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