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added new set of accelerated spectral methods based on derivative approximations. use spectral_derivative to set the kind of derivative you like. valid options are: 

‘continuous’: computed continuous derivatives (standard spectral method)

‘central_difference’: central difference approximation of derivatives

‘fwbw_difference’: forward difference for gradient and backward difference divergence
This commit is contained in:
Pratheek Shanthraj 2015-12-14 18:12:09 +00:00
parent ce2400c8dc
commit 3a7f4bf43a
3 changed files with 213 additions and 156 deletions
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4
code/DAMASK_spectral_solverBasicPETSc.f90
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@ -149,10 +149,10 @@ subroutine basicPETSc_init
call DMDACreate3d(PETSC_COMM_WORLD, & call DMDACreate3d(PETSC_COMM_WORLD, &
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, & ! cut off stencil at boundary DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, & ! cut off stencil at boundary
DMDA_STENCIL_BOX, & ! Moore (26) neighborhood around central point DMDA_STENCIL_BOX, & ! Moore (26) neighborhood around central point
grid(1),grid(2),grid(3), & ! global grid grid(1),grid(2),grid(3), & ! global grid
1, 1, worldsize, & 1, 1, worldsize, &
9, 0, & ! #dof (F tensor), ghost boundary width (domain overlap) 9, 0, & ! #dof (F tensor), ghost boundary width (domain overlap)
grid (1),grid (2),localK, & ! local grid grid (1),grid (2),localK, & ! local grid
da,ierr) ! handle, error da,ierr) ! handle, error
CHKERRQ(ierr) CHKERRQ(ierr)
call SNESSetDM(snes,da,ierr); CHKERRQ(ierr) call SNESSetDM(snes,da,ierr); CHKERRQ(ierr)

355
code/DAMASK_spectral_utilities.f90
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@ -13,8 +13,6 @@ module DAMASK_spectral_utilities
pInt pInt
use math, only: & use math, only: &
math_I3 math_I3
use numerics, only: &
spectral_filter
implicit none implicit none
private private
@ -50,9 +48,9 @@ module DAMASK_spectral_utilities
complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field fourier representation for fftw complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field fourier representation for fftw
real(C_DOUBLE), public, dimension(:,:,:), pointer :: scalarField_real !< scalar field real representation for fftw real(C_DOUBLE), public, dimension(:,:,:), pointer :: scalarField_real !< scalar field real representation for fftw
complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:), pointer :: scalarField_fourier !< scalar field fourier representation for fftw complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:), pointer :: scalarField_fourier !< scalar field fourier representation for fftw
real(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method complex(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
real(pReal), private, dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives complex(pReal), private, dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives
real(pReal), private, dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives complex(pReal), private, dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives
real(pReal), private, dimension(3,3,3,3) :: C_ref !< mechanic reference stiffness real(pReal), private, dimension(3,3,3,3) :: C_ref !< mechanic reference stiffness
real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence (Basic, Basic PETSc) real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence (Basic, Basic PETSc)
@ -121,12 +119,12 @@ module DAMASK_spectral_utilities
end type phaseFieldDataBin end type phaseFieldDataBin
enum, bind(c) enum, bind(c)
enumerator :: FILTER_NONE_ID, & enumerator :: DERIVATIVE_CONTINUOUS_ID, &
FILTER_GRADIENT_ID, & DERIVATIVE_CENTRAL_DIFF_ID, &
FILTER_COSINE_ID DERIVATIVE_FWBW_DIFF_ID
end enum end enum
integer(kind(FILTER_NONE_ID)) :: & integer(kind(DERIVATIVE_CONTINUOUS_ID)) :: &
spectral_filter_ID spectral_derivative_ID
public :: & public :: &
utilities_init, & utilities_init, &
@ -143,6 +141,8 @@ module DAMASK_spectral_utilities
utilities_curlRMS, & utilities_curlRMS, &
utilities_fourierScalarGradient, & utilities_fourierScalarGradient, &
utilities_fourierVectorDivergence, & utilities_fourierVectorDivergence, &
utilities_fourierVectorGradient, &
utilities_fourierTensorDivergence, &
utilities_maskedCompliance, & utilities_maskedCompliance, &
utilities_constitutiveResponse, & utilities_constitutiveResponse, &
utilities_calculateRate, & utilities_calculateRate, &
@ -154,7 +154,7 @@ module DAMASK_spectral_utilities
FIELD_THERMAL_ID, & FIELD_THERMAL_ID, &
FIELD_DAMAGE_ID FIELD_DAMAGE_ID
private :: & private :: &
utilities_getFilter utilities_getFreqDerivative
contains contains
@ -174,6 +174,7 @@ subroutine utilities_init()
IO_timeStamp, & IO_timeStamp, &
IO_open_file IO_open_file
use numerics, only: & use numerics, only: &
spectral_derivative, &
fftw_planner_flag, & fftw_planner_flag, &
fftw_timelimit, & fftw_timelimit, &
memory_efficient, & memory_efficient, &
@ -252,6 +253,17 @@ subroutine utilities_init()
write(6,'(a,3(es12.5))') ' size x y z: ', geomSize write(6,'(a,3(es12.5))') ' size x y z: ', geomSize
endif endif
select case (spectral_derivative)
case ('continuous') ! default, no weighting
spectral_derivative_ID = DERIVATIVE_CONTINUOUS_ID
case ('central_difference') ! cosine curve with 1 for avg and zero for highest freq
spectral_derivative_ID = DERIVATIVE_CENTRAL_DIFF_ID
case ('fwbw_difference') ! gradient, might need grid scaling as for cosine filter
spectral_derivative_ID = DERIVATIVE_FWBW_DIFF_ID
case default
call IO_error(892_pInt,ext_msg=trim(spectral_derivative))
end select
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and ! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and
! resolution-independent divergence ! resolution-independent divergence
@ -275,8 +287,8 @@ subroutine utilities_init()
gridFFTW = int(grid,C_INTPTR_T) gridFFTW = int(grid,C_INTPTR_T)
alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, & alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
MPI_COMM_WORLD, local_K, local_K_offset) MPI_COMM_WORLD, local_K, local_K_offset)
allocate (xi1st(3,grid1Red,grid(2),grid3),source = 0.0_pReal) ! frequencies, only half the size for first dimension allocate (xi1st (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies, only half the size for first dimension
allocate (xi2nd(3,grid1Red,grid(2),grid3),source = 0.0_pReal) ! frequencies, only half the size for first dimension allocate (xi2nd (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies, only half the size for first dimension
tensorField = fftw_alloc_complex(tensorSize*alloc_local) tensorField = fftw_alloc_complex(tensorSize*alloc_local)
call c_f_pointer(tensorField, tensorField_real, [3_C_INTPTR_T,3_C_INTPTR_T, & call c_f_pointer(tensorField, tensorField_real, [3_C_INTPTR_T,3_C_INTPTR_T, &
@ -353,31 +365,21 @@ subroutine utilities_init()
if(j > grid(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - grid(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1 if(j > grid(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - grid(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do i = 1_pInt, grid1Red do i = 1_pInt, grid1Red
k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1 k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
xi2nd(1:3,i,j,k-grid3Offset) = real(k_s, pReal)/scaledGeomSize ! if divergence_correction is set, frequencies are calculated on unit length xi2nd(1:3,i,j,k-grid3Offset) = utilities_getFreqDerivative(k_s) ! if divergence_correction is set, frequencies are calculated on unit length
where(mod(grid,2)==0 .and. [i,j,k] == grid/2+1) ! for even grids, set the Nyquist Freq component to 0.0 where(mod(grid,2)==0 .and. [i,j,k] == grid/2+1 .and. &
xi1st(1:3,i,j,k-grid3Offset) = 0.0_pReal spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) ! for even grids, set the Nyquist Freq component to 0.0
xi1st(1:3,i,j,k-grid3Offset) = cmplx(0.0_pReal,0.0_pReal,pReal)
elsewhere elsewhere
xi1st(1:3,i,j,k-grid3Offset) = xi2nd(1:3,i,j,k-grid3Offset) xi1st(1:3,i,j,k-grid3Offset) = xi2nd(1:3,i,j,k-grid3Offset)
endwhere endwhere
enddo; enddo; enddo enddo; enddo; enddo
if(memory_efficient) then ! allocate just single fourth order tensor if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(3,3,3,3,1,1,1), source = 0.0_pReal) allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pReal,0.0_pReal,pReal))
else ! precalculation of gamma_hat field else ! precalculation of gamma_hat field
allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = 0.0_pReal) allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
endif endif
select case (spectral_filter)
case ('none') ! default, no weighting
spectral_filter_ID = FILTER_NONE_ID
case ('cosine') ! cosine curve with 1 for avg and zero for highest freq
spectral_filter_ID = FILTER_COSINE_ID
case ('gradient') ! gradient, might need grid scaling as for cosine filter
spectral_filter_ID = FILTER_GRADIENT_ID
case default
call IO_error(892_pInt,ext_msg=trim(spectral_filter))
end select
end subroutine utilities_init end subroutine utilities_init
@ -399,15 +401,18 @@ subroutine utilities_updateGamma(C,saveReference)
grid3,& grid3,&
grid grid
use math, only: & use math, only: &
math_inv33 math_det33, &
math_invert
implicit none implicit none
real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness
logical , intent(in) :: saveReference !< save reference stiffness to file for restart logical , intent(in) :: saveReference !< save reference stiffness to file for restart
real(pReal), dimension(3,3) :: temp33_Real, xiDyad complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
real(pReal), dimension(6,6) :: matA, matInvA
integer(pInt) :: & integer(pInt) :: &
i, j, k, & i, j, k, &
l, m, n, o l, m, n, o
logical :: ierr
C_ref = C C_ref = C
if (saveReference) then if (saveReference) then
@ -424,12 +429,21 @@ subroutine utilities_updateGamma(C,saveReference)
do k = grid3Offset+1_pInt, grid3Offset+grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red do k = grid3Offset+1_pInt, grid3Offset+grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
if (any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 if (any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi1st(l, i,j,k-grid3Offset)*xi1st(m, i,j,k-grid3Offset) xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad) temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
temp33_Real = math_inv33(temp33_Real) matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)& matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_Real(l,n)*xiDyad(m,o) if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
call math_invert(6_pInt, matA, matInvA, ierr)
temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_complex(l,n)* &
conjg(-xi1st(o,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
else
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
gamma_hat(l,m,n,o,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
endif
endif endif
enddo; enddo; enddo enddo; enddo; enddo
endif endif
@ -446,18 +460,11 @@ subroutine utilities_FFTtensorForward()
grid grid
implicit none implicit none
integer(pInt) :: i, j, k
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! doing the tensor FFT ! doing the tensor FFT
call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
!--------------------------------------------------------------------------------------------------
! applying filter
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
tensorField_fourier(1:3,1:3,i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
tensorField_fourier(1:3,1:3,i,j,k)
end subroutine utilities_FFTtensorForward end subroutine utilities_FFTtensorForward
@ -483,18 +490,11 @@ subroutine utilities_FFTscalarForward()
grid grid
implicit none implicit none
integer(pInt) :: i, j, k
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! doing the scalar FFT ! doing the scalar FFT
call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier) call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
!--------------------------------------------------------------------------------------------------
! applying filter
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
scalarField_fourier(i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
scalarField_fourier(i,j,k)
end subroutine utilities_FFTscalarForward end subroutine utilities_FFTscalarForward
@ -521,18 +521,11 @@ subroutine utilities_FFTvectorForward()
grid grid
implicit none implicit none
integer(pInt) :: i, j, k
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! doing the vector FFT ! doing the vector FFT
call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier) call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
!--------------------------------------------------------------------------------------------------
! applying filter
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
vectorField_fourier(1:3,i,j,k) = utilities_getFilter(xi2nd(1:3,i,j,k))* &
vectorField_fourier(1:3,i,j,k)
end subroutine utilities_FFTvectorForward end subroutine utilities_FFTvectorForward
@ -556,7 +549,8 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
use numerics, only: & use numerics, only: &
memory_efficient memory_efficient
use math, only: & use math, only: &
math_inv33 math_det33, &
math_invert
use numerics, only: & use numerics, only: &
worldrank worldrank
use mesh, only: & use mesh, only: &
@ -566,12 +560,14 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
implicit none implicit none
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
real(pReal), dimension(3,3) :: xiDyad, temp33_Real complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
complex(pReal), dimension(3,3) :: temp33_complex real(pReal) :: matA(6,6), matInvA(6,6)
integer(pInt) :: & integer(pInt) :: &
i, j, k, & i, j, k, &
l, m, n, o l, m, n, o
logical :: ierr
if (worldrank == 0_pInt) then if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... doing gamma convolution ...............................................' write(6,'(/,a)') ' ... doing gamma convolution ...............................................'
@ -581,18 +577,25 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! do the actual spectral method calculation (mechanical equilibrium) ! do the actual spectral method calculation (mechanical equilibrium)
memoryEfficient: if(memory_efficient) then memoryEfficient: if(memory_efficient) then
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt, grid1Red
if(any([i,j,k+grid3Offset] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 if (any([i,j,k+grid3Offset] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi1st(l, i,j,k)*xi1st(m, i,j,k) xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad) temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
temp33_Real = math_inv33(temp33_Real) matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)& matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
gamma_hat(l,m,n,o, 1,1,1) = temp33_Real(l,n)*xiDyad(m,o) if (abs(math_det33(matA(1:3,1:3))) > 1e-16) then
call math_invert(6_pInt, matA, matInvA, ierr)
temp33_complex = cmplx(matInvA(1:3,1:3),matInvA(1:3,4:6),pReal)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*conjg(-xi1st(o,i,j,k))*xi1st(m,i,j,k)
else
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt) &
gamma_hat(l,m,n,o,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
endif
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3, 1,1,1) * & temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
tensorField_fourier(1:3,1:3,i,j,k))
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
endif endif
enddo; enddo; enddo enddo; enddo; enddo
@ -600,13 +603,13 @@ subroutine utilities_fourierGammaConvolution(fieldAim)
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) & forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k) * & temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k) * &
tensorField_fourier(1:3,1:3,i,j,k)) tensorField_fourier(1:3,1:3,i,j,k))
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
enddo; enddo; enddo enddo; enddo; enddo
endif memoryEfficient endif memoryEfficient
if (grid3Offset == 0_pInt) & if (grid3Offset == 0_pInt) &
tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal)
end subroutine utilities_fourierGammaConvolution end subroutine utilities_fourierGammaConvolution
@ -627,17 +630,15 @@ subroutine utilities_fourierGreenConvolution(D_ref, mobility_ref, deltaT)
implicit none implicit none
real(pReal), dimension(3,3), intent(in) :: D_ref !< desired average value of the field after convolution real(pReal), dimension(3,3), intent(in) :: D_ref !< desired average value of the field after convolution
real(pReal), intent(in) :: mobility_ref, deltaT !< desired average value of the field after convolution real(pReal), intent(in) :: mobility_ref, deltaT !< desired average value of the field after convolution
real(pReal), dimension(3) :: k_s complex(pReal) :: GreenOp_hat
real(pReal) :: GreenOp_hat
integer(pInt) :: i, j, k integer(pInt) :: i, j, k
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! do the actual spectral method calculation ! do the actual spectral method calculation
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
k_s = xi2nd(1:3,i,j,k)*scaledGeomSize GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ &
GreenOp_hat = 1.0_pReal/ & (cmplx(mobility_ref,0.0_pReal,pReal) + &
(mobility_ref + deltaT*sum((2.0_pReal*PI*k_s/geomSize)* & deltaT*sum(conjg(-xi1st(1:3,i,j,k))*matmul(D_ref,xi1st(1:3,i,j,k))))
math_mul33x3(D_ref,(2.0_pReal*PI*k_s/geomSize)))) !< GreenOp_hat = iK^{T} * D_ref * iK, K is frequency
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
enddo; enddo; enddo enddo; enddo; enddo
@ -648,12 +649,10 @@ end subroutine utilities_fourierGreenConvolution
!> @brief calculate root mean square of divergence of field_fourier !> @brief calculate root mean square of divergence of field_fourier
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
real(pReal) function utilities_divergenceRMS() real(pReal) function utilities_divergenceRMS()
use math, only: &
TWOPIIMG, &
math_mul33x3_complex
use numerics, only: & use numerics, only: &
worldrank worldrank
use mesh, only: & use mesh, only: &
geomSize, &
grid, & grid, &
grid3 grid3
@ -673,20 +672,20 @@ real(pReal) function utilities_divergenceRMS()
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) do k = 1_pInt, grid3; do j = 1_pInt, grid(2)
do i = 2_pInt, grid1Red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice. do i = 2_pInt, grid1Red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
utilities_divergenceRMS = utilities_divergenceRMS & utilities_divergenceRMS = utilities_divergenceRMS &
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again + 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi1st(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,i,j,k),& +sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
xi1st(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)) conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**2.0_pReal))
enddo enddo
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1) utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1)
+ sum( real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,1 ,j,k), & + sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
xi1st(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) & conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,1 ,j,k), & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
xi1st(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) & conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum( real(math_mul33x3_complex(tensorField_fourier(1:3,1:3,grid1Red,j,k), & + sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
xi1st(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal) & conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1:3,1:3,grid1Red,j,k), & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
xi1st(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal) conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal)
enddo; enddo enddo; enddo
if(grid(1) == 1_pInt) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1 if(grid(1) == 1_pInt) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
@ -700,10 +699,10 @@ end function utilities_divergenceRMS
!> @brief calculate max of curl of field_fourier !> @brief calculate max of curl of field_fourier
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
real(pReal) function utilities_curlRMS() real(pReal) function utilities_curlRMS()
use math
use numerics, only: & use numerics, only: &
worldrank worldrank
use mesh, only: & use mesh, only: &
geomSize, &
grid, & grid, &
grid3 grid3
@ -724,33 +723,33 @@ real(pReal) function utilities_curlRMS()
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do k = 1_pInt, grid3; do j = 1_pInt, grid(2);
do i = 2_pInt, grid1Red - 1_pInt do i = 2_pInt, grid1Red - 1_pInt
do l = 1_pInt, 3_pInt do l = 1_pInt, 3_pInt
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)& curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*geomSize(2)/scaledGeomSize(2) &
-tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k))*TWOPIIMG -tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*geomSize(3)/scaledGeomSize(3))
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)& curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)*geomSize(3)/scaledGeomSize(3) &
-tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k))*TWOPIIMG -tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k)*geomSize(1)/scaledGeomSize(1))
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)& curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)*geomSize(1)/scaledGeomSize(1) &
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k))*TWOPIIMG -tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*geomSize(2)/scaledGeomSize(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS + & utilities_curlRMS = utilities_curlRMS + &
2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! Has somewhere a conj. complex counterpart. Therefore count it twice. 2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! Has somewhere a conj. complex counterpart. Therefore count it twice.
enddo enddo
do l = 1_pInt, 3_pInt do l = 1_pInt, 3_pInt
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)& curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*geomSize(2)/scaledGeomSize(2) &
-tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k))*TWOPIIMG -tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k)*geomSize(3)/scaledGeomSize(3))
curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)& curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)*geomSize(3)/scaledGeomSize(3) &
-tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k))*TWOPIIMG -tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k)*geomSize(1)/scaledGeomSize(1))
curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)& curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)*geomSize(1)/scaledGeomSize(1) &
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k))*TWOPIIMG -tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*geomSize(2)/scaledGeomSize(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS + & utilities_curlRMS = utilities_curlRMS + &
sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1) sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
do l = 1_pInt, 3_pInt do l = 1_pInt, 3_pInt
curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)& curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*geomSize(2)/scaledGeomSize(2) &
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k))*TWOPIIMG -tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*geomSize(3)/scaledGeomSize(3))
curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)& curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*geomSize(3)/scaledGeomSize(3) &
-tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k))*TWOPIIMG -tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*geomSize(1)/scaledGeomSize(1))
curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)& curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*geomSize(1)/scaledGeomSize(1) &
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k))*TWOPIIMG -tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*geomSize(2)/scaledGeomSize(2))
enddo enddo
utilities_curlRMS = utilities_curlRMS + & utilities_curlRMS = utilities_curlRMS + &
sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1) sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
@ -882,9 +881,7 @@ subroutine utilities_fourierScalarGradient()
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal) vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)* & vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)
cmplx(0.0_pReal,2.0_pReal*PI*xi1st(1:3,i,j,k)* &
scaledGeomSize/geomSize,pReal)
enddo; enddo; enddo enddo; enddo; enddo
end subroutine utilities_fourierScalarGradient end subroutine utilities_fourierScalarGradient
@ -908,13 +905,56 @@ subroutine utilities_fourierVectorDivergence()
do m = 1_pInt, 3_pInt do m = 1_pInt, 3_pInt
scalarField_fourier(i,j,k) = & scalarField_fourier(i,j,k) = &
scalarField_fourier(i,j,k) + & scalarField_fourier(i,j,k) + &
vectorField_fourier(m,i,j,k)* & vectorField_fourier(m,i,j,k)*conjg(-xi1st(m,i,j,k))
cmplx(0.0_pReal,2.0_pReal*PI*xi1st(m,i,j,k)*scaledGeomSize(m)/geomSize(m),pReal)
enddo enddo
enddo; enddo; enddo enddo; enddo; enddo
end subroutine utilities_fourierVectorDivergence end subroutine utilities_fourierVectorDivergence
!--------------------------------------------------------------------------------------------------
!> @brief calculate vector gradient in fourier field
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierVectorGradient()
use mesh, only: &
grid3, &
grid, &
geomSize
implicit none
integer(pInt) :: i, j, k, m, n
tensorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
do m = 1_pInt, 3_pInt; do n = 1_pInt, 3_pInt
tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
enddo; enddo
enddo; enddo; enddo
end subroutine utilities_fourierVectorGradient
!--------------------------------------------------------------------------------------------------
!> @brief calculate tensor divergence in fourier field
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierTensorDivergence()
use mesh, only: &
grid3, &
grid, &
geomSize
implicit none
integer(pInt) :: i, j, k, m, n
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
do m = 1_pInt, 3_pInt; do n = 1_pInt, 3_pInt
vectorField_fourier(m,i,j,k) = &
vectorField_fourier(m,i,j,k) + &
tensorField_fourier(m,n,i,j,k)*conjg(-xi1st(n,i,j,k))
enddo; enddo
enddo; enddo; enddo
end subroutine utilities_fourierTensorDivergence
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief calculates constitutive response !> @brief calculates constitutive response
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -1122,29 +1162,54 @@ end function utilities_forwardField
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
!> @brief calculates filter for fourier convolution depending on type given in numerics.config !> @brief calculates filter for fourier convolution depending on type given in numerics.config
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
pure function utilities_getFilter(k) pure function utilities_getFreqDerivative(k_s)
use math, only: & use math, only: &
PI PI
use mesh, only: & use mesh, only: &
geomSize, &
grid grid
implicit none implicit none
real(pReal), intent(in), dimension(3) :: k !< indices of frequency integer(pInt), intent(in), dimension(3) :: k_s !< indices of frequency
complex(pReal) :: utilities_getFilter complex(pReal), dimension(3) :: utilities_getFreqDerivative
select case (spectral_derivative_ID)
case (DERIVATIVE_CONTINUOUS_ID)
utilities_getFreqDerivative = cmplx(0.0_pReal, 2.0_pReal*PI*real(k_s,pReal)/geomSize,pReal)
case (DERIVATIVE_CENTRAL_DIFF_ID)
utilities_getFreqDerivative = cmplx(0.0_pReal, sin(2.0_pReal*PI*real(k_s,pReal)/real(grid,pReal)), pReal)/ &
cmplx(2.0_pReal*geomSize/real(grid,pReal), 0.0_pReal, pReal)
case (DERIVATIVE_FWBW_DIFF_ID)
utilities_getFreqDerivative(1) = &
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) - 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
cmplx(4.0_pReal*geomSize(1)/real(grid(1),pReal), 0.0_pReal, pReal)
utilities_getFreqDerivative(2) = &
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) - 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
cmplx(4.0_pReal*geomSize(2)/real(grid(2),pReal), 0.0_pReal, pReal)
utilities_getFreqDerivative(3) = &
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) - 1.0_pReal, &
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
cmplx(4.0_pReal*geomSize(3)/real(grid(3),pReal), 0.0_pReal, pReal)
select case (spectral_filter_ID)
case (FILTER_NONE_ID) ! default, no weighting
utilities_getFilter = (1.0_pReal,0.0_pReal)
case (FILTER_COSINE_ID) ! cosine curve with 1 for avg and zero for highest freq
utilities_getFilter = cmplx(product(1.0_pReal + cos(PI*k*scaledGeomSize/grid))/8.0_pReal,&
0.0_pReal)
case (FILTER_GRADIENT_ID) ! gradient, might need grid scaling as for cosine filter
utilities_getFilter = cmplx(1.0_pReal/(1.0_pReal + sum(k**2)),0.0_pReal)
case default
utilities_getFilter = (0.0_pReal,0.0_pReal)
end select end select
end function end function utilities_getFreqDerivative
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
@ -1154,7 +1219,6 @@ end function
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
subroutine utilities_updateIPcoords(F) subroutine utilities_updateIPcoords(F)
use math, only: & use math, only: &
PI, &
math_mul33x3 math_mul33x3
use mesh, only: & use mesh, only: &
grid, & grid, &
@ -1166,41 +1230,34 @@ subroutine utilities_updateIPcoords(F)
real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F
integer(pInt) :: i, j, k, m integer(pInt) :: i, j, k, m
real(pReal), dimension(3) :: step, offset_coords, integrator real(pReal), dimension(3) :: step, offset_coords
real(pReal), dimension(3,3) :: Favg real(pReal), dimension(3,3) :: Favg
PetscErrorCode :: ierr PetscErrorCode :: ierr
external & external &
MPI_Bcast MPI_Bcast
!--------------------------------------------------------------------------------------------------
! integration in Fourier space
tensorField_real = 0.0_pReal tensorField_real = 0.0_pReal
tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F
call utilities_FFTtensorForward() call utilities_FFTtensorForward()
call utilities_fourierTensorDivergence()
integrator = geomSize * 0.5_pReal / PI do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
step = geomSize/real(grid, pReal) if (any(abs(xi1st(1:3,i,j,k)) > tiny(0.0_pReal))) &
vectorField_fourier(1:3,i,j,k) = vectorField_fourier(1:3,i,j,k)/ &
sum(conjg(-xi1st(1:3,i,j,k))*xi1st(1:3,i,j,k))
enddo; enddo; enddo
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! average F ! average F
if (grid3Offset == 0_pInt) Favg = real(tensorField_fourier(1:3,1:3,1,1,1),pReal)*wgt if (grid3Offset == 0_pInt) Favg = real(tensorField_fourier(1:3,1:3,1,1,1),pReal)*wgt
call MPI_Bcast(Favg,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr) call MPI_Bcast(Favg,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
!--------------------------------------------------------------------------------------------------
! integration in Fourier space
vectorField_fourier = cmplx(0.0_pReal, 0.0_pReal, pReal)
do k = 1_pInt, grid3; do j = 1_pInt, grid(2); do i = 1_pInt,grid1Red
do m = 1_pInt,3_pInt
vectorField_fourier(m,i,j,k) = sum(tensorField_fourier(m,1:3,i,j,k)*&
cmplx(0.0_pReal,xi2nd(1:3,i,j,k)*scaledGeomSize*integrator,pReal))
enddo
if (any(abs(xi2nd(1:3,i,j,k)) > tiny(0.0_pReal))) &
vectorField_fourier(1:3,i,j,k) = &
vectorField_fourier(1:3,i,j,k)/cmplx(-sum(xi2nd(1:3,i,j,k)*scaledGeomSize*xi2nd(1:3,i,j,k)* &
scaledGeomSize),0.0_pReal,pReal)
enddo; enddo; enddo
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
!-------------------------------------------------------------------------------------------------- !--------------------------------------------------------------------------------------------------
! add average to fluctuation and put (0,0,0) on (0,0,0) ! add average to fluctuation and put (0,0,0) on (0,0,0)
step = geomSize/real(grid, pReal)
if (grid3Offset == 0_pInt) offset_coords = vectorField_real(1:3,1,1,1) if (grid3Offset == 0_pInt) offset_coords = vectorField_real(1:3,1,1,1)
call MPI_Bcast(offset_coords,3,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr) call MPI_Bcast(offset_coords,3,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
offset_coords = math_mul33x3(Favg,step/2.0_pReal) - offset_coords offset_coords = math_mul33x3(Favg,step/2.0_pReal) - offset_coords

8
code/numerics.f90
View File

@ -113,7 +113,7 @@ module numerics
fftw_plan_mode = 'FFTW_PATIENT' !< reads the planing-rigor flag, see manual on www.fftw.org, Default FFTW_PATIENT: use patient planner flag fftw_plan_mode = 'FFTW_PATIENT' !< reads the planing-rigor flag, see manual on www.fftw.org, Default FFTW_PATIENT: use patient planner flag
character(len=64), protected, public :: & character(len=64), protected, public :: &
spectral_solver = 'basicpetsc' , & !< spectral solution method spectral_solver = 'basicpetsc' , & !< spectral solution method
spectral_filter = 'none' !< spectral filtering method spectral_derivative = 'continuous' !< spectral filtering method
character(len=1024), protected, public :: & character(len=1024), protected, public :: &
petsc_defaultOptions = '-mech_snes_type ngmres & petsc_defaultOptions = '-mech_snes_type ngmres &
&-damage_snes_type ngmres & &-damage_snes_type ngmres &
@ -432,8 +432,8 @@ subroutine numerics_init
fftw_timelimit = IO_floatValue(line,chunkPos,2_pInt) fftw_timelimit = IO_floatValue(line,chunkPos,2_pInt)
case ('fftw_plan_mode') case ('fftw_plan_mode')
fftw_plan_mode = IO_lc(IO_stringValue(line,chunkPos,2_pInt)) fftw_plan_mode = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('spectralfilter','myfilter') case ('spectralderivative')
spectral_filter = IO_lc(IO_stringValue(line,chunkPos,2_pInt)) spectral_derivative = IO_lc(IO_stringValue(line,chunkPos,2_pInt))
case ('divergence_correction') case ('divergence_correction')
divergence_correction = IO_intValue(line,chunkPos,2_pInt) divergence_correction = IO_intValue(line,chunkPos,2_pInt)
case ('update_gamma') case ('update_gamma')
@ -609,7 +609,7 @@ subroutine numerics_init
write(6,'(a24,1x,i8)') ' continueCalculation: ',continueCalculation write(6,'(a24,1x,i8)') ' continueCalculation: ',continueCalculation
write(6,'(a24,1x,L8)') ' memory_efficient: ',memory_efficient write(6,'(a24,1x,L8)') ' memory_efficient: ',memory_efficient
write(6,'(a24,1x,i8)') ' divergence_correction: ',divergence_correction write(6,'(a24,1x,i8)') ' divergence_correction: ',divergence_correction
write(6,'(a24,1x,a)') ' spectral filter: ',trim(spectral_filter) write(6,'(a24,1x,a)') ' spectral derivative: ',trim(spectral_derivative)
if(fftw_timelimit<0.0_pReal) then if(fftw_timelimit<0.0_pReal) then
write(6,'(a24,1x,L8)') ' fftw_timelimit: ',.false. write(6,'(a24,1x,L8)') ' fftw_timelimit: ',.false.
else else