!-------------------------------------------------------------------------------------------------- !> @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 #include use PETScSys use prec use DAMASK_interface use parallelization use math use rotations use IO use discretization_grid use discretization use homogenization implicit none private include 'fftw3-mpi.f03' !-------------------------------------------------------------------------------------------------- ! field labels information enum, bind(c); enumerator :: & FIELD_UNDEFINED_ID, & FIELD_MECH_ID, & FIELD_THERMAL_ID, & FIELD_DAMAGE_ID end enum !-------------------------------------------------------------------------------------------------- ! grid related information information real(pReal), protected, public :: wgt !< weighting factor 1/Nelems integer, protected, public :: grid1Red !< grid(1)/2 real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence !-------------------------------------------------------------------------------------------------- ! variables storing information for spectral method and FFTW 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 !-------------------------------------------------------------------------------------------------- ! 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 integer :: & iterationsNeeded = 0 logical :: & converged = .true., & stagConverged = .true., & termIll = .false. end type tSolutionState type, public :: tBoundaryCondition !< set of parameters defining a boundary condition real(pReal), dimension(3,3) :: values = 0.0_pReal, & maskFloat = 0.0_pReal logical, dimension(3,3) :: maskLogical = .false. character(len=pStringLen) :: myType = 'None' end type tBoundaryCondition type, public :: tLoadCase type(rotation) :: rot !< rotation of BC type(tBoundaryCondition) :: stress, & !< stress BC deformation !< deformation BC (Fdot or L) real(pReal) :: time = 0.0_pReal !< length of increment integer :: incs = 0, & !< number of increments outputfrequency = 1, & !< frequency of result writes restartfrequency = huge(0), & !< frequency of restart writes logscale = 0 !< 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 real(pReal), dimension(3,3) :: stress_mask, stress_BC type(rotation) :: rotation_BC real(pReal) :: timeinc real(pReal) :: timeincOld end type tSolutionParams type, private :: tNumerics real(pReal) :: & FFTW_timelimit !< timelimit for FFTW plan creation, see www.fftw.org integer :: & divergence_correction !< scale divergence/curl calculation: [0: no correction, 1: size scaled to 1, 2: size scaled to Npoints] logical :: & memory_efficient !< calculate gamma operator on the fly character(len=:), allocatable :: & spectral_derivative, & !< approximation used for derivatives in Fourier space FFTW_plan_mode !< FFTW plan mode, see www.fftw.org end type tNumerics type(tNumerics), private :: num ! numerics parameters. Better name? 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 :: & spectral_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_updateCoords, & utilities_saveReferenceStiffness, & FIELD_UNDEFINED_ID, & FIELD_MECH_ID, & FIELD_THERMAL_ID, & FIELD_DAMAGE_ID 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 bitwise coding !> provided by the debug module to logicals. !> Allocate all fields used by FFTW and create the corresponding plans depending on the debug !> level chosen. !> Initializes FFTW. !-------------------------------------------------------------------------------------------------- subroutine spectral_utilities_init PetscErrorCode :: ierr integer :: i, j, k, & FFTW_planner_flag integer, 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 character(len=*), parameter :: & PETSCDEBUG = ' -snes_view -snes_monitor ' class(tNode) , pointer :: & num_grid, & debug_grid ! pointer to grid debug options write(6,'(/,a)') ' <<<+- spectral_utilities init -+>>>' write(6,'(/,a)') ' Diehl, Diploma Thesis TU München, 2010' write(6,'(a)') ' https://doi.org/10.13140/2.1.3234.3840' write(6,'(/,a)') ' Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013' write(6,'(a)') ' https://doi.org/10.1016/j.ijplas.2012.09.012' write(6,'(/,a)') ' Shanthraj et al., International Journal of Plasticity 66:31–45, 2015' write(6,'(a)') ' https://doi.org/10.1016/j.ijplas.2014.02.006' write(6,'(/,a)') ' Shanthraj et al., Handbook of Mechanics of Materials, 2019' write(6,'(a)') ' https://doi.org/10.1007/978-981-10-6855-3_80' !-------------------------------------------------------------------------------------------------- ! set debugging parameters debug_grid => debug_root%get('grid',defaultVal=emptyList) debugGeneral = debug_grid%contains('basic') debugRotation = debug_grid%contains('rotation') debugPETSc = debug_grid%contains('petsc') if(debugPETSc) write(6,'(3(/,a),/)') & ' Initializing PETSc with debug options: ', & trim(PETScDebug), & ' add more using the PETSc_Options keyword in numerics.yaml '; flush(6) num_grid => numerics_root%get('grid',defaultVal=emptyDict) call PETScOptionsClear(PETSC_NULL_OPTIONS,ierr) CHKERRQ(ierr) if(debugPETSc) call PETScOptionsInsertString(PETSC_NULL_OPTIONS,trim(PETSCDEBUG),ierr) CHKERRQ(ierr) call PETScOptionsInsertString(PETSC_NULL_OPTIONS,& num_grid%get_asString('petsc_options',defaultVal=''),ierr) CHKERRQ(ierr) grid1Red = grid(1)/2 + 1 wgt = 1.0/real(product(grid),pReal) write(6,'(/,a,3(i12 ))') ' grid a b c: ', grid write(6,'(a,3(es12.5))') ' size x y z: ', geomSize num%memory_efficient = num_grid%get_asInt ('memory_efficient', defaultVal=1) > 0 num%FFTW_timelimit = num_grid%get_asFloat ('fftw_timelimit', defaultVal=-1.0_pReal) num%divergence_correction = num_grid%get_asInt ('divergence_correction', defaultVal=2) num%spectral_derivative = num_grid%get_asString('derivative', defaultVal='continuous') num%FFTW_plan_mode = num_grid%get_asString('fftw_plan_mode', defaultVal='FFTW_MEASURE') if (num%divergence_correction < 0 .or. num%divergence_correction > 2) & call IO_error(301,ext_msg='divergence_correction') select case (num%spectral_derivative) case ('continuous') spectral_derivative_ID = DERIVATIVE_CONTINUOUS_ID case ('central_difference') spectral_derivative_ID = DERIVATIVE_CENTRAL_DIFF_ID case ('FWBW_difference') spectral_derivative_ID = DERIVATIVE_FWBW_DIFF_ID case default call IO_error(892,ext_msg=trim(num%spectral_derivative)) end select !-------------------------------------------------------------------------------------------------- ! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and ! resolution-independent divergence if (num%divergence_correction == 1) then do j = 1, 3 if (j /= minloc(geomSize,1) .and. j /= maxloc(geomSize,1)) & scaledGeomSize = geomSize/geomSize(j) enddo elseif (num%divergence_correction == 2) then do j = 1, 3 if ( j /= int(minloc(geomSize/real(grid,pReal),1)) & .and. j /= int(maxloc(geomSize/real(grid,pReal),1))) & scaledGeomSize = geomSize/geomSize(j)*real(grid(j),pReal) enddo else scaledGeomSize = geomSize endif select case(IO_lc(num%FFTW_plan_mode)) ! setting parameters for the plan creation of FFTW. Basically a translation from fftw3.f case('fftw_estimate') ! ordered from slow execution (but fast plan creation) to fast execution FFTW_planner_flag = FFTW_ESTIMATE case('fftw_measure') FFTW_planner_flag = FFTW_MEASURE case('fftw_patient') FFTW_planner_flag = FFTW_PATIENT case('fftw_exhaustive') FFTW_planner_flag = FFTW_EXHAUSTIVE case default call IO_warning(warning_ID=47,ext_msg=trim(IO_lc(num%FFTW_plan_mode))) FFTW_planner_flag = FFTW_MEASURE end select !-------------------------------------------------------------------------------------------------- ! general initialization of FFTW (see manual on fftw.org for more details) if (pReal /= C_DOUBLE .or. kind(1) /= C_INT) call IO_error(0,ext_msg='Fortran to C') ! check for correct precision in C call fftw_set_timelimit(num%FFTW_timelimit) ! set timelimit for plan creation if (debugGeneral) write(6,'(/,a)') ' FFTW initialized'; flush(6) !-------------------------------------------------------------------------------------------------- ! MPI allocation gridFFTW = int(grid,C_INTPTR_T) alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, & PETSC_COMM_WORLD, local_K, local_K_offset) allocate (xi1st (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, only half the size for first dimension allocate (xi2nd (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for second derivatives, 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 PETSC_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 PETSC_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 PETSC_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 PETSC_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 PETSC_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 PETSC_COMM_WORLD, FFTW_planner_flag) ! use all processors, planer precision if (.not. C_ASSOCIATED(planScalarBack)) call IO_error(810, ext_msg='planScalarBack') !-------------------------------------------------------------------------------------------------- ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) do k = grid3Offset+1, grid3Offset+grid3 k_s(3) = k - 1 if(k > grid(3)/2 + 1) 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, grid(2) k_s(2) = j - 1 if(j > grid(2)/2 + 1) 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, grid1Red k_s(1) = i - 1 ! symmetry, junst running from 0,1,...,N/2,N/2+1 xi2nd(1:3,i,j,k-grid3Offset) = utilities_getFreqDerivative(k_s) 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(num%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 spectral_utilities_init !--------------------------------------------------------------------------------------------------- !> @brief updates reference 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 an on-the-fly calculation, only the reference stiffness is updated. !--------------------------------------------------------------------------------------------------- subroutine utilities_updateGamma(C) real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx real(pReal), dimension(6,6) :: A, A_inv integer :: & i, j, k, & l, m, n, o logical :: err C_ref = C if(.not. num%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, grid3Offset+grid3; do j = 1, grid(2); do i = 1, grid1Red if (any([i,j,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 forall(l = 1:3, m = 1:3) & xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset) forall(l = 1:3, m = 1:3) & temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx) A(1:3,1:3) = real(temp33_complex); A(4:6,4:6) = real(temp33_complex) A(1:3,4:6) = aimag(temp33_complex); A(4:6,1:3) = -aimag(temp33_complex) if (abs(math_det33(A(1:3,1:3))) > 1e-16) then call math_invert(A_inv, err, A) temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal) forall(l=1:3, m=1:3, n=1:3, o=1:3) & 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 FFT transform from real to complex. Extra padding entries are set ! to 0.0 !-------------------------------------------------------------------------------------------------- subroutine utilities_FFTtensorForward tensorField_real(1:3,1:3,grid(1)+1:grid1Red*2,:,:) = 0.0_pReal 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 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 FFT transform from real to complex. Extra padding entries are set ! to 0.0 !-------------------------------------------------------------------------------------------------- subroutine utilities_FFTscalarForward scalarField_real(grid(1)+1:grid1Red*2,:,:) = 0.0_pReal 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 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 FFT transform from real to complex. Extra padding entries are set ! to 0.0 !-------------------------------------------------------------------------------------------------- subroutine utilities_FFTvectorForward vectorField_real(1:3,grid(1)+1:grid1Red*2,:,:) = 0.0_pReal 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 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) 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), dimension(6,6) :: A, A_inv integer :: & i, j, k, & l, m, n, o logical :: err write(6,'(/,a)') ' ... doing gamma convolution ...............................................' flush(6) !-------------------------------------------------------------------------------------------------- ! do the actual spectral method calculation (mechanical equilibrium) memoryEfficient: if(num%memory_efficient) then do k = 1, grid3; do j = 1, grid(2); do i = 1, grid1Red if (any([i,j,k+grid3Offset] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 forall(l = 1:3, m = 1:3) & xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k) forall(l = 1:3, m = 1:3) & temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx) A(1:3,1:3) = real(temp33_complex); A(4:6,4:6) = real(temp33_complex) A(1:3,4:6) = aimag(temp33_complex); A(4:6,1:3) = -aimag(temp33_complex) if (abs(math_det33(A(1:3,1:3))) > 1e-16) then call math_invert(A_inv, err, A) temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal) forall(l=1:3, m=1:3, n=1:3, o=1:3) & 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 = 1:3, m = 1:3) & 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, grid3; do j = 1, grid(2); do i = 1,grid1Red forall(l = 1:3, m = 1:3) & 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) 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) real(pReal), dimension(3,3), intent(in) :: D_ref real(pReal), intent(in) :: mobility_ref, deltaT complex(pReal) :: GreenOp_hat integer :: i, j, k !-------------------------------------------------------------------------------------------------- ! do the actual spectral method calculation do k = 1, grid3; do j = 1, grid(2) ;do i = 1, grid1Red GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ & (cmplx(mobility_ref,0.0_pReal,pReal) + cmplx(deltaT,0.0_pReal)*& sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal),xi1st(1:3,i,j,k)))) 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() integer :: i, j, k, ierr complex(pReal), dimension(3) :: rescaledGeom write(6,'(/,a)') ' ... calculating divergence ................................................' flush(6) rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal) !-------------------------------------------------------------------------------------------------- ! calculating RMS divergence criterion in Fourier space utilities_divergenceRMS = 0.0_pReal do k = 1, grid3; do j = 1, grid(2) do i = 2, grid1Red -1 ! 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))*rescaledGeom))**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))*rescaledGeom))**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))*rescaledGeom))**2.0_pReal) & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), & conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) & + sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), & conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), & conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) enddo; enddo if(grid(1) == 1) 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) if(ierr /=0) call IO_error(894, ext_msg='utilities_divergenceRMS') 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() integer :: i, j, k, l, ierr complex(pReal), dimension(3,3) :: curl_fourier complex(pReal), dimension(3) :: rescaledGeom write(6,'(/,a)') ' ... calculating curl ......................................................' flush(6) rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal) !-------------------------------------------------------------------------------------------------- ! calculating max curl criterion in Fourier space utilities_curlRMS = 0.0_pReal do k = 1, grid3; do j = 1, grid(2); do i = 2, grid1Red - 1 do l = 1, 3 curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2) & -tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3)) curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3) & -tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1)) curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1) & -tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(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, 3 curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) & -tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3)) curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3) & -tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1)) curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1) & -tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(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, 3 curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) & -tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3)) curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3) & -tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1)) curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1) & -tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(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) if(ierr /=0) call IO_error(894, ext_msg='utilities_curlRMS') utilities_curlRMS = sqrt(utilities_curlRMS) * wgt if(grid(1) == 1) 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) real(pReal), dimension(3,3,3,3) :: utilities_maskedCompliance !< masked compliance real(pReal), intent(in), dimension(3,3,3,3) :: C !< current average stiffness type(rotation), intent(in) :: rot_BC !< rotation of load frame logical, intent(in), dimension(3,3) :: mask_stress !< mask of stress BC integer :: i, j logical, dimension(9) :: mask_stressVector logical, dimension(9,9) :: mask real(pReal), dimension(9,9) :: temp99_real integer :: size_reduced = 0 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=pStringLen):: formatString mask_stressVector = reshape(transpose(mask_stress), [9]) size_reduced = count(mask_stressVector) if(size_reduced > 0) then temp99_real = math_3333to99(rot_BC%rotate(C)) if(debugGeneral) 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)*1.0e-9_pReal flush(6) endif do i = 1,9; do j = 1,9 mask(i,j) = mask_stressVector(i) .and. mask_stressVector(j) enddo; enddo c_reduced = reshape(pack(temp99_Real,mask),[size_reduced,size_reduced]) allocate(s_reduced,mold = c_reduced) call math_invert(s_reduced, errmatinv, c_reduced) ! invert reduced stiffness if (any(IEEE_is_NaN(s_reduced))) errmatinv = .true. if (errmatinv) call IO_error(error_ID=400,ext_msg='utilities_maskedCompliance') !-------------------------------------------------------------------------------------------------- ! check if inversion was successful sTimesC = matmul(c_reduced,s_reduced) errmatinv = errmatinv .or. any(dNeq(sTimesC,math_identity2nd(size_reduced),1.0e-12_pReal)) if (debugGeneral .or. errmatinv) then write(formatString, '(i2)') 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) if(errmatinv) call IO_error(error_ID=400,ext_msg='utilities_maskedCompliance') endif temp99_real = reshape(unpack(reshape(s_reduced,[size_reduced**2]),reshape(mask,[81]),0.0_pReal),[9,9]) else temp99_real = 0.0_pReal endif utilities_maskedCompliance = math_99to3333(temp99_Real) if(debugGeneral) then write(6,'(/,a,/,9(9(2x,f10.5,1x)/),/)',advance='no') & ' Masked Compliance (load) * GPa =', transpose(temp99_Real)*1.0e9_pReal flush(6) endif end function utilities_maskedCompliance !-------------------------------------------------------------------------------------------------- !> @brief calculate scalar gradient in fourier field !-------------------------------------------------------------------------------------------------- subroutine utilities_fourierScalarGradient() integer :: i, j, k do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k) ! ToDo: no -conjg? enddo; enddo; enddo end subroutine utilities_fourierScalarGradient !-------------------------------------------------------------------------------------------------- !> @brief calculate vector divergence in fourier field !-------------------------------------------------------------------------------------------------- subroutine utilities_fourierVectorDivergence() integer :: i, j, k do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red scalarField_fourier(i,j,k) = sum(vectorField_fourier(1:3,i,j,k)*conjg(-xi1st(1:3,i,j,k))) enddo; enddo; enddo end subroutine utilities_fourierVectorDivergence !-------------------------------------------------------------------------------------------------- !> @brief calculate vector gradient in fourier field !-------------------------------------------------------------------------------------------------- subroutine utilities_fourierVectorGradient() integer :: i, j, k, m, n do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red do m = 1, 3; do n = 1, 3 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() integer :: i, j, k do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red vectorField_fourier(:,i,j,k) = matmul(tensorField_fourier(:,:,i,j,k),conjg(-xi1st(:,i,j,k))) enddo; enddo; enddo end subroutine utilities_fourierTensorDivergence !-------------------------------------------------------------------------------------------------- !> @brief calculate constitutive response from materialpoint_F0 to F during timeinc !-------------------------------------------------------------------------------------------------- subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,& F,timeinc,rotation_BC) 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 real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: F !< deformation gradient target real(pReal), intent(in) :: timeinc !< loading time type(rotation), intent(in), optional :: rotation_BC !< rotation of load frame integer :: & i,ierr real(pReal), dimension(3,3,3,3) :: dPdF_max, dPdF_min real(pReal) :: dPdF_norm_max, dPdF_norm_min real(pReal), dimension(2) :: valueAndRank !< pair of min/max norm of dPdF to synchronize min/max of dPdF write(6,'(/,a)') ' ... evaluating constitutive response ......................................' flush(6) materialpoint_F = reshape(F,[3,3,1,product(grid(1:2))*grid3]) ! set materialpoint target F to estimated field call materialpoint_stressAndItsTangent(.true.,timeinc) ! calculate P field 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) & write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress (lab) / MPa =',& transpose(P_av)*1.e-6_pReal if(present(rotation_BC)) & P_av = rotation_BC%rotate(P_av) write(6,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress / MPa =',& transpose(P_av)*1.e-6_pReal flush(6) dPdF_max = 0.0_pReal dPdF_norm_max = 0.0_pReal dPdF_min = huge(1.0_pReal) dPdF_norm_min = huge(1.0_pReal) do i = 1, product(grid(1:2))*grid3 if (dPdF_norm_max < sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)) then dPdF_max = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i) dPdF_norm_max = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal) endif if (dPdF_norm_min > sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)) then dPdF_min = materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i) dPdF_norm_min = sum(materialpoint_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal) endif end do valueAndRank = [dPdF_norm_max,real(worldrank,pReal)] call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1, MPI_2DOUBLE_PRECISION, MPI_MAXLOC, PETSC_COMM_WORLD, ierr) if (ierr /= 0) call IO_error(894, ext_msg='MPI_Allreduce max') call MPI_Bcast(dPdF_max,81,MPI_DOUBLE,int(valueAndRank(2)),PETSC_COMM_WORLD, ierr) if (ierr /= 0) call IO_error(894, ext_msg='MPI_Bcast max') valueAndRank = [dPdF_norm_min,real(worldrank,pReal)] call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1, MPI_2DOUBLE_PRECISION, MPI_MINLOC, PETSC_COMM_WORLD, ierr) if (ierr /= 0) call IO_error(894, ext_msg='MPI_Allreduce min') call MPI_Bcast(dPdF_min,81,MPI_DOUBLE,int(valueAndRank(2)),PETSC_COMM_WORLD, ierr) if (ierr /= 0) call IO_error(894, ext_msg='MPI_Bcast min') C_minmaxAvg = 0.5_pReal*(dPdF_max + dPdF_min) C_volAvg = sum(sum(materialpoint_dPdF,dim=6),dim=5) call MPI_Allreduce(MPI_IN_PLACE,C_volAvg,81,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) C_volAvg = C_volAvg * wgt end subroutine utilities_constitutiveResponse !-------------------------------------------------------------------------------------------------- !> @brief calculates forward rate, either guessing or just add delta/timeinc !-------------------------------------------------------------------------------------------------- pure function utilities_calculateRate(heterogeneous,field0,field,dt,avRate) real(pReal), intent(in), dimension(3,3) :: & avRate !< homogeneous addon real(pReal), intent(in) :: & dt !< timeinc between field0 and field logical, intent(in) :: & heterogeneous !< calculate field of rates real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: & field0, & !< data of previous step field !< data of current step real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: & utilities_calculateRate if (heterogeneous) then utilities_calculateRate = (field-field0) / dt 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) 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 !< - aim PetscErrorCode :: ierr utilities_forwardField = field_lastInc + rate*timeinc if (present(aim)) then !< correct to match average fieldDiff = sum(sum(sum(utilities_forwardField,dim=5),dim=4),dim=3)*wgt call MPI_Allreduce(MPI_IN_PLACE,fieldDiff,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr) fieldDiff = fieldDiff - aim utilities_forwardField = utilities_forwardField - & spread(spread(spread(fieldDiff,3,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 !> @details this is the full operator to calculate derivatives, i.e. 2 \pi i k for the ! standard approach !-------------------------------------------------------------------------------------------------- pure function utilities_getFreqDerivative(k_s) integer, 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_updateCoords(F) real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F real(pReal), dimension(3, grid(1),grid(2),grid3) :: IPcoords real(pReal), dimension(3, grid(1),grid(2),grid3+2) :: IPfluct_padded ! Fluctuations of cell center displacement (padded along z for MPI) real(pReal), dimension(3, grid(1)+1,grid(2)+1,grid3+1) :: nodeCoords integer :: & i,j,k,n, & rank_t, & rank_b, & c, r, & ierr integer, dimension(MPI_STATUS_SIZE) :: & s real(pReal), dimension(3) :: step real(pReal), dimension(3,3) :: Favg integer, dimension(3) :: me integer, dimension(3,8) :: & neighbor = reshape([ & 0, 0, 0, & 1, 0, 0, & 1, 1, 0, & 0, 1, 0, & 0, 0, 1, & 1, 0, 1, & 1, 1, 1, & 0, 1, 1 ], [3,8]) step = geomSize/real(grid, pReal) !-------------------------------------------------------------------------------------------------- ! integration in Fourier space to get fluctuations of cell center discplacements tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F call utilities_FFTtensorForward() do k = 1, grid3; do j = 1, grid(2); do i = 1, grid1Red if(any([i,j,k+grid3Offset] /= 1)) then vectorField_fourier(1:3,i,j,k) = matmul(tensorField_fourier(1:3,1:3,i,j,k),xi2nd(1:3,i,j,k)) & / sum(conjg(-xi2nd(1:3,i,j,k))*xi2nd(1:3,i,j,k)) * cmplx(wgt,0.0,pReal) else vectorField_fourier(1:3,i,j,k) = cmplx(0.0,0.0,pReal) endif enddo; enddo; enddo call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real) !-------------------------------------------------------------------------------------------------- ! average F if (grid3Offset == 0) 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) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Bcast') !-------------------------------------------------------------------------------------------------- ! pad cell center fluctuations along z-direction (needed when running MPI simulation) IPfluct_padded(1:3,1:grid(1),1:grid(2),2:grid3+1) = vectorField_real(1:3,1:grid(1),1:grid(2),1:grid3) c = product(shape(IPfluct_padded(:,:,:,1))) !< amount of data to transfer rank_t = modulo(worldrank+1,worldsize) rank_b = modulo(worldrank-1,worldsize) ! send bottom layer to process below call MPI_Isend(IPfluct_padded(:,:,:,2), c,MPI_DOUBLE,rank_b,0,PETSC_COMM_WORLD,r,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Isend') call MPI_Irecv(IPfluct_padded(:,:,:,grid3+2),c,MPI_DOUBLE,rank_t,0,PETSC_COMM_WORLD,r,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Irecv') call MPI_Wait(r,s,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Wait') ! send top layer to process above call MPI_Isend(IPfluct_padded(:,:,:,grid3+1),c,MPI_DOUBLE,rank_t,0,PETSC_COMM_WORLD,r,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Isend') call MPI_Irecv(IPfluct_padded(:,:,:,1), c,MPI_DOUBLE,rank_b,0,PETSC_COMM_WORLD,r,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Irecv') call MPI_Wait(r,s,ierr) if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Wait') !-------------------------------------------------------------------------------------------------- ! calculate nodal displacements nodeCoords = 0.0_pReal do k = 0,grid3; do j = 0,grid(2); do i = 0,grid(1) nodeCoords(1:3,i+1,j+1,k+1) = matmul(Favg,step*(real([i,j,k+grid3Offset],pReal))) averageFluct: do n = 1,8 me = [i+neighbor(1,n),j+neighbor(2,n),k+neighbor(3,n)] nodeCoords(1:3,i+1,j+1,k+1) = nodeCoords(1:3,i+1,j+1,k+1) & + IPfluct_padded(1:3,modulo(me(1)-1,grid(1))+1,modulo(me(2)-1,grid(2))+1,me(3)+1)*0.125_pReal enddo averageFluct enddo; enddo; enddo !-------------------------------------------------------------------------------------------------- ! calculate cell center displacements do k = 1,grid3; do j = 1,grid(2); do i = 1,grid(1) IPcoords(1:3,i,j,k) = vectorField_real(1:3,i,j,k) & + matmul(Favg,step*(real([i,j,k+grid3Offset],pReal)-0.5_pReal)) enddo; enddo; enddo call discretization_setNodeCoords(reshape(NodeCoords,[3,(grid(1)+1)*(grid(2)+1)*(grid3+1)])) call discretization_setIPcoords (reshape(IPcoords, [3,grid(1)*grid(2)*grid3])) end subroutine utilities_updateCoords !--------------------------------------------------------------------------------------------------- !> @brief Write out the current reference stiffness for restart. !--------------------------------------------------------------------------------------------------- subroutine utilities_saveReferenceStiffness integer :: & fileUnit if (worldrank == 0) then write(6,'(a)') ' writing reference stiffness data required for restart to file'; flush(6) fileUnit = IO_open_binary(trim(getSolverJobName())//'.C_ref','w') write(fileUnit) C_ref close(fileUnit) endif end subroutine utilities_saveReferenceStiffness end module spectral_utilities