iktx
kx=kxa(ikx)
DO ikyp=1,iktyp
iky=ikyp+iktyp*mype
ky=kya(iky)
kh2=kx*kx + ky*ky
if(kh2/=0 .and. L(ikx,iky)==1 ) then
do iz=1,n3
br(iz)=dz*dz*Bu*DBLE( bt(ikx,iz,ikyp) )
bi(iz)=dz*dz*Bu*DIMAG( bt(ikx,iz,ikyp) )
end do
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz/4. )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, br, n3, info )
if(info/=0) write(*,*) "problem in helmdouble", info
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz/4. )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, bi, n3, info )
if(info/=0) write(*,*) "problem in helmdouble (imag)", info
!*** Put the solution in pt ***!
DO iz=1,n3
at(ikx,iz,ikyp)=br(iz)+i*bi(iz)
END DO
else
!set kh=0 modes to zero...
DO iz=1,n3
at(ikx,iz,ikyp)=(0.,0.)
END DO
end if
END DO
END DO
!*********** Transposition to z-parallelized p ***************!
call mpitranspose(at,iktx,n3,iktyp,ak,ikty,n3h0)
END SUBROUTINE A_SOLVER_YBJ_PLUS_ORIGINAL
SUBROUTINE A_solver_ybj_plus(ak,bt,ck)
! This subroutines solves the elliptic equation a_ell(z) d^2 psi/dz^2 + b_ell(z) d psi/dz - kh2 psi = q for the streamfunction psi.
double complex, dimension(iktx,ikty,n3h0), intent(out) :: ak !A in usual z-parallelization
double complex, dimension(iktx,n3, iktyp) :: at !Transposed (ky-parallelization) A
double complex, dimension(iktx,n3, iktyp), intent(in) :: bt !Transposed (ky-parallelization) right-hand side
double complex, dimension(iktx,ikty,n3h0), intent(out) :: ck !C=A_z in usual z-parallelization
double complex, dimension(iktx,n3, iktyp) :: ct !Transposed (ky-parallelization) C
integer :: info ! Returns error for sgtsv
double precision :: d(n3),dl(n3-1),du(n3-1) !diagonal value
double precision :: br(n3), bi(n3) !real and imaginary parts of rhs
DO ikx=1,iktx
kx=kxa(ikx)
DO ikyp=1,iktyp
iky=ikyp+iktyp*mype
ky=kya(iky)
kh2=kx*kx + ky*ky
if(kh2/=0 .and. L(ikx,iky)==1 ) then
do iz=1,n3
br(iz)=dz*dz*Bu*DBLE( bt(ikx,iz,ikyp) )
bi(iz)=dz*dz*Bu*DIMAG( bt(ikx,iz,ikyp) )
end do
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz/4. )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, br, n3, info )
if(info/=0) write(*,*) "problem in helmdouble", info
do iz=1,n3
if(iz==1) then
d(iz) = -( rho_ut(iz)*a_ell_ut(iz)/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
elseif(iz==n3) then
d(iz) = -( rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz) + kh2*dz*dz/4. )
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
else !1<iz<n3
d(iz) = -( (rho_ut(iz)*a_ell_ut(iz) + rho_ut(iz-1)*a_ell_ut(iz-1))/rho_st(iz) + kh2*dz*dz/4. )
du(iz) = rho_ut(iz)*a_ell_ut(iz)/rho_st(iz)
dl(iz-1) = rho_ut(iz-1)*a_ell_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3, 1, dl, d, du, bi, n3, info )
if(info/=0) write(*,*) "problem in helmdouble (imag)", info
!*** Put the solution in pt ***!
DO iz=1,n3
at(ikx,iz,ikyp)=br(iz)+i*bi(iz)
END DO
else
!set kh=0 modes to zero...
DO iz=1,n3
at(ikx,iz,ikyp)=(0.,0.)
END DO
end if
END DO
END DO
!Compute C=A_z while transposed!
!******************************!
DO ikx=1,iktx
DO ikyp=1,iktyp
do iz=1,n3-1
ct(ikx,iz,ikyp) = ( at(ikx,iz+1,ikyp) - at(ikx,iz,ikyp) )/dz
end do
!Top: C = A_z = 0
ct(ikx,n3,ikyp) = (0.D0,0.D0)
end DO
end DO
!Transpose the result back to z-parallelized space!
call mpitranspose(ct,iktx,n3,iktyp,ck,ikty,n3h0)
!*********** Transposition to z-parallelized p ***************!
call mpitranspose(at,iktx,n3,iktyp,ak,ikty,n3h0)
END SUBROUTINE A_SOLVER_YBJ_PLUS
SUBROUTINE omega_equation(wak,qt)
! This subroutines solves the elliptic equation a_ell(z) d^2 psi/dz^2 + b_ell(z) d psi/dz - kh2 psi = q for the streamfunction psi.
double complex, dimension(iktx,ikty,n3h1), intent(out) :: wak !vertical velocity in usual z-parallelization
double complex, dimension(iktx,n3d1, iktyp) :: wat !Transposed (ky-parallelization) wak
double complex, dimension(iktx,n3, iktyp), intent(in) :: qt !Transposed (ky-parallelization) right-hand side
integer :: step1,step2 !Intermediate steps in calculation of indices
integer :: info ! Returns error for sgtsv
double precision :: d(n3-1),dl(n3-2),du(n3-2) !diagonal value
double precision :: br(n3-1), bi(n3-1) !real and imaginary parts of rhs
DO ikx=1,iktx
kx=kxa(ikx)
DO ikyp=1,iktyp
iky=ikyp+iktyp*mype
ky=kya(iky)
kh2=kx*kx + ky*ky
if(kh2/=0 .and. L(ikx,iky)==1 ) then
do iz=1,n3-1
br(iz)=dz*dz*DBLE( qt(ikx,iz,ikyp) )
bi(iz)=dz*dz*DIMAG( qt(ikx,iz,ikyp) )
end do
do iz=1,n3-1
if(iz==1) then
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
!-(rho_ut(iz)/(rho_st(iz+1)+rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz)) WRONG
du(iz) = rho_ut(iz+1)/rho_st(iz+1)
elseif(iz==(n3-1)) then
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
dl(iz-1) = rho_ut(iz-1)/rho_st(iz)
else !1<iz<n3-1
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
du(iz) = rho_ut(iz+1)/rho_st(iz+1)
dl(iz-1) = rho_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3-1, 1, dl, d, du, br, n3-1, info )
if(info/=0) write(*,*) "problem in helmdouble", info
do iz=1,n3-1
if(iz==1) then
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
du(iz) = rho_ut(iz+1)/rho_st(iz+1)
elseif(iz==(n3-1)) then
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
dl(iz-1) = rho_ut(iz-1)/rho_st(iz)
else !1<iz<n3-1
d(iz) = -(rho_ut(iz)*(rho_st(iz+1)+rho_st(iz))/(rho_st(iz+1)*rho_st(iz)) + dz*dz*kh2/a_ell_ut(iz))
du(iz) = rho_ut(iz+1)/rho_st(iz+1)
dl(iz-1) = rho_ut(iz-1)/rho_st(iz)
end if
end do
call DGTSV( n3-1, 1, dl, d, du, bi, n3-1, info )
if(info/=0) write(*,*) "problem in helmdouble (imag)", info
!*** Put the solution in pt ***!
do izth=1,n3d1
step1=(izth-1)/n3h1 !mype
step2=izth-n3h1*step1 !position in mype
iz=step1*n3h0+step2-1 !-1 factor since h1 fields
if(izth/=1 .and. izth/=n3d1 .and. iz/=n3) then !Difference with psi_solver, if iz=n3, w=0. I didn't even solve the equation for that point...
wat(ikx,izth,ikyp)=br(iz)+i*bi(iz)
else
wat(ikx,izth,ikyp)=(0.,0.)
end if
end do
else
!set kh=0 modes to zero...
DO izth=1,n3d1
wat(ikx,izth,ikyp)=(0.,0.)
END DO
end if
END DO
END DO
!*********** Transposition to z-parallelized p ***************!
call mpitranspose(wat,iktx,n3d1,iktyp,wak,ikty,n3h1)
END SUBROUTINE OMEGA_EQUATION
END MODULE elliptic