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DAMASK_EICMD
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DAMASK_EICMD/code/spectral_utilities.f90

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set up build system with CMake
2016-02-24 02:57:37 +05:30
!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @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 spectral_utilities
use, intrinsic :: iso_c_binding
use prec, only: &
pReal, &
pInt
use math, only: &
math_I3
implicit none
private
#include <petsc/finclude/petscsys.h>
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
integer(pInt), public :: nActiveFields = 0_pInt
!--------------------------------------------------------------------------------------------------
! field labels information
enum, bind(c)
enumerator :: FIELD_UNDEFINED_ID, &
FIELD_MECH_ID, &
FIELD_THERMAL_ID, &
FIELD_DAMAGE_ID, &
FIELD_VACANCYDIFFUSION_ID
end enum
!--------------------------------------------------------------------------------------------------
! 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 :: tensorField_real !< real representation (some stress or deformation) of field_fourier
complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:,:), pointer :: tensorField_fourier !< field on which the Fourier transform operates
real(C_DOUBLE), public, dimension(:,:,:,:), pointer :: vectorField_real !< vector field real 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
complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:), pointer :: scalarField_fourier !< scalar field fourier representation for fftw
complex(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
complex(pReal), private, dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first 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), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence (Basic, Basic PETSc)
!--------------------------------------------------------------------------------------------------
! plans for FFTW
type(C_PTR), private :: &
planTensorForth, & !< FFTW MPI plan P(x) to P(k)
planTensorBack, & !< FFTW MPI plan F(k) to F(x)
planVectorForth, & !< FFTW MPI plan v(x) to v(k)
planVectorBack, & !< FFTW MPI plan v(k) to v(x)
planScalarForth, & !< FFTW MPI plan s(x) to s(k)
planScalarBack !< FFTW MPI plan s(k) to s(x)
!--------------------------------------------------------------------------------------------------
! variables controlling debugging
logical, private :: &
debugGeneral, & !< general debugging of spectral solver
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 :: stagConverged = .true.
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 :: tLoadCase
real(pReal), dimension (3,3) :: rotation = math_I3 !< rotation of BC
type(tBoundaryCondition) :: P, & !< stress BC
deformation !< deformation BC (Fdot or L)
real(pReal) :: time = 0.0_pReal !< length of increment
integer(pInt) :: incs = 0_pInt, & !< number of increments
outputfrequency = 1_pInt, & !< frequency of result writes
restartfrequency = 0_pInt, & !< frequency of restart writes
logscale = 0_pInt !< linear/logarithmic time inc flag
logical :: followFormerTrajectory = .true. !< follow trajectory of former loadcase
integer(kind(FIELD_UNDEFINED_ID)), allocatable :: ID(:)
end type tLoadCase
type, public :: tSolutionParams !< @todo use here the type definition for a full loadcase including mask
real(pReal), dimension(3,3) :: P_BC, rotation_BC
real(pReal) :: timeinc
real(pReal) :: timeincOld
real(pReal) :: density
end type tSolutionParams
type(tSolutionParams), private :: params
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
enum, bind(c)
enumerator :: DERIVATIVE_CONTINUOUS_ID, &
DERIVATIVE_CENTRAL_DIFF_ID, &
DERIVATIVE_FWBW_DIFF_ID
end enum
integer(kind(DERIVATIVE_CONTINUOUS_ID)) :: &
spectral_derivative_ID
public :: &
utilities_init, &
utilities_updateGamma, &
utilities_FFTtensorForward, &
utilities_FFTtensorBackward, &
utilities_FFTvectorForward, &
utilities_FFTvectorBackward, &
utilities_FFTscalarForward, &
utilities_FFTscalarBackward, &
utilities_fourierGammaConvolution, &
utilities_fourierGreenConvolution, &
utilities_divergenceRMS, &
utilities_curlRMS, &
utilities_fourierScalarGradient, &
utilities_fourierVectorDivergence, &
utilities_fourierVectorGradient, &
utilities_fourierTensorDivergence, &
utilities_maskedCompliance, &
utilities_constitutiveResponse, &
utilities_calculateRate, &
utilities_forwardField, &
utilities_destroy, &
utilities_updateIPcoords, &
FIELD_UNDEFINED_ID, &
FIELD_MECH_ID, &
FIELD_THERMAL_ID, &
FIELD_DAMAGE_ID
private :: &
utilities_getFreqDerivative
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, &
IO_timeStamp, &
IO_open_file
use numerics, only: &
spectral_derivative, &
fftw_planner_flag, &
fftw_timelimit, &
memory_efficient, &
petsc_defaultOptions, &
petsc_options, &
divergence_correction, &
worldrank
use debug, only: &
debug_level, &
debug_SPECTRAL, &
debug_LEVELBASIC, &
debug_SPECTRALDIVERGENCE, &
debug_SPECTRALFFTW, &
debug_SPECTRALPETSC, &
debug_SPECTRALROTATION
use debug, only: &
PETSCDEBUG
use math
use mesh, only: &
grid, &
grid3, &
grid3Offset, &
geomSize
implicit none
external :: &
PETScOptionsClear, &
PETScOptionsInsertString, &
MPI_Abort
PetscErrorCode :: ierr
integer(pInt) :: i, j, k
integer(pInt), dimension(3) :: k_s
type(C_PTR) :: &
tensorField, & !< field containing data for FFTW in real and fourier space (in place)
vectorField, & !< field containing data for FFTW in real space when debugging FFTW (no in place)
scalarField !< field containing data for FFTW in real space when debugging FFTW (no in place)
integer(C_INTPTR_T), dimension(3) :: gridFFTW
integer(C_INTPTR_T) :: alloc_local, local_K, local_K_offset
integer(C_INTPTR_T), parameter :: &
scalarSize = 1_C_INTPTR_T, &
vecSize = 3_C_INTPTR_T, &
tensorSize = 9_C_INTPTR_T
mainProcess: if (worldrank == 0) then
write(6,'(/,a)') ' <<<+- spectral_utilities init -+>>>'
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
debugRotation = iand(debug_level(debug_SPECTRAL),debug_SPECTRALROTATION) /= 0
debugPETSc = iand(debug_level(debug_SPECTRAL),debug_SPECTRALPETSC) /= 0
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_defaultOptions),ierr); CHKERRQ(ierr)
call PetscOptionsInsertString(trim(petsc_options),ierr); CHKERRQ(ierr)
grid1Red = grid(1)/2_pInt + 1_pInt
wgt = 1.0/real(product(grid),pReal)
if (worldrank == 0) then
write(6,'(a,3(i12 ))') ' grid a b c: ', grid
write(6,'(a,3(es12.5))') ' size x y z: ', geomSize
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
! resolution-independent divergence
if (divergence_correction == 1_pInt) then
do j = 1_pInt, 3_pInt
if (j /= minloc(geomSize,1) .and. j /= maxloc(geomSize,1)) &
scaledGeomSize = geomSize/geomSize(j)
enddo
elseif (divergence_correction == 2_pInt) then
do j = 1_pInt, 3_pInt
if (j /= minloc(geomSize/grid,1) .and. j /= maxloc(geomSize/grid,1)) &
scaledGeomSize = geomSize/geomSize(j)*grid(j)
enddo
else
scaledGeomSize = geomSize
endif
!--------------------------------------------------------------------------------------------------
! MPI allocation
gridFFTW = int(grid,C_INTPTR_T)
alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
MPI_COMM_WORLD, local_K, local_K_offset)
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 = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies, only half the size for first dimension
tensorField = fftw_alloc_complex(tensorSize*alloc_local)
call c_f_pointer(tensorField, tensorField_real, [3_C_INTPTR_T,3_C_INTPTR_T, &
2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T),gridFFTW(2),local_K]) ! place a pointer for a real tensor representation
call c_f_pointer(tensorField, tensorField_fourier, [3_C_INTPTR_T,3_C_INTPTR_T, &
gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T , gridFFTW(2),local_K]) ! place a pointer for a fourier tensor representation
vectorField = fftw_alloc_complex(vecSize*alloc_local)
call c_f_pointer(vectorField, vectorField_real, [3_C_INTPTR_T,&
2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T),gridFFTW(2),local_K]) ! place a pointer for a real vector representation
call c_f_pointer(vectorField, vectorField_fourier,[3_C_INTPTR_T,&
gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T, gridFFTW(2),local_K]) ! place a pointer for a fourier vector representation
scalarField = fftw_alloc_complex(scalarSize*alloc_local) ! allocate data for real representation (no in place transform)
call c_f_pointer(scalarField, scalarField_real, &
[2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1),gridFFTW(2),local_K]) ! place a pointer for a real scalar representation
call c_f_pointer(scalarField, scalarField_fourier, &
[ gridFFTW(1)/2_C_INTPTR_T + 1 ,gridFFTW(2),local_K]) ! place a pointer for a fourier scarlar representation
!--------------------------------------------------------------------------------------------------
! tensor MPI fftw plans
planTensorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
tensorField_real, tensorField_fourier, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
if (.not. C_ASSOCIATED(planTensorForth)) call IO_error(810, ext_msg='planTensorForth')
planTensorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
tensorField_fourier,tensorField_real, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! all processors, planer precision
if (.not. C_ASSOCIATED(planTensorBack)) call IO_error(810, ext_msg='planTensorBack')
!--------------------------------------------------------------------------------------------------
! vector MPI fftw plans
planVectorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
vectorField_real, vectorField_fourier, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
if (.not. C_ASSOCIATED(planVectorForth)) call IO_error(810, ext_msg='planVectorForth')
planVectorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
vectorField_fourier,vectorField_real, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! all processors, planer precision
if (.not. C_ASSOCIATED(planVectorBack)) call IO_error(810, ext_msg='planVectorBack')
!--------------------------------------------------------------------------------------------------
! scalar MPI fftw plans
planScalarForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
scalarField_real, scalarField_fourier, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
if (.not. C_ASSOCIATED(planScalarForth)) call IO_error(810, ext_msg='planScalarForth')
planScalarBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order, no. of transforms
scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
scalarField_fourier,scalarField_real, & ! input data, output data
MPI_COMM_WORLD, fftw_planner_flag) ! use all processors, planer precision
if (.not. C_ASSOCIATED(planScalarBack)) call IO_error(810, ext_msg='planScalarBack')
!--------------------------------------------------------------------------------------------------
! 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 = grid3Offset+1_pInt, grid3Offset+grid3
k_s(3) = k - 1_pInt
if(k > grid(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - grid(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
do j = 1_pInt, grid(2)
k_s(2) = j - 1_pInt
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
k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
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 .and. &
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
xi1st(1:3,i,j,k-grid3Offset) = xi2nd(1:3,i,j,k-grid3Offset)
endwhere
enddo; enddo; enddo
if(memory_efficient) then ! allocate just single fourth order tensor
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
allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = cmplx(0.0_pReal,0.0_pReal,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.
!> 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: &
grid3Offset, &
grid3,&
grid
use math, only: &
math_det33, &
math_invert
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
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
real(pReal), dimension(6,6) :: matA, matInvA
integer(pInt) :: &
i, j, k, &
l, m, n, o
logical :: ierr
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
gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal) ! for the singular point and any non invertible A
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
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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) &
temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
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)
endif
endif
enddo; enddo; enddo
endif
end subroutine utilities_updateGamma
!--------------------------------------------------------------------------------------------------
!> @brief forward FFT of data in field_real to field_fourier
!> @details Does an unweighted filtered FFT transform from real to complex
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTtensorForward()
implicit none
!--------------------------------------------------------------------------------------------------
! doing the tensor FFT
call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
end subroutine utilities_FFTtensorForward
!--------------------------------------------------------------------------------------------------
!> @brief backward FFT of data in field_fourier to field_real
!> @details Does an weighted inverse FFT transform from complex to real
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTtensorBackward()
implicit none
call fftw_mpi_execute_dft_c2r(planTensorBack,tensorField_fourier,tensorField_real)
tensorField_real = tensorField_real * wgt ! normalize the result by number of elements
end subroutine utilities_FFTtensorBackward
!--------------------------------------------------------------------------------------------------
!> @brief forward FFT of data in scalarField_real to scalarField_fourier
!> @details Does an unweighted filtered FFT transform from real to complex
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTscalarForward()
implicit none
!--------------------------------------------------------------------------------------------------
! doing the scalar FFT
call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
end subroutine utilities_FFTscalarForward
!--------------------------------------------------------------------------------------------------
!> @brief backward FFT of data in scalarField_fourier to scalarField_real
!> @details Does an weighted inverse FFT transform from complex to real
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTscalarBackward()
implicit none
call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real)
scalarField_real = scalarField_real * wgt ! normalize the result by number of elements
end subroutine utilities_FFTscalarBackward
!--------------------------------------------------------------------------------------------------
!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
!> @details Does an unweighted filtered FFT transform from real to complex.
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTvectorForward()
implicit none
!--------------------------------------------------------------------------------------------------
! doing the vector FFT
call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
end subroutine utilities_FFTvectorForward
!--------------------------------------------------------------------------------------------------
!> @brief backward FFT of data in field_fourier to field_real
!> @details Does an weighted inverse FFT transform from complex to real
!--------------------------------------------------------------------------------------------------
subroutine utilities_FFTvectorBackward()
implicit none
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
vectorField_real = vectorField_real * wgt ! normalize the result by number of elements
end subroutine utilities_FFTvectorBackward
!--------------------------------------------------------------------------------------------------
!> @brief doing convolution gamma_hat * field_real, ensuring that average value = fieldAim
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierGammaConvolution(fieldAim)
use numerics, only: &
memory_efficient
use math, only: &
math_det33, &
math_invert
use numerics, only: &
worldrank
use mesh, only: &
grid3, &
grid, &
grid3Offset
implicit none
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
real(pReal) :: matA(6,6), matInvA(6,6)
integer(pInt) :: &
i, j, k, &
l, m, n, o
logical :: ierr
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... doing gamma convolution ...............................................'
flush(6)
endif
!--------------------------------------------------------------------------------------------------
! do the actual spectral method calculation (mechanical equilibrium)
memoryEfficient: if(memory_efficient) then
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
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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) &
temp33_complex(l,m) = sum(C_ref(l,1:3,m,1:3)*xiDyad_cmplx)
matA(1:3,1:3) = real(temp33_complex); matA(4:6,4:6) = real(temp33_complex)
matA(1:3,4:6) = aimag(temp33_complex); matA(4:6,1:3) = -aimag(temp33_complex)
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
gamma_hat(1:3,1:3,1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
endif
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)*tensorField_fourier(1:3,1:3,i,j,k))
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
endif
enddo; enddo; enddo
else memoryEfficient
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) &
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) = temp33_Complex
enddo; enddo; enddo
endif memoryEfficient
if (grid3Offset == 0_pInt) &
tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal)
end subroutine utilities_fourierGammaConvolution
!--------------------------------------------------------------------------------------------------
!> @brief doing convolution DamageGreenOp_hat * field_real
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierGreenConvolution(D_ref, mobility_ref, deltaT)
use math, only: &
math_mul33x3, &
PI
use mesh, only: &
grid, &
grid3
implicit none
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
complex(pReal) :: GreenOp_hat
integer(pInt) :: i, j, k
!--------------------------------------------------------------------------------------------------
! do the actual spectral method calculation
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ &
(cmplx(mobility_ref,0.0_pReal,pReal) + &
deltaT*sum(conjg(xi1st(1:3,i,j,k))*matmul(D_ref,xi1st(1:3,i,j,k)))) ! why not use dot_product
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
enddo; enddo; enddo
end subroutine utilities_fourierGreenConvolution
!--------------------------------------------------------------------------------------------------
!> @brief calculate root mean square of divergence of field_fourier
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_divergenceRMS()
use numerics, only: &
worldrank
use mesh, only: &
geomSize, &
grid, &
grid3
implicit none
integer(pInt) :: i, j, k
PetscErrorCode :: ierr
external :: &
MPI_Allreduce
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, grid3; do j = 1_pInt, grid(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(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
conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
conjg(-xi1st(1:3,i,j,k))*geomSize/scaledGeomSize))**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(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
conjg(-xi1st(1:3,1,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal) &
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
conjg(-xi1st(1:3,grid1Red,j,k))*geomSize/scaledGeomSize))**2.0_pReal)
enddo; enddo
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)
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
end function utilities_divergenceRMS
!--------------------------------------------------------------------------------------------------
!> @brief calculate max of curl of field_fourier
!--------------------------------------------------------------------------------------------------
real(pReal) function utilities_curlRMS()
use numerics, only: &
worldrank
use mesh, only: &
geomSize, &
grid, &
grid3
implicit none
integer(pInt) :: i, j, k, l
complex(pReal), dimension(3,3) :: curl_fourier
PetscErrorCode :: ierr
external :: &
MPI_Reduce, &
MPI_Allreduce
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, grid3; do j = 1_pInt, grid(2);
do i = 2_pInt, grid1Red - 1_pInt
do l = 1_pInt, 3_pInt
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)*geomSize(3)/scaledGeomSize(3))
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)*geomSize(1)/scaledGeomSize(1))
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)*geomSize(2)/scaledGeomSize(2))
enddo
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.
enddo
do l = 1_pInt, 3_pInt
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)*geomSize(3)/scaledGeomSize(3))
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)*geomSize(1)/scaledGeomSize(1))
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)*geomSize(2)/scaledGeomSize(2))
enddo
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)
do l = 1_pInt, 3_pInt
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)*geomSize(3)/scaledGeomSize(3))
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)*geomSize(1)/scaledGeomSize(1))
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)*geomSize(2)/scaledGeomSize(2))
enddo
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)
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(grid(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 prec, only: &
prec_isNaN
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 (any(prec_isNaN(s_reduced))) errmatinv = .true.
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 calculate scalar gradient in fourier field
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierScalarGradient()
use mesh, only: &
grid3, &
grid
implicit none
integer(pInt) :: i, j, k
vectorField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k)
end subroutine utilities_fourierScalarGradient
!--------------------------------------------------------------------------------------------------
!> @brief calculate vector divergence in fourier field
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierVectorDivergence()
use mesh, only: &
grid3, &
grid
implicit none
integer(pInt) :: i, j, k
scalarField_fourier = cmplx(0.0_pReal,0.0_pReal,pReal)
forall(k = 1_pInt:grid3, j = 1_pInt:grid(2), i = 1_pInt:grid1Red) &
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k) + &
sum(vectorField_fourier(1:3,i,j,k)*conjg(-xi1st(1:3,i,j,k)))
end subroutine utilities_fourierVectorDivergence
!--------------------------------------------------------------------------------------------------
!> @brief calculate vector gradient in fourier field
!--------------------------------------------------------------------------------------------------
subroutine utilities_fourierVectorGradient()
use mesh, only: &
grid3, &
grid
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
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
!--------------------------------------------------------------------------------------------------
subroutine utilities_constitutiveResponse(F_lastInc,F,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: &
grid,&
grid3
use FEsolving, only: &
restartWrite
use CPFEM2, only: &
CPFEM_general
use homogenization, only: &
materialpoint_F0, &
materialpoint_F, &
materialpoint_P, &
materialpoint_dPdF
implicit none
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
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,grid(1),grid(2),grid3) :: P !< PK stress
logical :: &
age
integer(pInt) :: &
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
external :: &
MPI_Reduce, &
MPI_Allreduce
if (worldrank == 0_pInt) then
write(6,'(/,a)') ' ... evaluating constitutive response ......................................'
flush(6)
endif
age = .False.
if (forwardData) then ! aging results
age = .True.
materialpoint_F0 = reshape(F_lastInc, [3,3,1,product(grid(1:2))*grid3])
endif
if (cutBack) then ! restore saved variables
age = .False.
endif
materialpoint_F = reshape(F,[3,3,1,product(grid(1:2))*grid3])
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(grid(1:2))*grid3
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(age,timeinc)
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(grid(1:2))*grid3
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,grid(1),grid(2),grid3])
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: &
grid3, &
grid
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,grid(1),grid(2),grid3) :: &
field_lastInc, & !< data of previous step
field !< data of current step
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: &
utilities_calculateRate
if (guess) then
utilities_calculateRate = (field-field_lastInc) / timeinc_old
else
utilities_calculateRate = spread(spread(spread(avRate,3,grid(1)),4,grid(2)),5,grid3)
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: &
grid3, &
grid
implicit none
real(pReal), intent(in) :: &
timeinc !< timeinc of current step
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
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,grid(1),grid(2),grid3) :: &
utilities_forwardField
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
PetscErrorCode :: ierr
external :: &
MPI_Allreduce
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,grid(1)),4,grid(2)),5,grid3)
endif
end function utilities_forwardField
!--------------------------------------------------------------------------------------------------
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
!--------------------------------------------------------------------------------------------------
pure function utilities_getFreqDerivative(k_s)
use math, only: &
PI
use mesh, only: &
geomSize, &
grid
implicit none
integer(pInt), intent(in), dimension(3) :: k_s !< indices of frequency
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)
end select
end function utilities_getFreqDerivative
!--------------------------------------------------------------------------------------------------
!> @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, only: &
math_mul33x3
use mesh, only: &
grid, &
grid3, &
grid3Offset, &
geomSize, &
mesh_ipCoordinates
implicit none
real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F
integer(pInt) :: i, j, k, m
real(pReal), dimension(3) :: step, offset_coords
real(pReal), dimension(3,3) :: Favg
PetscErrorCode :: ierr
external &
MPI_Bcast
!--------------------------------------------------------------------------------------------------
! integration in Fourier space
tensorField_real = 0.0_pReal
tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F
call utilities_FFTtensorForward()
call utilities_fourierTensorDivergence()
do k = 1_pInt, grid3; do j = 1_pInt, grid(2) ;do i = 1_pInt, grid1Red
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
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)
!--------------------------------------------------------------------------------------------------
! 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)
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,grid3; do j = 1_pInt,grid(2); do i = 1_pInt,grid(1)
mesh_ipCoordinates(1:3,1,m) = vectorField_real(1:3,i,j,k) &
+ offset_coords &
+ math_mul33x3(Favg,step*real([i,j,k+grid3Offset]-1_pInt,pReal))
m = m+1_pInt
enddo; enddo; enddo
end subroutine utilities_updateIPcoords
!--------------------------------------------------------------------------------------------------
!> @brief cleans up
!--------------------------------------------------------------------------------------------------
subroutine utilities_destroy()
implicit none
call fftw_destroy_plan(planTensorForth)
call fftw_destroy_plan(planTensorBack)
call fftw_destroy_plan(planVectorForth)
call fftw_destroy_plan(planVectorBack)
call fftw_destroy_plan(planScalarForth)
call fftw_destroy_plan(planScalarBack)
end subroutine utilities_destroy
end module spectral_utilities