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gyacomo/src/nonlinear_mod.F90
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nonlinear_mod.F90
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MODULE nonlinear
USE array, ONLY : dnjs, Sepj, Sipj, kernel_i, kernel_e,&
moments_e_ZF, moments_i_ZF, phi_ZF
USE initial_par, ONLY : ACT_ON_MODES
USE basic
USE fourier
USE fields, ONLY : phi, moments_e, moments_i
USE grid
USE model
USE prec_const
USE time_integration, ONLY : updatetlevel
IMPLICIT NONE
INCLUDE 'fftw3-mpi.f03'
COMPLEX(dp), DIMENSION(:,:), ALLOCATABLE :: F_cmpx, G_cmpx
COMPLEX(dp), DIMENSION(:,:), ALLOCATABLE :: Fx_cmpx, Gy_cmpx
COMPLEX(dp), DIMENSION(:,:), ALLOCATABLE :: Fy_cmpx, Gx_cmpx, F_conv_G
INTEGER :: in, is, p_int, j_int
INTEGER :: nmax, smax ! Upper bound of the sums
REAL(dp):: kx, ky, kerneln
PUBLIC :: compute_Sapj, nonlinear_init
CONTAINS
SUBROUTINE nonlinear_init
ALLOCATE( F_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE( G_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE(Fx_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE(Gy_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE(Fy_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE(Gx_cmpx(ikys:ikye,ikxs:ikxe))
ALLOCATE(F_conv_G(ikys:ikye,ikxs:ikxe))
END SUBROUTINE nonlinear_init
SUBROUTINE compute_Sapj
! This routine is meant to compute the non linear term for each specie and degree
!! In real space Sapj ~ b*(grad(phi) x grad(g)) which in moments in fourier becomes
!! Sapj = Sum_n (ikx Kn phi)#(iky Sum_s d_njs Naps) - (iky Kn phi)#(ikx Sum_s d_njs Naps)
!! where # denotes the convolution.
! Execution time start
CALL cpu_time(t0_Sapj)
SELECT CASE(LINEARITY)
CASE ('nonlinear')
CALL compute_nonlinear
CASE ('ZF_semilin')
CALL compute_semi_linear_ZF
CASE ('NZ_semilin')
CALL compute_semi_linear_NZ
CASE ('linear')
Sepj = 0._dp; Sipj = 0._dp
CASE DEFAULT
IF(my_id.EQ.0) write(*,*) '/!\ Linearity not recognized /!\'
stop
END SELECT
! Execution time END
CALL cpu_time(t1_Sapj)
tc_Sapj = tc_Sapj + (t1_Sapj - t0_Sapj)
END SUBROUTINE compute_Sapj
SUBROUTINE compute_nonlinear
IMPLICIT NONE
!!!!!!!!!!!!!!!!!!!! ELECTRON non linear term computation (Sepj)!!!!!!!!!!
IF(KIN_E) THEN
zloope: DO iz = izs,ize
ploope: DO ip = ips_e,ipe_e ! Loop over Hermite moments
eo = MODULO(parray_e(ip),2)
p_int = parray_e(ip)
jloope: DO ij = ijs_e, ije_e ! Loop over Laguerre moments
j_int=jarray_e(ij)
IF((CLOS .NE. 1) .OR. (p_int+2*j_int .LE. dmaxe)) THEN !compute
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxe
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxe-j_int
ELSE
nmax = min(NL_CLOS,Jmaxe-j_int)
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloope: DO in = 1,nmax+1 ! Loop over laguerre for the sum
! First convolution terms
F_cmpx(ikxs:ikxe,ikxs:ikxe) = phi(ikxs:ikxe,ikxs:ikxe,iz) * kernel_e(in, ikxs:ikxe,ikxs:ikxe, iz, eo)
! Second convolution terms
G_cmpx(ikxs:ikxe,ikxs:ikxe) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), Jmaxe );
DO is = 1, smax+1 ! sum truncation on number of moments
G_cmpx(ikxs:ikxe,ikxs:ikxe) = G_cmpx(ikxs:ikxe,ikxs:ikxe) + &
dnjs(in,ij,is) * moments_e(ip,is,ikxs:ikxe,ikxs:ikxe,iz,updatetlevel)
ENDDO
!/!\ this function add its result to bracket_sum_r (hard to read sorry) /!\
CALL poisson_bracket_and_sum(F_cmpx,G_cmpx)
ENDDO nloope
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO iky = ikys, ikye
Sepj(ip,ij,iky,ikxs:ikxe,iz) = bracket_sum_c(ikxs:ikxe,iky-local_nky_offset)*AA_x(ikxs:ikxe)*AA_y(iky) !Anti aliasing filter
ENDDO
ELSE
Sepj(ip,ij,:,:,iz) = 0._dp
ENDIF
ENDDO jloope
ENDDO ploope
ENDDO zloope
ENDIF
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!! ION non linear term computation (Sipj)!!!!!!!!!!
zloopi: DO iz = izs,ize
ploopi: DO ip = ips_i,ipe_i ! Loop over Hermite moments
p_int = parray_i(ip)
eo = MODULO(parray_i(ip),2)
jloopi: DO ij = ijs_i, ije_i ! Loop over Laguerre moments
j_int=jarray_i(ij)
IF((CLOS .NE. 1) .OR. (p_int+2*j_int .LE. dmaxi)) THEN !compute
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxi
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxi-j_int
ELSE
nmax = min(NL_CLOS,Jmaxi-j_int)
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloopi: DO in = 1,nmax+1 ! Loop over laguerre for the sum
! First convolution terms
F_cmpx(ikys:ikye,ikxs:ikxe) = phi(ikys:ikye,ikxs:ikxe,iz) * kernel_i(in, ikys:ikye,ikxs:ikxe, iz, eo)
! Second convolution terms
G_cmpx(ikys:ikye,ikxs:ikxe) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), jmaxi );
DO is = 1, smax+1 ! sum truncation on number of moments
G_cmpx(ikys:ikye,ikxs:ikxe) = G_cmpx(ikys:ikye,ikxs:ikxe) + &
dnjs(in,ij,is) * moments_i(ip,is,ikys:ikye,ikxs:ikxe,iz,updatetlevel)
ENDDO
!/!\ this function add its result to bracket_sum_r (hard to read sorry) /!\
CALL poisson_bracket_and_sum(F_cmpx,G_cmpx)
ENDDO nloopi
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO iky = ikys, ikye
Sipj(ip,ij,iky,ikxs:ikxe,iz) = bracket_sum_c(ikxs:ikxe,iky-local_nky_offset)*AA_x(ikxs:ikxe)*AA_y(iky)
ENDDO
ELSE
Sipj(ip,ij,:,:,iz) = 0._dp
ENDIF
ENDDO jloopi
ENDDO ploopi
ENDDO zloopi
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
END SUBROUTINE compute_nonlinear
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Semi linear computation : Only NZ-ZF convolutions are kept
SUBROUTINE compute_semi_linear_ZF
IMPLICIT NONE
!!!!!!!!!!!!!!!!!!!! ELECTRON semi linear term computation (Sepj)!!!!!!!!!!
IF(KIN_E) THEN
zloope: DO iz = izs,ize
ploope: DO ip = ips_e,ipe_e ! Loop over Hermite moments
eo = MODULO(parray_e(ip),2)
jloope: DO ij = ijs_e, ije_e ! Loop over Laguerre moments
j_int=jarray_e(ij)
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxe
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxe-(ij-1)
ELSE
nmax = NL_CLOS
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloope: DO in = 1,nmax+1 ! Loop over laguerre for the sum
! Build the terms to convolve
kxloope: DO ikx = ikxs,ikxe ! Loop over kx
kyloope: DO iky = ikys,ikye ! Loop over ky
kx = kxarray(ikx)
ky = kyarray(iky)
kerneln = kernel_e(in, ikx, iky, iz, eo)
! Zonal terms (=0 for all ky not 0)
Fx_cmpx(iky,ikx) = 0._dp
Gx_cmpx(iky,ikx) = 0._dp
IF(iky .EQ. iky_0) THEN
Fx_cmpx(iky,ikx) = imagu*kx* phi(iky,ikx,iz) * kerneln
smax = MIN( (in-1)+(ij-1), jmaxe );
DO is = 1, smax+1 ! sum truncation on number of moments
Gx_cmpx(iky,ikx) = Gx_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_e(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gx_cmpx(iky,ikx) = imagu*kx*Gx_cmpx(iky,ikx)
ENDIF
! NZ terms
Fy_cmpx(iky,ikx) = imagu*ky* phi(iky,ikx,iz) * kerneln
Gy_cmpx(iky,ikx) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), jmaxe );
DO is = 1, smax+1 ! sum truncation on number of moments
Gy_cmpx(iky,ikx) = Gy_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_e(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gy_cmpx(iky,ikx) = imagu*ky*Gy_cmpx(iky,ikx)
ENDDO kyloope
ENDDO kxloope
! First term df/dx x dg/dy
CALL convolve_and_add(Fx_cmpx,Gy_cmpx)
! Second term -df/dy x dg/dx
CALL convolve_and_add(-Fy_cmpx,Gx_cmpx)
ENDDO nloope
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO ikx = ikxs, ikxe
DO iky = ikys, ikye
Sepj(ip,ij,iky,ikx,iz) = bracket_sum_c(ikx,iky-local_nky_offset)*AA_x(ikx)*AA_y(iky) !Anti aliasing filter
ENDDO
ENDDO
ENDDO jloope
ENDDO ploope
ENDDO zloope
ENDIF
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!! ION non linear term computation (Sipj)!!!!!!!!!!
zloopi: DO iz = izs,ize
ploopi: DO ip = ips_i,ipe_i ! Loop over Hermite moments
eo = MODULO(parray_i(ip),2)
jloopi: DO ij = ijs_i, ije_i ! Loop over Laguerre moments
j_int=jarray_i(ij)
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxi
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxi-(ij-1)
ELSE
nmax = NL_CLOS
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloopi: DO in = 1,nmax+1 ! Loop over laguerre for the sum
kxloopi: DO ikx = ikxs,ikxe ! Loop over kx
kyloopi: DO iky = ikys,ikye ! Loop over ky
! Zonal terms (=0 for all ky not 0)
Fx_cmpx(iky,ikx) = 0._dp
Gx_cmpx(iky,ikx) = 0._dp
IF(iky .EQ. iky_0) THEN
Fx_cmpx(iky,ikx) = imagu*kx* phi(iky,ikx,iz) * kerneln
smax = MIN( (in-1)+(ij-1), jmaxi );
DO is = 1, smax+1 ! sum truncation on number of moments
Gx_cmpx(iky,ikx) = Gx_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_i(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gx_cmpx(iky,ikx) = imagu*kx*Gx_cmpx(iky,ikx)
ENDIF
! NZ terms
Fy_cmpx(iky,ikx) = imagu*ky* phi(iky,ikx,iz) * kerneln
Gy_cmpx(iky,ikx) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), jmaxi );
DO is = 1, smax+1 ! sum truncation on number of moments
Gy_cmpx(iky,ikx) = Gy_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_i(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gy_cmpx(iky,ikx) = imagu*ky*Gy_cmpx(iky,ikx)
ENDDO kyloopi
ENDDO kxloopi
! First term drphi x dzf
CALL convolve_and_add(Fy_cmpx,Gx_cmpx)
! Second term -dzphi x drf
CALL convolve_and_add(Fy_cmpx,Gx_cmpx)
ENDDO nloopi
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO ikx = ikxs, ikxe
DO iky = ikys, ikye
Sipj(ip,ij,iky,ikx,iz) = bracket_sum_c(ikx,iky-local_nky_offset)*AA_x(ikx)*AA_y(iky)
ENDDO
ENDDO
ENDDO jloopi
ENDDO ploopi
ENDDO zloopi
END SUBROUTINE compute_semi_linear_ZF
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Semi linear computation : Only kx=0*all convolutions are kept
SUBROUTINE compute_semi_linear_NZ
IMPLICIT NONE
!!!!!!!!!!!!!!!!!!!! ELECTRON semi linear term computation (Sepj)!!!!!!!!!!
IF(KIN_E) THEN
zloope: DO iz = izs,ize
ploope: DO ip = ips_e,ipe_e ! Loop over Hermite moments
eo = MODULO(parray_e(ip),2)
jloope: DO ij = ijs_e, ije_e ! Loop over Laguerre moments
j_int=jarray_e(ij)
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxe
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxe-(ij-1)
ELSE
nmax = NL_CLOS
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloope: DO in = 1,nmax+1 ! Loop over laguerre for the sum
! Build the terms to convolve
kxloope: DO ikx = ikxs,ikxe ! Loop over kx
kyloope: DO iky = ikys,ikye ! Loop over ky
kx = kxarray(ikx)
ky = kyarray(iky)
kerneln = kernel_e(in, ikx, iky, iz, eo)
! All terms
Fx_cmpx(iky,ikx) = imagu*kx* phi(iky,ikx,iz) * kerneln
smax = MIN( (in-1)+(ij-1), jmaxe );
DO is = 1, smax+1 ! sum truncation on number of moments
Gx_cmpx(iky,ikx) = Gx_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_e(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gx_cmpx(iky,ikx) = imagu*kx*Gx_cmpx(iky,ikx)
! Kx = 0 terms
Fy_cmpx(iky,ikx) = 0._dp
Gy_cmpx(iky,ikx) = 0._dp
IF (ikx .EQ. ikx_0) THEN
Fy_cmpx(iky,ikx) = imagu*ky* phi(iky,ikx,iz) * kerneln
Gy_cmpx(iky,ikx) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), jmaxe );
DO is = 1, smax+1 ! sum truncation on number of moments
Gy_cmpx(iky,ikx) = Gy_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_e(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gy_cmpx(iky,ikx) = imagu*ky*Gy_cmpx(iky,ikx)
ENDIF
ENDDO kyloope
ENDDO kxloope
! First term df/dx x dg/dy
CALL convolve_and_add(Fx_cmpx,Gy_cmpx)
! Second term -df/dy x dg/dx
CALL convolve_and_add(-Fy_cmpx,Gx_cmpx)
ENDDO nloope
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO ikx = ikxs, ikxe
DO iky = ikys, ikye
Sepj(ip,ij,iky,ikx,iz) = bracket_sum_c(ikx,iky-local_nky_offset)*AA_x(ikx)*AA_y(iky) !Anti aliasing filter
ENDDO
ENDDO
ENDDO jloope
ENDDO ploope
ENDDO zloope
ENDIF
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!! ION non linear term computation (Sipj)!!!!!!!!!!
zloopi: DO iz = izs,ize
ploopi: DO ip = ips_i,ipe_i ! Loop over Hermite moments
eo = MODULO(parray_i(ip),2)
jloopi: DO ij = ijs_i, ije_i ! Loop over Laguerre moments
j_int=jarray_i(ij)
! Set non linear sum truncation
IF (NL_CLOS .EQ. -2) THEN
nmax = Jmaxi
ELSEIF (NL_CLOS .EQ. -1) THEN
nmax = Jmaxi-(ij-1)
ELSE
nmax = NL_CLOS
ENDIF
bracket_sum_r = 0._dp ! initialize sum over real nonlinear term
nloopi: DO in = 1,nmax+1 ! Loop over laguerre for the sum
kxloopi: DO ikx = ikxs,ikxe ! Loop over kx
kyloopi: DO iky = ikys,ikye ! Loop over ky
! Zonal terms (=0 for all ky not 0)
Fx_cmpx(iky,ikx) = imagu*kx* phi(iky,ikx,iz) * kerneln
smax = MIN( (in-1)+(ij-1), jmaxi );
DO is = 1, smax+1 ! sum truncation on number of moments
Gx_cmpx(iky,ikx) = Gx_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_i(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gx_cmpx(iky,ikx) = imagu*kx*Gx_cmpx(iky,ikx)
! Kx = 0 terms
Fy_cmpx(iky,ikx) = 0._dp
Gy_cmpx(iky,ikx) = 0._dp
IF (ikx .EQ. ikx_0) THEN
Fy_cmpx(iky,ikx) = imagu*ky* phi(iky,ikx,iz) * kerneln
Gy_cmpx(iky,ikx) = 0._dp ! initialization of the sum
smax = MIN( (in-1)+(ij-1), jmaxi );
DO is = 1, smax+1 ! sum truncation on number of moments
Gy_cmpx(iky,ikx) = Gy_cmpx(iky,ikx) + &
dnjs(in,ij,is) * moments_i(ip,is,iky,ikx,iz,updatetlevel)
ENDDO
Gy_cmpx(iky,ikx) = imagu*ky*Gy_cmpx(iky,ikx)
ENDIF
ENDDO kyloopi
ENDDO kxloopi
! First term drphi x dzf
CALL convolve_and_add(Fy_cmpx,Gx_cmpx)
! Second term -dzphi x drf
CALL convolve_and_add(Fy_cmpx,Gx_cmpx)
ENDDO nloopi
! Put the real nonlinear product into k-space
call fftw_mpi_execute_dft_r2c(planf, bracket_sum_r, bracket_sum_c)
! Retrieve convolution in input format
DO ikx = ikxs, ikxe
DO iky = ikys, ikye
Sipj(ip,ij,iky,ikx,iz) = bracket_sum_c(ikx,iky-local_nky_offset)*AA_x(ikx)*AA_y(iky)
ENDDO
ENDDO
ENDDO jloopi
ENDDO ploopi
ENDDO zloopi
END SUBROUTINE compute_semi_linear_NZ
END MODULE nonlinear
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