!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @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
private
#ifdef PETSc
#include <petsc-finclude/petscsys.h>
#endif
include 'fftw3-mpi.f03'
logical, public :: cutBack =.false. !< cut back of BVP solver in case convergence is not achieved or a material point is terminally ill
integer(pInt), public, parameter :: maxPhaseFields = 2_pInt
!--------------------------------------------------------------------------------------------------
! grid related information information
real(pReal), public :: wgt !< weighting factor 1/Nelems
!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
integer(pInt), public :: grid1Red !< grid(1)/2
real (C_DOUBLE), public, dimension(:,:,:,:,:), pointer :: field_realMPI !< real representation (some stress or deformation) of field_fourier
complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:,:), pointer :: field_fourierMPI !< 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
real(pReal), private, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence (Basic, Basic PETSc)
!--------------------------------------------------------------------------------------------------
! debug fftw
real(C_DOUBLE), private, dimension(:,:,:), pointer :: scalarField_realMPI !< scalar field real representation for debugging fftw
complex(C_DOUBLE_COMPLEX),private, dimension(:,:,:), pointer :: scalarField_fourierMPI !< scalar field fourier representation for debugging fftw
!--------------------------------------------------------------------------------------------------
! geometry reconstruction
real(C_DOUBLE), private, dimension(:,:,:,:), pointer :: coords_realMPI !< vector field real representation for geometry reconstruction
complex(C_DOUBLE_COMPLEX),private, dimension(:,:,:,:), pointer :: coords_fourierMPI !< vector field fourier representation for geometry reconstruction
!--------------------------------------------------------------------------------------------------
! debug divergence
real(C_DOUBLE), private, dimension(:,:,:,:), pointer :: divRealMPI !< vector field real representation for debugging divergence calculation
complex(C_DOUBLE_COMPLEX),private, dimension(:,:,:,:), pointer :: divFourierMPI !< vector field fourier representation for debugging divergence calculation
!--------------------------------------------------------------------------------------------------
! plans for FFTW
type(C_PTR), private :: &
planForthMPI, & !< FFTW MPI plan P(x) to P(k)
planBackMPI, & !< FFTW MPI plan F(k) to F(x)
planDebugForthMPI, & !< FFTW MPI plan for scalar field
planDebugBackMPI, & !< FFTW MPI plan for scalar field inverse
planDivMPI, & !< FFTW MPI plan for FFTW in case of debugging divergence calculation
planCoordsMPI !< FFTW MPI plan for geometry reconstruction
!--------------------------------------------------------------------------------------------------
! variables controlling debugging
logical, private :: &
debugGeneral, & !< general debugging of spectral solver
debugDivergence, & !< debugging of divergence calculation (comparison to function used for post processing)
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, public :: 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, public :: 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
type, public :: phaseFieldDataBin !< set of parameters defining a phase field
real(pReal) :: diffusion = 0.0_pReal, & !< thermal conductivity
mobility = 0.0_pReal, & !< thermal mobility
phaseField0 = 0.0_pReal !< homogeneous damage field starting condition
logical :: active = .false.
character(len=64) :: label = ''
end type phaseFieldDataBin
public :: &
utilities_init, &
utilities_updateGamma, &
utilities_FFTforward, &
utilities_FFTbackward, &
utilities_fourierConvolution, &
utilities_inverseLaplace, &
utilities_divergenceRMS, &
utilities_curlRMS, &
utilities_maskedCompliance, &
utilities_constitutiveResponse, &
utilities_calculateRate, &
utilities_forwardField, &
utilities_destroy, &
utilities_updateIPcoords
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 DAMASK_interface, only: &
geometryFile
use IO, only: &
IO_error, &
IO_warning, &
IO_timeStamp, &
IO_open_file
use numerics, only: &
DAMASK_NumThreadsInt, &
fftw_planner_flag, &
fftw_timelimit, &
memory_efficient, &
petsc_options, &
divergence_correction, &
worldrank
use debug, only: &
debug_level, &
debug_SPECTRAL, &
debug_LEVELBASIC, &
debug_SPECTRALDIVERGENCE, &
debug_SPECTRALFFTW, &
debug_SPECTRALPETSC, &
debug_SPECTRALROTATION
#ifdef PETSc
use debug, only: &
PETSCDEBUG
#endif
use math
use mesh, only: &
gridGlobal, &
gridLocal, &
gridOffset, &
geomSizeGlobal, &
geomSizeLocal, &
geomSizeOffset
implicit none
#ifdef PETSc
external :: &
PETScOptionsClear, &
PETScOptionsInsertString, &
MPI_Abort
PetscErrorCode :: ierr
#endif
integer(pInt) :: i, j, k
integer(pInt), parameter :: fileUnit = 228_pInt
integer(pInt), dimension(3) :: k_s
type(C_PTR) :: &
tensorFieldMPI, & !< field cotaining data for FFTW in real and fourier space (in place)
scalarFieldMPI, & !< field cotaining data for FFTW in real space when debugging FFTW (no in place)
div, & !< field cotaining data for FFTW in real and fourier space when debugging divergence (in place)
coordsMPI
integer(C_INTPTR_T) :: gridFFTW(3), alloc_local, local_K, local_K_offset, &
dimSize = 3, scalarSize = 1, vecSize = 3, tensorSize = 9
mainProcess: if (worldrank == 0) then
write(6,'(/,a)') ' <<<+- DAMASK_spectral_utilities init -+>>>'
write(6,'(a)') ' $Id$'
write(6,'(a15,a)') ' Current time: ',IO_timeStamp()
#include "compilation_info.f90"
endif mainProcess
!--------------------------------------------------------------------------------------------------
! set debugging parameters
debugGeneral = iand(debug_level(debug_SPECTRAL),debug_LEVELBASIC) /= 0
debugDivergence = iand(debug_level(debug_SPECTRAL),debug_SPECTRALDIVERGENCE) /= 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 .and. worldrank == 0_pInt) write(6,'(3(/,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
if(debugPETSc) call IO_warning(41_pInt, ext_msg='debug PETSc')
#endif
grid1Red = gridLocal(1)/2_pInt + 1_pInt
wgt = 1.0/real(product(gridGlobal),pReal)
if (worldrank == 0) then
write(6,'(a,3(i12 ))') ' grid a b c: ', gridGlobal
write(6,'(a,3(es12.5))') ' size x y z: ', geomSizeGlobal
endif
!--------------------------------------------------------------------------------------------------
! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and reso-
! lution-independent divergence
if (divergence_correction == 1_pInt) then
do j = 1_pInt, 3_pInt
if (j /= minloc(geomSizeGlobal,1) .and. j /= maxloc(geomSizeGlobal,1)) &
scaledGeomSize = geomSizeGlobal/geomSizeGlobal(j)
enddo
elseif (divergence_correction == 2_pInt) then
do j = 1_pInt, 3_pInt
if (j /= minloc(geomSizeGlobal/gridGlobal,1) .and. j /= maxloc(geomSizeGlobal/gridGlobal,1)) &
scaledGeomSize = geomSizeGlobal/geomSizeGlobal(j)*gridGlobal(j)
enddo
else
scaledGeomSize = geomSizeGlobal
endif
!--------------------------------------------------------------------------------------------------
! MPI allocation
gridFFTW = gridGlobal
alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
MPI_COMM_WORLD, local_K, local_K_offset)
tensorFieldMPI = fftw_alloc_complex(9*alloc_local)
call c_f_pointer(tensorFieldMPI, field_realMPI, [dimSize,dimSize,2*(gridFFTW(1)/2 + 1),gridFFTW(2),local_K])
call c_f_pointer(tensorFieldMPI, field_fourierMPI,[dimSize,dimSize, gridFFTW(1)/2 + 1 ,gridFFTW(2),local_K])
allocate (xi(3,grid1Red,gridLocal(2),gridLocal(3)),source = 0.0_pReal) ! frequencies, only half the size for first dimension
coordsMPI = fftw_alloc_complex(3*alloc_local)
call c_f_pointer(coordsMPI, coords_realMPI, [dimSize,2*(gridFFTW(1)/2 + 1),gridFFTW(2),local_K]) ! place a pointer for a real representation on coords_fftw
call c_f_pointer(coordsMPI, coords_fourierMPI, [dimSize, gridFFTW(1)/2 + 1 ,gridFFTW(2),local_K]) ! place a pointer for a real representation on coords_fftw
!--------------------------------------------------------------------------------------------------
! MPI fftw plans
planForthMPI = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], tensorSize, & ! dimension, logical length in each dimension in reversed order, no. of transforms
FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! default iblock and oblock
field_realMPI, field_fourierMPI, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
planBackMPI = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], tensorSize, & ! dimension, logical length in each dimension in reversed order, no. of transforms
FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! default iblock and oblock
field_fourierMPI,field_realMPI, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! all processors, planer precision
!--------------------------------------------------------------------------------------------------
! Coordinates MPI fftw plans
planCoordsMPI = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], vecSize, & ! dimension, logical length in each dimension in reversed order, no. of transforms
FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! default iblock and oblock
coords_fourierMPI,coords_realMPI, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
!--------------------------------------------------------------------------------------------------
! depending on debug options, allocate more memory and create additional plans
if (debugDivergence) then
div = fftw_alloc_complex(3*alloc_local)
call c_f_pointer(div,divRealMPI, [dimSize,2*(gridFFTW(1)/2 + 1),gridFFTW(2),local_K])
call c_f_pointer(div,divFourierMPI,[dimSize, gridFFTW(1)/2 + 1 ,gridFFTW(2),local_K])
planDivMPI = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2) ,gridFFTW(1)],vecSize, &
FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &
divFourierMPI, divRealMPI, &
MPI_COMM_WORLD, fftw_planner_flag)
endif
if (debugFFTW) then
scalarFieldMPI = fftw_alloc_complex(alloc_local) ! allocate data for real representation (no in place transform)
call c_f_pointer(scalarFieldMPI, scalarField_realMPI, &
[2*(gridFFTW(1)/2 + 1),gridFFTW(2),local_K]) ! place a pointer for a real representation
call c_f_pointer(scalarFieldMPI, scalarField_fourierMPI, &
[ gridFFTW(1)/2 + 1 ,gridFFTW(2),local_K]) ! place a pointer for a fourier representation
planDebugForthMPI = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], &
scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &
scalarField_realMPI, scalarField_fourierMPI, &
MPI_COMM_WORLD, fftw_planner_flag)
planDebugBackMPI = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], &
scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &
scalarField_fourierMPI,scalarField_realMPI, &
MPI_COMM_WORLD, fftw_planner_flag)
endif
!--------------------------------------------------------------------------------------------------
! 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
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
if (debugGeneral .and. worldrank == 0_pInt) write(6,'(/,a)') ' FFTW initialized'
flush(6)
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
do k = gridOffset+1_pInt, gridOffset+gridLocal(3)
k_s(3) = k - 1_pInt
if(k > gridGlobal(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - gridGlobal(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do j = 1_pInt, gridLocal(2)
k_s(2) = j - 1_pInt
if(j > gridGlobal(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - gridGlobal(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do i = 1_pInt, grid1Red
k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
xi(1:3,i,j,k-gridOffset) = real(k_s, pReal)/scaledGeomSize ! 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,grid1Red,gridLocal(2),gridLocal(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_jobRealFile
use numerics, only: &
memory_efficient, &
worldrank
use mesh, only: &
gridOffset, &
gridLocal
use math, only: &
math_inv33
use mesh, only: &
gridLocal
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
integer(pInt) :: &
i, j, k, &
l, m, n, o
C_ref = C
if (saveReference) then
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' writing reference stiffness to file'
flush(6)
call IO_write_jobRealFile(777,'C_ref',size(C_ref))
write (777,rec=1) C_ref
close(777)
endif
endif
if(.not. memory_efficient) then
do k = gridOffset+1_pInt, gridOffset+gridLocal(3); do j = 1_pInt, gridLocal(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
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi(l, i,j,k-gridOffset)*xi(m, i,j,k-gridOffset)
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)
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-gridOffset) = temp33_Real(l,n)*xiDyad(m,o)
endif
enddo; enddo; enddo
endif
end subroutine utilities_updateGamma
!--------------------------------------------------------------------------------------------------
!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
!> @details 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()
use math
use numerics, only: &
worldrank
use mesh, only: &
gridOffset, &
gridLocal
implicit none
integer(pInt) :: row, column ! if debug FFTW, compare 3D array field of row and column
real(pReal), dimension(2) :: myRand, maxScalarField ! random numbers
integer(pInt) :: i, j, k
PetscErrorCode :: ierr
!--------------------------------------------------------------------------------------------------
! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
if (worldrank == 0_pInt) then
call random_number(myRand) ! two numbers: 0 <= x < 1
row = nint(myRand(1)*2_pReal + 1_pReal,pInt)
column = nint(myRand(2)*2_pReal + 1_pReal,pInt)
endif
call MPI_Bcast(row ,1,MPI_INTEGER,0,PETSC_COMM_WORLD,ierr)
call MPI_Bcast(column,1,MPI_INTEGER,0,PETSC_COMM_WORLD,ierr)
scalarField_realMPI = 0.0_pReal
scalarField_realMPI(1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)) = &
field_realMPI(row,column,1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)) ! store the selected component
endif
!--------------------------------------------------------------------------------------------------
! doing the FFT
call fftw_mpi_execute_dft_r2c(planForthMPI,field_realMPI,field_fourierMPI)
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
call fftw_mpi_execute_dft_r2c(planDebugForthMPI,scalarField_realMPI,scalarField_fourierMPI)
where(abs(scalarField_fourierMPI(1:grid1Red,1:gridLocal(2),1:gridLocal(3))) > tiny(1.0_pReal)) ! avoid division by zero
scalarField_fourierMPI(1:grid1Red,1:gridLocal(2),1:gridLocal(3)) = &
(scalarField_fourierMPI(1:grid1Red,1:gridLocal(2),1:gridLocal(3))-&
field_fourierMPI(row,column,1:grid1Red,1:gridLocal(2),1:gridLocal(3)))/&
scalarField_fourierMPI(1:grid1Red,1:gridLocal(2),1:gridLocal(3))
else where
scalarField_realMPI = cmplx(0.0,0.0,pReal)
end where
maxScalarField(1) = maxval(real (scalarField_fourierMPI(1:grid1Red,1:gridLocal(2), &
1:gridLocal(3))))
maxScalarField(2) = maxval(aimag(scalarField_fourierMPI(1:grid1Red,1:gridLocal(2), &
1:gridLocal(3))))
call MPI_reduce(MPI_IN_PLACE,maxScalarField,2,MPI_DOUBLE,MPI_MAX,0,PETSC_COMM_WORLD,ierr)
if (worldrank == 0_pInt) then
write(6,'(/,a,i1,1x,i1,a)') ' .. checking FT results of compontent ', row, column, ' ..'
write(6,'(/,a,2(es11.4,1x))') ' max FT relative error = ',& ! print real and imaginary part seperately
maxScalarField(1),maxScalarField(2)
flush(6)
endif
endif
!--------------------------------------------------------------------------------------------------
! applying filter
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2); do i = 1_pInt,grid1Red
field_fourierMPI(1:3,1:3,i,j,k) = utilities_getFilter(xi(1:3,i,j,k))* &
field_fourierMPI(1:3,1:3,i,j,k)
enddo; enddo; enddo
end subroutine utilities_FFTforward
!--------------------------------------------------------------------------------------------------
!> @brief backward FFT of data in field_fourier to field_real
!> @details 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()
use math
use numerics, only: &
worldrank
use mesh, only: &
gridLocal
implicit none
integer(pInt) :: row, column !< if debug FFTW, compare 3D array field of row and column
real(pReal), dimension(2) :: myRand
real(pReal) :: maxScalarField
PetscErrorCode :: ierr
!--------------------------------------------------------------------------------------------------
! unpack FFT data for conj complex symmetric part. This data is not transformed when using c2r
if (debugFFTW) then
if (worldrank == 0_pInt) then
call random_number(myRand) ! two numbers: 0 <= x < 1
row = nint(myRand(1)*2_pReal + 1_pReal,pInt)
column = nint(myRand(2)*2_pReal + 1_pReal,pInt)
endif
call MPI_Bcast(row ,1,MPI_INTEGER,0,PETSC_COMM_WORLD,ierr)
call MPI_Bcast(column,1,MPI_INTEGER,0,PETSC_COMM_WORLD,ierr)
scalarField_fourierMPI(1:grid1Red,1:gridLocal(2),1:gridLocal(3)) = &
field_fourierMPI(row,column,1:grid1Red,1:gridLocal(2),1:gridLocal(3))
endif
!--------------------------------------------------------------------------------------------------
! doing the iFFT
call fftw_mpi_execute_dft_c2r(planBackMPI,field_fourierMPI,field_realMPI) ! back transform of fluct deformation gradient
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 inverse FT results
if (debugFFTW) then
call fftw_mpi_execute_dft_c2r(planDebugBackMPI,scalarField_fourierMPI,scalarField_realMPI)
where(abs(real(scalarField_realMPI,pReal)) > tiny(1.0_pReal)) ! avoid division by zero
scalarField_realMPI(1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)) = &
(scalarField_realMPI(1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)) &
- field_realMPI (row,column,1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)))/ &
scalarField_realMPI(1:gridLocal(1),1:gridLocal(2),1:gridLocal(3))
else where
scalarField_realMPI = cmplx(0.0,0.0,pReal)
end where
maxScalarField = maxval(real (scalarField_realMPI(1:gridLocal(1),1:gridLocal(2),1:gridLocal(3))))
call MPI_reduce(MPI_IN_PLACE,maxScalarField,1,MPI_DOUBLE,MPI_MAX,0,PETSC_COMM_WORLD,ierr)
if (worldrank == 0_pInt) then
write(6,'(/,a,i1,1x,i1,a)') ' ... checking iFT results of compontent ', row, column, ' ..'
write(6,'(/,a,es11.4)') ' max iFT relative error = ', maxScalarField
flush(6)
endif
endif
field_realMPI = field_realMPI * wgt ! normalize the result by number of elements
end subroutine utilities_FFTbackward
!--------------------------------------------------------------------------------------------------
!> @brief doing convolution with inverse laplace kernel
!--------------------------------------------------------------------------------------------------
subroutine utilities_inverseLaplace()
use math, only: &
math_inv33, &
PI
use numerics, only: &
worldrank
use mesh, only: &
gridLocal, &
gridOffset, &
geomSizeGlobal
implicit none
integer(pInt) :: i, j, k
real(pReal), dimension(3) :: k_s
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... doing inverse laplace .................................................'
flush(6)
endif
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2); do i = 1_pInt, grid1Red
k_s = xi(1:3,i,j,k)*scaledGeomSize
if (any(k_s /= 0_pInt)) field_fourierMPI(1:3,1:3,i,j,k-gridOffset) = &
field_fourierMPI(1:3,1:3,i,j,k-gridOffset)/ &
cmplx(-sum((2.0_pReal*PI*k_s/geomSizeGlobal)* &
(2.0_pReal*PI*k_s/geomSizeGlobal)),0.0_pReal,pReal)
enddo; enddo; enddo
if (gridOffset == 0_pInt) &
field_fourierMPI(1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
end subroutine utilities_inverseLaplace
!--------------------------------------------------------------------------------------------------
!> @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 numerics, only: &
worldrank
use mesh, only: &
gridLocal, &
gridOffset
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
complex(pReal), dimension(3,3) :: temp33_complex
integer(pInt) :: &
i, j, k, &
l, m, n, o
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... doing convolution .....................................................'
flush(6)
endif
!--------------------------------------------------------------------------------------------------
! do 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, gridLocal(3); do j = 1_pInt, gridLocal(2) ;do i = 1_pInt, grid1Red
if(any([i,j,k+gridOffset] /= 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)
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_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_fourierMPI(1:3,1:3,i,j,k))
field_fourierMPI(1:3,1:3,i,j,k) = temp33_Complex
endif
enddo; enddo; enddo
else ! use precalculated gamma-operator
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2); do i = 1_pInt,grid1Red
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) * field_fourierMPI(1:3,1:3,i,j,k))
field_fourierMPI(1:3,1:3,i,j,k) = temp33_Complex
enddo; enddo; enddo
endif
if (gridOffset == 0_pInt) &
field_fourierMPI(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
end subroutine utilities_fourierConvolution
!--------------------------------------------------------------------------------------------------
!> @brief calculate root mean square of divergence of field_fourier
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_divergenceRMS()
use math
use numerics, only: &
worldrank
use mesh, only: &
gridLocal, &
gridGlobal
implicit none
integer(pInt) :: i, j, k
real(pReal) :: &
err_real_div_RMS, & !< RMS of divergence in real space
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
PetscErrorCode :: ierr
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... calculating divergence ................................................'
flush(6)
endif
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
utilities_divergenceRMS = 0.0_pReal
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2)
do i = 2_pInt, grid1Red -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_fourierMPI(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
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(field_fourierMPI(1:3,1:3,i,j,k),&
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 (if grid(1) /= 1)
+ sum( real(math_mul33x3_complex(field_fourierMPI(1:3,1:3,1 ,j,k), &
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) &
+ sum(aimag(math_mul33x3_complex(field_fourierMPI(1:3,1:3,1 ,j,k), &
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal) &
+ sum( real(math_mul33x3_complex(field_fourierMPI(1:3,1:3,grid1Red,j,k), &
xi(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal) &
+ sum(aimag(math_mul33x3_complex(field_fourierMPI(1:3,1:3,grid1Red,j,k), &
xi(1:3,grid1Red,j,k))*TWOPIIMG)**2.0_pReal)
enddo; enddo
if(gridGlobal(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)
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, gridLocal(3); do j = 1_pInt, gridLocal(2); do i = 1_pInt, grid1Red
temp3_Complex = math_mul33x3_complex(field_fourierMPI(1:3,1:3,i,j,k)*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))
divFourierMPI(1:3,i,j,k) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_mpi_execute_dft_c2r(planDivMPI,divFourierMPI,divRealMPI) ! already weighted
err_real_div_RMS = sum(divRealMPI**2.0_pReal)
call MPI_reduce(MPI_IN_PLACE,err_real_div_RMS,1,MPI_DOUBLE,MPI_SUM,0,PETSC_COMM_WORLD,ierr)
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
err_real_div_max = maxval(sum(divRealMPI**2.0_pReal,dim=4)) ! max in real space
call MPI_reduce(MPI_IN_PLACE,err_real_div_max,1,MPI_DOUBLE,MPI_MAX,0,PETSC_COMM_WORLD,ierr)
err_real_div_max = sqrt(err_real_div_max)
call MPI_reduce(MPI_IN_PLACE,err_div_max,1,MPI_DOUBLE,MPI_MAX,0,PETSC_COMM_WORLD,ierr)
err_div_max = sqrt( err_div_max) ! max in Fourier space
if (worldrank == 0_pInt) then
write(6,'(/,1x,a,es11.4)') 'error divergence FT RMS = ',utilities_divergenceRMS
write(6,'(1x,a,es11.4)') 'error divergence Real RMS = ',err_real_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
endif
end function utilities_divergenceRMS
!--------------------------------------------------------------------------------------------------
!> @brief calculate max of curl of field_fourier
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_curlRMS()
use math
use numerics, only: &
worldrank
use mesh, only: &
gridLocal, &
gridGlobal
implicit none
integer(pInt) :: i, j, k, l
complex(pReal), dimension(3,3) :: curl_fourier
PetscErrorCode :: ierr
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... calculating curl ......................................................'
flush(6)
endif
!--------------------------------------------------------------------------------------------------
! calculating max curl criterion in Fourier space
utilities_curlRMS = 0.0_pReal
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2);
do i = 2_pInt, grid1Red - 1_pInt
do l = 1_pInt, 3_pInt
curl_fourier(l,1) = (+field_fourierMPI(l,3,i,j,k)*xi(2,i,j,k)&
-field_fourierMPI(l,2,i,j,k)*xi(3,i,j,k))*TWOPIIMG
curl_fourier(l,2) = (+field_fourierMPI(l,1,i,j,k)*xi(3,i,j,k)&
-field_fourierMPI(l,3,i,j,k)*xi(1,i,j,k))*TWOPIIMG
curl_fourier(l,3) = (+field_fourierMPI(l,2,i,j,k)*xi(1,i,j,k)&
-field_fourierMPI(l,1,i,j,k)*xi(2,i,j,k))*TWOPIIMG
enddo
utilities_curlRMS = utilities_curlRMS + &
2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)
enddo
do l = 1_pInt, 3_pInt
curl_fourier = (+field_fourierMPI(l,3,1,j,k)*xi(2,1,j,k)&
-field_fourierMPI(l,2,1,j,k)*xi(3,1,j,k))*TWOPIIMG
curl_fourier = (+field_fourierMPI(l,1,1,j,k)*xi(3,1,j,k)&
-field_fourierMPI(l,3,1,j,k)*xi(1,1,j,k))*TWOPIIMG
curl_fourier = (+field_fourierMPI(l,2,1,j,k)*xi(1,1,j,k)&
-field_fourierMPI(l,1,1,j,k)*xi(2,1,j,k))*TWOPIIMG
enddo
utilities_curlRMS = utilities_curlRMS + &
2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)
do l = 1_pInt, 3_pInt
curl_fourier = (+field_fourierMPI(l,3,grid1Red,j,k)*xi(2,grid1Red,j,k)&
-field_fourierMPI(l,2,grid1Red,j,k)*xi(3,grid1Red,j,k))*TWOPIIMG
curl_fourier = (+field_fourierMPI(l,1,grid1Red,j,k)*xi(3,grid1Red,j,k)&
-field_fourierMPI(l,3,grid1Red,j,k)*xi(1,grid1Red,j,k))*TWOPIIMG
curl_fourier = (+field_fourierMPI(l,2,grid1Red,j,k)*xi(1,grid1Red,j,k)&
-field_fourierMPI(l,1,grid1Red,j,k)*xi(2,grid1Red,j,k))*TWOPIIMG
enddo
utilities_curlRMS = utilities_curlRMS + &
2.0_pReal*sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal)
enddo; enddo
call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
utilities_curlRMS = sqrt(utilities_curlRMS) * wgt
if(gridGlobal(1) == 1_pInt) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
end function utilities_curlRMS
!--------------------------------------------------------------------------------------------------
!> @brief calculates mask compliance tensor used to adjust F to fullfill stress BC
!--------------------------------------------------------------------------------------------------
function utilities_maskedCompliance(rot_BC,mask_stress,C)
use IO, only: &
IO_error
use numerics, only: &
worldrank
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 .and. worldrank == 0_pInt) then
write(6,'(/,a)') ' ... updating masked compliance ............................................'
write(6,'(/,a,/,9(9(2x,f12.7,1x)/))',advance='no') ' Stiffness C (load) / 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 successful
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) .and. (worldrank == 0_pInt)) 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 (load) ', &
transpose(matmul(c_reduced,s_reduced))
write(6,trim(formatString),advance='no') ' S (load) ', 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 .and. worldrank == 0_pInt) & ! report
write(6,'(/,a,/,9(9(2x,f12.7,1x)/),/)',advance='no') ' Masked Compliance (load) * 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_volAvg,C_minmaxAvg,P_av,forwardData,rotation_BC)
use debug, only: &
debug_reset, &
debug_info
use numerics, only: &
worldrank
use math, only: &
math_transpose33, &
math_rotate_forward33, &
math_det33
use mesh, only: &
gridLocal
use FEsolving, only: &
restartWrite
use CPFEM, only: &
CPFEM_general, &
CPFEM_COLLECT, &
CPFEM_CALCRESULTS, &
CPFEM_AGERESULTS
use homogenization, only: &
materialpoint_F0, &
materialpoint_F, &
materialpoint_P, &
materialpoint_dPdF
use thermal_isothermal, only: &
thermal_isothermal_temperature
implicit none
real(pReal), intent(in) :: temperature !< temperature (no field)
real(pReal), intent(in), dimension(3,3,gridLocal(1),gridLocal(2),gridLocal(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_volAvg, C_minmaxAvg !< average stiffness
real(pReal),intent(out), dimension(3,3) :: P_av !< average PK stress
real(pReal),intent(out), dimension(3,3,gridLocal(1),gridLocal(2),gridLocal(3)) :: P !< PK stress
integer(pInt) :: &
calcMode, & !< CPFEM mode for calculation
j,k
real(pReal), dimension(3,3,3,3) :: max_dPdF, min_dPdF
real(pReal) :: max_dPdF_norm, min_dPdF_norm, defgradDetMin, defgradDetMax, defgradDet
PetscErrorCode :: ierr
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... evaluating constitutive response ......................................'
flush(6)
endif
calcMode = CPFEM_CALCRESULTS
if (forwardData) then ! aging results
calcMode = ior(calcMode, CPFEM_AGERESULTS)
materialpoint_F0 = reshape(F_lastInc, [3,3,1,product(gridLocal)])
endif
if (cutBack) then ! restore saved variables
calcMode = iand(calcMode, not(CPFEM_AGERESULTS))
endif
call CPFEM_general(CPFEM_COLLECT,F_lastInc(1:3,1:3,1,1,1),F(1:3,1:3,1,1,1), &
temperature,timeinc,1_pInt,1_pInt)
thermal_isothermal_temperature(:) = temperature
materialpoint_F = reshape(F,[3,3,1,product(gridLocal)])
call debug_reset()
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
if(debugGeneral) then
defgradDetMax = -huge(1.0_pReal)
defgradDetMin = +huge(1.0_pReal)
do j = 1_pInt, product(gridLocal)
defgradDet = math_det33(materialpoint_F(1:3,1:3,1,j))
defgradDetMax = max(defgradDetMax,defgradDet)
defgradDetMin = min(defgradDetMin,defgradDet)
end do
call MPI_reduce(MPI_IN_PLACE,defgradDetMax,1,MPI_DOUBLE,MPI_MAX,0,PETSC_COMM_WORLD,ierr)
call MPI_reduce(MPI_IN_PLACE,defgradDetMin,1,MPI_DOUBLE,MPI_MIN,0,PETSC_COMM_WORLD,ierr)
if (worldrank == 0_pInt) then
write(6,'(a,1x,es11.4)') ' max determinant of deformation =', defgradDetMax
write(6,'(a,1x,es11.4)') ' min determinant of deformation =', defgradDetMin
flush(6)
endif
endif
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)
max_dPdF = 0.0_pReal
max_dPdF_norm = 0.0_pReal
min_dPdF = huge(1.0_pReal)
min_dPdF_norm = huge(1.0_pReal)
do k = 1_pInt, product(gridLocal)
if (max_dPdF_norm < sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)) then
max_dPdF = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)
max_dPdF_norm = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)
endif
if (min_dPdF_norm > sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)) then
min_dPdF = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)
min_dPdF_norm = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,k)**2.0_pReal)
endif
end do
call MPI_Allreduce(MPI_IN_PLACE,max_dPdF,81,MPI_DOUBLE,MPI_MAX,PETSC_COMM_WORLD,ierr)
call MPI_Allreduce(MPI_IN_PLACE,min_dPdF,81,MPI_DOUBLE,MPI_MIN,PETSC_COMM_WORLD,ierr)
C_minmaxAvg = 0.5_pReal*(max_dPdF + min_dPdF)
C_volAvg = sum(sum(materialpoint_dPdF,dim=6),dim=5) * wgt
call MPI_Allreduce(MPI_IN_PLACE,C_volAvg,81,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
call debug_info()
restartWrite = .false. ! reset restartWrite status
cutBack = .false. ! reset cutBack status
P = reshape(materialpoint_P, [3,3,gridLocal(1),gridLocal(2),gridLocal(3)])
P_av = sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt ! average of P
call MPI_Allreduce(MPI_IN_PLACE,P_av,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
if (debugRotation .and. worldrank == 0_pInt) &
write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress (lab) / MPa =',&
math_transpose33(P_av)*1.e-6_pReal
P_av = math_rotate_forward33(P_av,rotation_BC)
if (worldrank == 0_pInt) then
write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress / MPa =',&
math_transpose33(P_av)*1.e-6_pReal
flush(6)
endif
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: &
gridLocal
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,gridLocal(1),gridLocal(2),gridLocal(3)) :: &
field_lastInc, & !< data of previous step
field !< data of current step
real(pReal), dimension(3,3,gridLocal(1),gridLocal(2),gridLocal(3)) :: &
utilities_calculateRate
if (guess) then
utilities_calculateRate = (field-field_lastInc) / timeinc_old
else
utilities_calculateRate = spread(spread(spread(avRate,3,gridLocal(1)),4,gridLocal(2)), &
5,gridLocal(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
!--------------------------------------------------------------------------------------------------
function utilities_forwardField(timeinc,field_lastInc,rate,aim)
use mesh, only: &
gridLocal
implicit none
real(pReal), intent(in) :: &
timeinc !< timeinc of current step
real(pReal), intent(in), dimension(3,3,gridLocal(1),gridLocal(2),gridLocal(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,gridLocal(1),gridLocal(2),gridLocal(3)) :: &
utilities_forwardField
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
PetscErrorCode :: ierr
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
call MPI_Allreduce(MPI_IN_PLACE,fieldDiff,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
fieldDiff = fieldDiff - aim
utilities_forwardField = utilities_forwardField - &
spread(spread(spread(fieldDiff,3,gridLocal(1)),4,gridLocal(2)),5,gridLocal(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: &
spectral_filter
use math, only: &
PI
use mesh, only: &
gridGlobal
implicit none
real(pReal),intent(in), dimension(3) :: k !< indices of frequency
utilities_getFilter = 1.0_pReal
select case (spectral_filter)
case ('none') ! default, no weighting
case ('cosine') ! cosine curve with 1 for avg and zero for highest freq
utilities_getFilter = product(1.0_pReal + cos(PI*k*scaledGeomSize/gridGlobal))/8.0_pReal
case ('gradient') ! gradient, might need grid scaling as for cosine filter
utilities_getFilter = 1.0_pReal/(1.0_pReal + &
(k(1)*k(1) + k(2)*k(2) + k(3)*k(3)))
case default
call IO_error(error_ID = 892_pInt, ext_msg = trim(spectral_filter))
end select
if (gridGlobal(1) /= 1_pInt .and. k(1) == real(grid1Red - 1_pInt, pReal)/scaledGeomSize(1)) &
utilities_getFilter = 0.0_pReal
if (gridGlobal(2) /= 1_pInt .and. k(2) == real(gridGlobal(2)/2_pInt, pReal)/scaledGeomSize(2)) &
utilities_getFilter = 0.0_pReal ! do not delete the whole slice in case of 2D calculation
if (gridGlobal(2) /= 1_pInt .and. k(2) == real(gridGlobal(2)/2_pInt + mod(gridGlobal(2),2_pInt), pReal)/scaledGeomSize(2)) &
utilities_getFilter = 0.0_pReal ! do not delete the whole slice in case of 2D calculation
if (gridGlobal(3) /= 1_pInt .and. k(3) == real(gridGlobal(3)/2_pInt, pReal)/scaledGeomSize(3)) &
utilities_getFilter = 0.0_pReal ! do not delete the whole slice in case of 2D calculation
if (gridGlobal(3) /= 1_pInt .and. k(3) == real(gridGlobal(3)/2_pInt + mod(gridGlobal(3),2_pInt), pReal)/scaledGeomSize(3)) &
utilities_getFilter = 0.0_pReal ! do not delete the whole slice in case of 2D calculation
end function utilities_getFilter
!--------------------------------------------------------------------------------------------------
!> @brief cleans up
!--------------------------------------------------------------------------------------------------
subroutine utilities_destroy()
use math
implicit none
if (debugDivergence) call fftw_destroy_plan(planDivMPI)
if (debugFFTW) call fftw_destroy_plan(planDebugForthMPI)
if (debugFFTW) call fftw_destroy_plan(planDebugBackMPI)
call fftw_destroy_plan(planForthMPI)
call fftw_destroy_plan(planBackMPI)
call fftw_destroy_plan(planCoordsMPI)
end subroutine utilities_destroy
!--------------------------------------------------------------------------------------------------
!> @brief calculate coordinates in current configuration for given defgrad field
! using integration in Fourier space. Similar as in mesh.f90, but using data already defined for
! convolution
!--------------------------------------------------------------------------------------------------
subroutine utilities_updateIPcoords(F)
use math
use mesh, only: &
gridGlobal, &
gridLocal, &
gridOffset, &
geomSizeGlobal, &
mesh_ipCoordinates
implicit none
real(pReal), dimension(3,3,gridLocal(1),gridLocal(2),gridLocal(3)), intent(in) :: F
integer(pInt) :: i, j, k, m
real(pReal), dimension(3) :: step, offset_coords, integrator
real(pReal), dimension(3,3) :: Favg
PetscErrorCode :: ierr
field_realMPI = 0.0_pReal
field_realMPI(1:3,1:3,1:gridLocal(1),1:gridLocal(2),1:gridLocal(3)) = F
call utilities_FFTforward()
integrator = geomSizeGlobal * 0.5_pReal / PI
step = geomSizeGlobal/real(gridGlobal, pReal)
!--------------------------------------------------------------------------------------------------
! average F
if (gridOffset == 0_pInt) Favg = real(field_fourierMPI(1:3,1:3,1,1,1),pReal)*wgt
call MPI_Bcast(Favg,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
!--------------------------------------------------------------------------------------------------
! integration in Fourier space
coords_fourierMPI = cmplx(0.0_pReal, 0.0_pReal, pReal)
do k = 1_pInt, gridLocal(3); do j = 1_pInt, gridLocal(2); do i = 1_pInt,grid1Red
do m = 1_pInt,3_pInt
coords_fourierMPI(m,i,j,k) = sum(field_fourierMPI(m,1:3,i,j,k)*&
cmplx(0.0_pReal,xi(1:3,i,j,k)*scaledGeomSize*integrator,pReal))
enddo
if (any(xi(1:3,i,j,k) /= 0.0_pReal)) coords_fourierMPI(1:3,i,j,k) = &
coords_fourierMPI(1:3,i,j,k)/cmplx(-sum(xi(1:3,i,j,k)*scaledGeomSize*xi(1:3,i,j,k)* &
scaledGeomSize),0.0_pReal,pReal)
enddo; enddo; enddo
call fftw_mpi_execute_dft_c2r(planCoordsMPI,coords_fourierMPI,coords_realMPI)
!--------------------------------------------------------------------------------------------------
! add average to fluctuation and put (0,0,0) on (0,0,0)
if (gridOffset == 0_pInt) offset_coords = coords_realMPI(1:3,1,1,1)
call MPI_Bcast(offset_coords,3,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
offset_coords = math_mul33x3(Favg,step/2.0_pReal) - offset_coords
m = 1_pInt
do k = 1_pInt,gridLocal(3); do j = 1_pInt,gridLocal(2); do i = 1_pInt,gridLocal(1)
mesh_ipCoordinates(1:3,1,m) = coords_realMPI(1:3,i,j,k) &
+ offset_coords &
+ math_mul33x3(Favg,step*real([i,j,k+gridOffset]-1_pInt,pReal))
m = m+1_pInt
enddo; enddo; enddo
end subroutine utilities_updateIPcoords
end module DAMASK_spectral_utilities