!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief Utilities used by the different spectral solver variants
!--------------------------------------------------------------------------------------------------
module DAMASK_spectral_utilities
use, intrinsic :: iso_c_binding
use prec, only: &
pReal, &
pInt
implicit none
#ifdef PETSc
#include <finclude/petscsys.h>
#endif
logical, public :: cutBack =.false. !< cut back of BVP solver in case convergence is not achieved or a material point is terminally ill
!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
real(pReal), public, dimension(:,:,:,:,:), pointer :: field_real !< real representation (some stress or deformation) of field_fourier
complex(pReal),private, dimension(:,:,:,:,:), pointer :: field_fourier !< field on which the Fourier transform operates
real(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
real(pReal), private, dimension(:,:,:,:), allocatable :: xi !< wave vector field for divergence and for gamma operator
real(pReal), private, dimension(3,3,3,3) :: C_ref !< reference stiffness
!--------------------------------------------------------------------------------------------------
! debug fftw
complex(pReal),private, dimension(:,:,:), pointer :: scalarField_real, & !< scalar field real representation for debug of FFTW
scalarField_fourier !< scalar field complex representation for debug of FFTW
!--------------------------------------------------------------------------------------------------
! debug divergence
real(pReal), private, dimension(:,:,:,:), pointer :: divergence_real !< scalar field real representation for debugging divergence calculation
complex(pReal),private, dimension(:,:,:,:), pointer :: divergence_fourier !< scalar field real representation for debugging divergence calculation
real(pReal), private, dimension(:,:,:,:), allocatable :: divergence_post !< data of divergence calculation using function from core modules (serves as a reference)
!--------------------------------------------------------------------------------------------------
! plans for FFTW
type(C_PTR), private :: plan_scalarField_forth, plan_scalarField_back !< plans for FFTW in case of debugging the Fourier transform
type(C_PTR), private :: plan_forward, plan_backward !< plans for FFTW
type(C_PTR), private :: plan_divergence !< plan for FFTW in case of debugging divergence calculation
!--------------------------------------------------------------------------------------------------
! variables controlling debugging
logical, public :: &
debugGeneral, & !< general debugging of spectral solver
debugDivergence, & !< debugging of divergence calculation (comparison to function used for post processing)
debugRestart, & !< debbuging of restart features
debugFFTW, & !< doing additional FFT on scalar field and compare to results of strided 3D FFT
debugRotation, & !< also printing out results in lab frame
debugPETSc !< use some in debug defined options for more verbose PETSc solution
!--------------------------------------------------------------------------------------------------
! derived types
type tSolutionState !< return type of solution from spectral solver variants
logical :: converged = .true.
logical :: regrid = .false.
logical :: termIll = .false.
integer(pInt) :: iterationsNeeded = 0_pInt
end type tSolutionState
type tBoundaryCondition !< set of parameters defining a boundary condition
real(pReal), dimension(3,3) :: values = 0.0_pReal
real(pReal), dimension(3,3) :: maskFloat = 0.0_pReal
logical, dimension(3,3) :: maskLogical = .false.
character(len=64) :: myType = 'None'
end type tBoundaryCondition
public :: &
utilities_init, &
utilities_updateGamma, &
utilities_FFTforward, &
utilities_FFTbackward, &
utilities_fourierConvolution, &
utilities_divergenceRMS, &
utilities_maskedCompliance, &
utilities_constitutiveResponse, &
utilities_calculateRate, &
utilities_forwardField, &
utilities_destroy
private :: &
utilities_getFilter
contains
!--------------------------------------------------------------------------------------------------
!> @brief allocates all neccessary fields, sets debug flags, create plans for FFTW
!> @details Sets the debug levels for general, divergence, restart and FFTW from the biwise coding
!> provided by the debug module to logicals.
!> Allocates all fields used by FFTW and create the corresponding plans depending on the debug
!> level chosen.
!> Initializes FFTW.
!--------------------------------------------------------------------------------------------------
subroutine utilities_init()
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
use IO, only: &
IO_error, &
IO_warning
use numerics, only: &
DAMASK_NumThreadsInt, &
fftw_planner_flag, &
fftw_timelimit, &
memory_efficient, &
petsc_options
use debug, only: &
debug_level, &
debug_spectral, &
debug_levelBasic, &
debug_spectralDivergence, &
debug_spectralRestart, &
debug_spectralFFTW, &
debug_spectralPETSc, &
debug_spectralRotation
#ifdef PETSc
use debug, only: &
debug_spectralPETSc, &
PETScDebug
#endif
use mesh, only: &
res, &
res1_red, &
scaledDim
use math ! must use the whole module for use of FFTW
implicit none
#ifdef PETSc
PetscErrorCode :: ierr
#endif
integer(pInt) :: i, j, k
integer(pInt), dimension(3) :: k_s
type(C_PTR) :: &
tensorField, & !< field cotaining data for FFTW in real and fourier space (in place)
scalarField_realC, & !< field cotaining data for FFTW in real space when debugging FFTW (no in place)
scalarField_fourierC, & !< field cotaining data for FFTW in fourier space when debugging FFTW (no in place)
divergence !< field cotaining data for FFTW in real and fourier space when debugging divergence (in place)
write(6,'(/,a)') ' <<<+- DAMASK_spectral_utilities init -+>>>'
write(6,'(a)') ' $Id$'
#include "compilation_info.f90"
write(6,'(a)') ''
flush(6)
!--------------------------------------------------------------------------------------------------
! set debugging parameters
debugGeneral = iand(debug_level(debug_spectral),debug_levelBasic) /= 0
debugDivergence = iand(debug_level(debug_spectral),debug_spectralDivergence) /= 0
debugRestart = iand(debug_level(debug_spectral),debug_spectralRestart) /= 0
debugFFTW = iand(debug_level(debug_spectral),debug_spectralFFTW) /= 0
debugRotation = iand(debug_level(debug_spectral),debug_spectralRotation) /= 0
debugPETSc = iand(debug_level(debug_spectral),debug_spectralPETSc) /= 0
#ifdef PETSc
if(debugPETSc) write(6,'(/,a)') ' Initializing PETSc with debug options: ', trim(PETScDebug), &
' add more using the PETSc_Options keyword in numerics.config '
flush(6)
call PetscOptionsClear(ierr); CHKERRQ(ierr)
if(debugPETSc) call PetscOptionsInsertString(trim(PETScDebug),ierr); CHKERRQ(ierr)
call PetscOptionsInsertString(trim(petsc_options),ierr); CHKERRQ(ierr)
#else
call IO_warning(41_pInt, ext_msg='debug PETSc')
#endif
!--------------------------------------------------------------------------------------------------
! allocation
allocate (xi(3,res1_red,res(2),res(3)),source = 0.0_pReal) ! frequencies, only half the size for first dimension
tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate aligned data using a C function, C_SIZE_T is of type integer(8)
call c_f_pointer(tensorField, field_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
call c_f_pointer(tensorField, field_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
!--------------------------------------------------------------------------------------------------
! general initialization of FFTW (see manual on fftw.org for more details)
if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(0_pInt,ext_msg='Fortran to C') ! check for correct precision in C
!$ if(DAMASK_NumThreadsInt > 0_pInt) then
!$ i = fftw_init_threads() ! returns 0 in case of problem
!$ if (i == 0_pInt) call IO_error(error_ID = 809_pInt)
!$ call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
!$ endif
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! creating plans for the convolution
plan_forward = fftw_plan_many_dft_r2c(3, [res(3),res(2) ,res(1)], 9,& ! dimensions, logical length in each dimension in reversed order, no. of transforms
field_real, [res(3),res(2) ,res(1)+2_pInt],& ! input data, physical length in each dimension in reversed order
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding, product of physical length in the 3 dimensions
field_fourier, [res(3),res(2) ,res1_red],& ! output data, physical length in each dimension in reversed order
1, res(3)*res(2)* res1_red, fftw_planner_flag) ! striding, product of physical length in the 3 dimensions, planner precision
plan_backward = fftw_plan_many_dft_c2r(3, [res(3),res(2) ,res(1)], 9,& ! dimensions, logical length in each dimension in reversed order, no. of transforms
field_fourier, [res(3),res(2) ,res1_red],& ! input data, physical length in each dimension in reversed order
1, res(3)*res(2)* res1_red,& ! striding, product of physical length in the 3 dimensions
field_real, [res(3),res(2) ,res(1)+2_pInt],& ! output data, physical length in each dimension in reversed order
1, res(3)*res(2)*(res(1)+2_pInt), fftw_planner_flag) ! striding, product of physical length in the 3 dimensions, planner precision
!--------------------------------------------------------------------------------------------------
! depending on debug options, allocate more memory and create additional plans
if (debugDivergence) then
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
allocate (divergence_post(res(1),res(2),res(3),3),source = 0.0_pReal)
plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
divergence_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,&
divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
endif
if (debugFFTW) then
scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! allocate data for real representation (no in place transform)
scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! allocate data for fourier representation (no in place transform)
call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)]) ! place a pointer for a real representation
call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)]) ! place a pointer for a fourier representation
plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& ! reversed order (C style)
scalarField_real,scalarField_fourier,-1,fftw_planner_flag) ! input, output, forward FFT(-1), planner precision
plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& ! reversed order (C style)
scalarField_fourier,scalarField_real,+1,fftw_planner_flag) ! input, output, backward (1), planner precision
endif
if (debugGeneral) write(6,'(/,a)') ' FFTW initialized'
flush(6)
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
do k = 1_pInt, res(3)
k_s(3) = k - 1_pInt
if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do j = 1_pInt, res(2)
k_s(2) = j - 1_pInt
if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do i = 1_pInt, res1_red
k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
xi(1:3,i,j,k) = real(k_s, pReal)/scaledDim ! if divergence_correction is set, frequencies are calculated on unit length
enddo; enddo; enddo
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(3,3,3,3,1,1,1), source = 0.0_pReal)
else ! precalculation of gamma_hat field
allocate (gamma_hat(3,3,3,3,res1_red ,res(2),res(3)), source =0.0_pReal)
endif
end subroutine utilities_init
!--------------------------------------------------------------------------------------------------
!> @brief updates references stiffness and potentially precalculated gamma operator
!> @details Sets the current reference stiffness to the stiffness given as an argument.
!> If the gamma operator is precalculated, it is calculated with this stiffness.
!> In case of a on-the-fly calculation, only the reference stiffness is updated.
!> The gamma operator is filtered depening on the filter selected in numerics.
!> Also writes out the current reference stiffness for restart.
!--------------------------------------------------------------------------------------------------
subroutine utilities_updateGamma(C,saveReference)
use IO, only: &
IO_write_jobBinaryFile
use numerics, only: &
memory_efficient
use math, only: &
math_inv33
use mesh, only: &
res, &
res1_red
implicit none
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
real(pReal), dimension(3,3) :: temp33_Real, xiDyad
real(pReal) :: filter !< weighting of current component
integer(pInt) :: &
i, j, k, &
l, m, n, o
C_ref = C
if (saveReference) then
write(6,'(/,a)') ' writing reference stiffness to file'
flush(6)
call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
write (777,rec=1) C_ref
close(777)
endif
if(.not. memory_efficient) then
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
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) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
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_Real = math_inv33(temp33_Real)
filter = utilities_getFilter(xi(1:3,i,j,k)) ! weighting factor computed by getFilter function
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) = filter*temp33_Real(l,n)*xiDyad(m,o)
endif
enddo; enddo; enddo
gamma_hat(1:3,1:3,1:3,1:3, 1,1,1) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
endif
end subroutine utilities_updateGamma
!--------------------------------------------------------------------------------------------------
!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
!> @detailed Does an unweighted FFT transform from real to complex.
!> In case of debugging the FFT, also one component of the tensor (specified by row and column)
!> is independetly transformed complex to complex and compared to the whole tensor transform
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTforward(row,column)
use math
use mesh, only : &
scaledDim, &
res, &
res1_red
implicit none
integer(pInt), intent(in), optional :: row, column !< if debug FFTW, compare 3D array field of row and column
!--------------------------------------------------------------------------------------------------
! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
if (.not. present(row) .or. .not. present(column)) stop
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
cmplx(field_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
endif
!--------------------------------------------------------------------------------------------------
! call function to calculate divergence from math (for post processing) to check results
if (debugDivergence) &
divergence_post = math_divergenceFFT(scaledDim,field_real(1:res(1),1:res(2),1:res(3),1:3,1:3)) ! some elements are padded
!--------------------------------------------------------------------------------------------------
! doing the FFT
call fftw_execute_dft_r2c(plan_forward,field_real,field_fourier)
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
write(6,'(/,a,i1,1x,i1,a)') ' .. checking FT results of compontent ', row, column, ' ..'
flush(6)
write(6,'(/,a,2(es11.4,1x))') ' max FT relative error = ',& ! print real and imaginary part seperately
maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
flush(6)
endif
!--------------------------------------------------------------------------------------------------
! removing highest frequencies
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
field_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
if(res(3)>1_pInt) & ! do not delete the whole slice in case of 2D calculation
field_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
end subroutine utilities_FFTforward
!--------------------------------------------------------------------------------------------------
!> @brief backward FFT of data in field_fourier to field_real
!> @detailed Does an inverse FFT transform from complex to real
!> In case of debugging the FFT, also one component of the tensor (specified by row and column)
!> is independetly transformed complex to complex and compared to the whole tensor transform
!> results is weighted by number of points stored in wgt
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTbackward(row,column)
use math !< must use the whole module for use of FFTW
use mesh, only: &
wgt, &
res, &
res1_red
implicit none
integer(pInt), intent(in), optional :: row, column !< if debug FFTW, compare 3D array field of row and column
integer(pInt) :: i, j, k, m, n
!--------------------------------------------------------------------------------------------------
! unpack FFT data for conj complex symmetric part. This data is not transformed when using c2r
if (debugFFTW) then
scalarField_fourier = field_fourier(1:res1_red,1:res(2),1:res(3),row,column)
do i = 0_pInt, res(1)/2_pInt-2_pInt
m = 1_pInt
do k = 1_pInt, res(3)
n = 1_pInt
do j = 1_pInt, res(2)
scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
if(n == 1_pInt) n = res(2) + 1_pInt
n = n-1_pInt
enddo
if(m == 1_pInt) m = res(3) + 1_pInt
m = m -1_pInt
enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! doing the iFFT
call fftw_execute_dft_c2r(plan_backward,field_fourier,field_real) ! back transform of fluct deformation gradient
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 inverse FT results
if (debugFFTW) then
write(6,'(/,a,i1,1x,i1,a)') ' ... checking iFT results of compontent ', row, column, ' ..'
flush(6)
call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
write(6,'(/,a,es11.4)') ' max iFT relative error = ',&
maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
field_real(1:res(1),1:res(2),1:res(3),row,column))/&
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
flush(6)
endif
field_real = field_real * wgt ! normalize the result by number of elements
!--------------------------------------------------------------------------------------------------
! calculate some additional output
! if(debugGeneral) then
! maxCorrectionSkew = 0.0_pReal
! maxCorrectionSym = 0.0_pReal
! temp33_Real = 0.0_pReal
! do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
! maxCorrectionSym = max(maxCorrectionSym,&
! maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
! maxCorrectionSkew = max(maxCorrectionSkew,&
! maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
! temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
! enddo; enddo; enddo
! write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
! maxCorrectionSym*wgt
! write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
! maxCorrectionSkew*wgt
! write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
! maxval(math_symmetric33(temp33_real))/&
! maxval(math_skew33(temp33_real))
! endif
end subroutine utilities_FFTbackward
!--------------------------------------------------------------------------------------------------
!> @brief doing convolution gamma_hat * field_real, ensuring that average value = fieldAim
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierConvolution(fieldAim)
use numerics, only: &
memory_efficient
use math, only: &
math_inv33
use mesh, only: &
mesh_NcpElems, &
res, &
res1_red
implicit none
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
real(pReal), dimension(3,3) :: xiDyad, temp33_Real
real(pReal) :: filter !< weighting of current component
complex(pReal), dimension(3,3) :: temp33_complex
integer(pInt) :: &
i, j, k, &
l, m, n, o
write(6,'(/,a)') ' ... doing convolution .....................................................'
flush(6)
!--------------------------------------------------------------------------------------------------
! to the actual spectral method calculation (mechanical equilibrium)
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
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) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
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_Real = math_inv33(temp33_Real)
filter = utilities_getFilter(xi(1:3,i,j,k)) ! weighting factor computed by getFilter function
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) = filter*temp33_Real(l,n)*xiDyad(m,o)
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) * field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k,1:3,1:3) = temp33_Complex
endif
enddo; enddo; enddo
else ! use precalculated gamma-operator
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
temp33_Complex(m,n) = sum(gamma_hat(m,n,1:3,1:3, i,j,k) * field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
enddo; enddo; enddo
endif
field_fourier(1,1,1,1:3,1:3) = cmplx(fieldAim*real(mesh_NcpElems,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
end subroutine utilities_fourierConvolution
!--------------------------------------------------------------------------------------------------
!> @brief calculate root mean square of divergence of field_fourier
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_divergenceRMS()
use math !< must use the whole module for use of FFTW
use mesh, only: &
wgt, &
res, &
res1_red
implicit none
integer(pInt) :: i, j, k
real(pReal) :: &
err_div_RMS, & !< RMS of divergence in Fourier space
err_real_div_RMS, & !< RMS of divergence in real space
err_post_div_RMS, & !< RMS of divergence in Fourier space, calculated using function for post processing
err_div_max, & !< maximum value of divergence in Fourier space
err_real_div_max !< maximum value of divergence in real space
complex(pReal), dimension(3) :: temp3_complex
write(6,'(/,a)') ' ... calculating divergence ................................................'
flush(6)
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
utilities_divergenceRMS = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2)
do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
utilities_divergenceRMS = utilities_divergenceRMS &
+ 2.0_pReal*(sum (real(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
enddo
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ sum( real(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum( real(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
enddo; enddo
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) *wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
!--------------------------------------------------------------------------------------------------
! calculate additional divergence criteria and report
if (debugDivergence) then ! calculate divergence again
err_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
temp3_Complex = math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
xi(1:3,i,j,k))*TWOPIIMG
err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
err_real_div_RMS = sqrt(wgt*sum(divergence_real**2.0_pReal)) ! RMS in real space
err_post_div_RMS = sqrt(wgt*sum(divergence_post**2.0_pReal)) ! RMS in real space from funtion in math.f90
err_real_div_max = sqrt(maxval(sum(divergence_real**2.0_pReal,dim=4))) ! max in real space
err_div_max = sqrt( err_div_max) ! max in Fourier space
write(6,'(/,1x,a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
write(6,'(1x,a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
write(6,'(1x,a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
write(6,'(1x,a,es11.4)') 'error divergence FT max = ',err_div_max
write(6,'(1x,a,es11.4)') 'error divergence Real max = ',err_real_div_max
flush(6)
endif
end function utilities_divergenceRMS
!--------------------------------------------------------------------------------------------------
!> @brief calculates mask compliance tensor
!--------------------------------------------------------------------------------------------------
function utilities_maskedCompliance(rot_BC,mask_stress,C)
use IO, only: &
IO_error
use math, only: &
math_Plain3333to99, &
math_plain99to3333, &
math_rotate_forward3333, &
math_rotate_forward33, &
math_invert
implicit none
real(pReal), dimension(3,3,3,3) :: utilities_maskedCompliance !< masked compliance
real(pReal), intent(in) , dimension(3,3,3,3) :: C !< current average stiffness
real(pReal), intent(in) , dimension(3,3) :: rot_BC !< rotation of load frame
logical, intent(in), dimension(3,3) :: mask_stress !< mask of stress BC
integer(pInt) :: j, k, m, n
logical, dimension(9) :: mask_stressVector
real(pReal), dimension(9,9) :: temp99_Real
integer(pInt) :: size_reduced = 0_pInt
real(pReal), dimension(:,:), allocatable :: &
s_reduced, & !< reduced compliance matrix (depending on number of stress BC)
c_reduced, & !< reduced stiffness (depending on number of stress BC)
sTimesC !< temp variable to check inversion
logical :: errmatinv
character(len=1024):: formatString
mask_stressVector = reshape(transpose(mask_stress), [9])
size_reduced = int(count(mask_stressVector), pInt)
if(size_reduced > 0_pInt )then
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
allocate (sTimesC(size_reduced,size_reduced), source =0.0_pReal)
temp99_Real = math_Plain3333to99(math_rotate_forward3333(C,rot_BC))
if(debugGeneral) then
write(6,'(/,a)') ' ... updating masked compliance ............................................'
write(6,'(/,a,/,9(9(2x,f12.7,1x)/))',advance='no') ' Stiffness C rotated / GPa =',&
transpose(temp99_Real)/1.e9_pReal
flush(6)
endif
k = 0_pInt ! calculate reduced stiffness
do n = 1_pInt,9_pInt
if(mask_stressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(mask_stressVector(m)) then
j = j + 1_pInt
c_reduced(k,j) = temp99_Real(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(error_ID=400_pInt,ext_msg='utilities_maskedCompliance')
temp99_Real = 0.0_pReal ! fill up compliance with zeros
k = 0_pInt
do n = 1_pInt,9_pInt
if(mask_stressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(mask_stressVector(m)) then
j = j + 1_pInt
temp99_Real(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
!--------------------------------------------------------------------------------------------------
! check if inversion was successfull
sTimesC = matmul(c_reduced,s_reduced)
do m=1_pInt, size_reduced
do n=1_pInt, size_reduced
if(m==n .and. abs(sTimesC(m,n)) > (1.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! diagonal elements of S*C should be 1
if(m/=n .and. abs(sTimesC(m,n)) > (0.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! off diagonal elements of S*C should be 0
enddo
enddo
if(debugGeneral .or. errmatinv) then ! report
write(formatString, '(I16.16)') size_reduced
formatString = '(/,a,/,'//trim(formatString)//'('//trim(formatString)//'(2x,es9.2,1x)/))'
write(6,trim(formatString),advance='no') ' C * S', transpose(matmul(c_reduced,s_reduced))
write(6,trim(formatString),advance='no') ' S', transpose(s_reduced)
endif
if(errmatinv) call IO_error(error_ID=400_pInt,ext_msg='utilities_maskedCompliance')
deallocate(c_reduced)
deallocate(s_reduced)
deallocate(sTimesC)
else
temp99_real = 0.0_pReal
endif
if(debugGeneral) & ! report
write(6,'(/,a,/,9(9(2x,f12.7,1x)/),/)',advance='no') ' Masked Compliance * GPa =', &
transpose(temp99_Real*1.e9_pReal)
flush(6)
utilities_maskedCompliance = math_Plain99to3333(temp99_Real)
end function utilities_maskedCompliance
!--------------------------------------------------------------------------------------------------
!> @brief calculates constitutive response
!--------------------------------------------------------------------------------------------------
subroutine utilities_constitutiveResponse(F_lastInc,F,temperature,timeinc,&
P,C,P_av,forwardData,rotation_BC)
use debug, only: &
debug_reset, &
debug_info
use math, only: &
math_transpose33, &
math_rotate_forward33
use FEsolving, only: &
restartWrite
use mesh, only: &
res, &
wgt, &
mesh_NcpElems
use CPFEM, only: &
CPFEM_general
use homogenization, only: &
materialpoint_F0, &
materialpoint_F, &
materialpoint_Temperature, &
materialpoint_P, &
materialpoint_dPdF
implicit none
real(pReal), intent(inout) :: temperature !< temperature (no field)
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
F_lastInc, & !< target deformation gradient
F !< previous deformation gradient
real(pReal), intent(in) :: timeinc !< loading time
logical, intent(in) :: forwardData !< age results
real(pReal), intent(in), dimension(3,3) :: rotation_BC !< rotation of load frame
real(pReal),intent(out), dimension(3,3,3,3) :: C !< average stiffness
real(pReal),intent(out), dimension(3,3) :: P_av !< average PK stress
real(pReal),intent(out), dimension(3,3,res(1),res(2),res(3)) :: P !< PK stress
integer(pInt) :: &
calcMode, & !< CPFEM mode for calculation
collectMode !< CPFEM mode for collection
real(pReal), dimension(3,3,3,3) :: dPdF !< d P / d F
real(pReal), dimension(6) :: sigma !< cauchy stress in mandel notation
real(pReal), dimension(6,6) :: dsde !< d sigma / d Epsilon
write(6,'(/,a)') ' ... evaluating constitutive response ......................................'
if (forwardData) then ! aging results
calcMode = 1_pInt
collectMode = 4_pInt
else ! normal calculation
calcMode = 2_pInt
collectMode = 3_pInt
endif
if (cutBack) then ! restore saved variables
calcMode = 2_pInt
collectMode = 5_pInt
endif
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
! if(debugGeneral) then
! defgradDetMax = -huge(1.0_pReal)
! defgradDetMin = +huge(1.0_pReal)
! do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
! defgradDet = math_det33(F(i,j,k,1:3,1:3))
! defgradDetMax = max(defgradDetMax,defgradDet)
! defgradDetMin = min(defgradDetMin,defgradDet)
! enddo; enddo; enddo
! write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
! write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
! endif
if (DebugGeneral) write(6,'(/,2(a,i1.1))') ' collect mode: ', collectMode,' calc mode: ', calcMode
flush(6)
call CPFEM_general(collectMode,F_lastInc(1:3,1:3,1,1,1),F(1:3,1:3,1,1,1), & ! collect mode handles Jacobian backup / restoration
temperature,timeinc,1_pInt,1_pInt,sigma,dsde,P(1:3,1:3,1,1,1),dPdF)
materialpoint_F0 = reshape(F_lastInc, [3,3,1,mesh_NcpElems])
materialpoint_F = reshape(F, [3,3,1,mesh_NcpElems])
materialpoint_Temperature = temperature
call debug_reset()
call CPFEM_general(calcMode,F_lastInc(1:3,1:3,1,1,1), F(1:3,1:3,1,1,1), & ! first call calculates everything
temperature,timeinc,1_pInt,1_pInt,sigma,dsde,P(1:3,1:3,1,1,1),dPdF)
P = reshape(materialpoint_P, [3,3,res(1),res(2),res(3)])
C = sum(sum(materialpoint_dPdF,dim=6),dim=5) * wgt
call debug_info()
restartWrite = .false. ! reset restartWrite status
cutBack = .false. ! reset cutBack status
P_av = sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt ! average of P
if (debugRotation) &
write(6,'(/,a,/,3(3(2x,f12.7,1x)/))',advance='no') ' Piola--Kirchhoff stress (lab) / MPa =',&
math_transpose33(P_av)/1.e6_pReal
P_av = math_rotate_forward33(P_av,rotation_BC)
write(6,'(/,a,/,3(3(2x,f12.7,1x)/))',advance='no') ' Piola--Kirchhoff stress / MPa =',&
math_transpose33(P_av)/1.e6_pReal
end subroutine utilities_constitutiveResponse
!--------------------------------------------------------------------------------------------------
!> @brief calculates forward rate, either guessing or just add delta/timeinc
!--------------------------------------------------------------------------------------------------
pure function utilities_calculateRate(avRate,timeinc_old,guess,field_lastInc,field)
use mesh, only: &
res
implicit none
real(pReal), intent(in), dimension(3,3) :: avRate !< homogeneous addon
real(pReal), intent(in) :: &
timeinc_old !< timeinc of last step
logical, intent(in) :: &
guess !< guess along former trajectory
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
field_lastInc, & !< data of previous step
field !< data of current step
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: utilities_calculateRate
if(guess) then
utilities_calculateRate = (field-field_lastInc) / timeinc_old
else
utilities_calculateRate = spread(spread(spread(avRate,3,res(1)),4,res(2)),5,res(3))
endif
end function utilities_calculateRate
!--------------------------------------------------------------------------------------------------
!> @brief forwards a field with a pointwise given rate, if aim is given,
!> ensures that the average matches the aim
!--------------------------------------------------------------------------------------------------
pure function utilities_forwardField(timeinc,field_lastInc,rate,aim)
use mesh, only: &
res, &
wgt
implicit none
real(pReal), intent(in) :: &
timeinc !< timeinc of current step
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
field_lastInc, & !< initial field
rate !< rate by which to forward
real(pReal), intent(in), optional, dimension(3,3) :: &
aim !< average field value aim
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: utilities_forwardField
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
utilities_forwardField = field_lastInc + rate*timeinc
if (present(aim)) then !< correct to match average
fieldDiff = sum(sum(sum(utilities_forwardField,dim=5),dim=4),dim=3)*wgt - aim
utilities_forwardField = utilities_forwardField - &
spread(spread(spread(fieldDiff,3,res(1)),4,res(2)),5,res(3))
endif
end function utilities_forwardField
!--------------------------------------------------------------------------------------------------
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_getFilter(k)
use IO, only: &
IO_error
use numerics, only: &
myfilter
use mesh, only: &
res
use math, only: &
PI
implicit none
real(pReal),intent(in), dimension(3) :: k !< indices of frequency
select case (myfilter)
case ('none')
utilities_getFilter = 1.0_pReal
case ('cosine') !< cosine curve with 1 for avg and zero for highest freq
utilities_getFilter = (1.0_pReal + cos(PI*k(3)/res(3))) &
*(1.0_pReal + cos(PI*k(2)/res(2))) &
*(1.0_pReal + cos(PI*k(1)/res(1)))/8.0_pReal
case default
call IO_error(error_ID = 892_pInt, ext_msg = trim(myfilter))
end select
end function utilities_getFilter
!--------------------------------------------------------------------------------------------------
!> @brief cleans up
!--------------------------------------------------------------------------------------------------
subroutine utilities_destroy()
use math
implicit none
if (debugDivergence) call fftw_destroy_plan(plan_divergence)
if (debugFFTW) call fftw_destroy_plan(plan_scalarField_forth)
if (debugFFTW) call fftw_destroy_plan(plan_scalarField_back)
call fftw_destroy_plan(plan_forward)
call fftw_destroy_plan(plan_backward)
end subroutine utilities_destroy
end module DAMASK_spectral_utilities