!-------------------------------------------------------------------------------------------------- !> @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 #include use PETScSys #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY) use MPI_f08 #endif use FFTW3 use prec use CLI use parallelization use math use rotations use IO use config use discretization_grid use discretization use homogenization #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY) implicit none(type,external) #else implicit none #endif private !-------------------------------------------------------------------------------------------------- ! grid related information real(pReal), protected, public :: wgt !< weighting factor 1/Nelems real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence integer :: & cells1Red, & !< cells(1)/2+1 cells2, & !< (local) cells in 2nd direction cells2Offset !< (local) cells offset in 2nd direction !-------------------------------------------------------------------------------------------------- ! variables storing information for spectral method and FFTW real(C_DOUBLE), dimension(:,:,:,:,:), pointer :: tensorField_real !< tensor field in real space real(C_DOUBLE), dimension(:,:,:,:), pointer :: vectorField_real !< vector field in real space real(C_DOUBLE), dimension(:,:,:), pointer :: scalarField_real !< scalar field in real space complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:,:), pointer :: tensorField_fourier !< tensor field in Fourier space complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field in Fourier space complex(C_DOUBLE_COMPLEX), dimension(:,:,:), pointer :: scalarField_fourier !< scalar field in Fourier space complex(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method complex(pReal), dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives complex(pReal), dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives real(pReal), dimension(3,3,3,3) :: C_ref !< mechanic reference stiffness !-------------------------------------------------------------------------------------------------- ! plans for FFTW type(C_PTR) :: & 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) !-------------------------------------------------------------------------------------------------- ! 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 logical, dimension(3,3) :: mask = .true. character(len=:), allocatable :: myType end type tBoundaryCondition type, public :: tSolutionParams real(pReal), dimension(3,3) :: stress_BC logical, dimension(3,3) :: stress_mask type(tRotation) :: rotation_BC real(pReal) :: Delta_t end type tSolutionParams type :: tNumerics 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 end type tNumerics type(tNumerics) :: 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_GammaConvolution, & utilities_GreenConvolution, & utilities_divergenceRMS, & utilities_curlRMS, & utilities_scalarGradient, & utilities_vectorDivergence, & utilities_maskedCompliance, & utilities_constitutiveResponse, & utilities_calculateRate, & utilities_forwardField, & utilities_updateCoords contains !-------------------------------------------------------------------------------------------------- !> @brief Allocate all neccessary fields and create plans for FFTW. !-------------------------------------------------------------------------------------------------- subroutine spectral_utilities_init() PetscErrorCode :: err_PETSc integer :: i, j, k, & FFTW_planner_flag integer, dimension(3) :: k_s type(C_PTR) :: & tensorField, & !< tensor data for FFTW in real and Fourier space (in-place) vectorField, & !< vector data for FFTW in real and Fourier space (in-place) scalarField !< scalar data for FFTW in real and Fourier space (in-place) integer(C_INTPTR_T), dimension(3) :: cellsFFTW integer(C_INTPTR_T) :: N, & cells3FFTW, & !< # of cells in 3. dim on current process in real space cells3_offset, & !< offset for cells in 3. dim on current process in real space cells2FFTW, & !< # of cells in 2. dim on current process in Fourier space cells2_offset !< offset for cells in 2. dim on curren process in Fourier space integer(C_INTPTR_T), parameter :: & vectorSize = 3_C_INTPTR_T, & tensorSize = 9_C_INTPTR_T type(tDict) , pointer :: & num_grid print'(/,1x,a)', '<<<+- spectral_utilities init -+>>>' print'(/,1x,a)', 'M. Diehl, Diploma Thesis TU München, 2010' print'( 1x,a)', 'https://doi.org/10.13140/2.1.3234.3840'//IO_EOL print'( 1x,a)', 'P. Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013' print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2012.09.012'//IO_EOL print'( 1x,a)', 'P. Shanthraj et al., International Journal of Plasticity 66:31–45, 2015' print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2014.02.006'//IO_EOL print'( 1x,a)', 'P. Shanthraj et al., Handbook of Mechanics of Materials, 2019' print'( 1x,a)', 'https://doi.org/10.1007/978-981-10-6855-3_80' num_grid => config_numerics%get_dict('grid',defaultVal=emptyDict) call PetscOptionsClear(PETSC_NULL_OPTIONS,err_PETSc) CHKERRQ(err_PETSc) call PetscOptionsInsertString(PETSC_NULL_OPTIONS,& num_grid%get_asString('PETSc_options',defaultVal=''),err_PETSc) CHKERRQ(err_PETSc) cells1Red = cells(1)/2 + 1 wgt = real(product(cells),pReal)**(-1) num%memory_efficient = num_grid%get_asInt('memory_efficient', defaultVal=1) > 0 ! ToDo: should be logical in YAML file num%divergence_correction = num_grid%get_asInt('divergence_correction', defaultVal=2) if (num%divergence_correction < 0 .or. num%divergence_correction > 2) & call IO_error(301,ext_msg='divergence_correction') select case (num_grid%get_asString('derivative',defaultVal='continuous')) 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_grid%get_asString('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) end do elseif (num%divergence_correction == 2) then do j = 1, 3 if ( j /= int(minloc(geomSize/real(cells,pReal),1)) & .and. j /= int(maxloc(geomSize/real(cells,pReal),1))) & scaledGeomSize = geomSize/geomSize(j)*real(cells(j),pReal) end do else scaledGeomSize = geomSize end if select case(IO_lc(num_grid%get_asString('fftw_plan_mode',defaultVal='FFTW_MEASURE'))) 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(47,'using default FFTW_MEASURE instead of "'//trim(num_grid%get_asString('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) error stop 'C and Fortran datatypes do not match' call fftw_set_timelimit(num_grid%get_asFloat('fftw_timelimit',defaultVal=300.0_pReal)) print'(/,1x,a)', 'FFTW initialized'; flush(IO_STDOUT) cellsFFTW = int(cells,C_INTPTR_T) N = fftw_mpi_local_size_many_transposed(3,[cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T)], & tensorSize,FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK,PETSC_COMM_WORLD, & cells3FFTW,cells3_offset,cells2FFTW,cells2_offset) cells2 = int(cells2FFTW) cells2Offset = int(cells2_offset) if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (tensor, real space)' tensorField = fftw_alloc_complex(N) call c_f_pointer(tensorField,tensorField_real, & [3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW]) call c_f_pointer(tensorField,tensorField_fourier, & [3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW]) N = fftw_mpi_local_size_many_transposed(3,[cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T)], & vectorSize,FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK,PETSC_COMM_WORLD, & cells3FFTW,cells3_offset,cells2FFTW,cells2_offset) if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (vector, real space)' if (int(cells2FFTW) /= cells2) error stop 'domain decomposition mismatch (vector, Fourier space)' vectorField = fftw_alloc_complex(N) call c_f_pointer(vectorField,vectorField_real, & [3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW]) call c_f_pointer(vectorField,vectorField_fourier, & [3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW]) N = fftw_mpi_local_size_3d_transposed(cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T), & PETSC_COMM_WORLD,cells3FFTW,cells3_offset,cells2FFTW,cells2_offset) if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (scalar, real space)' if (int(cells2FFTW) /= cells2) error stop 'domain decomposition mismatch (scalar, Fourier space)' scalarField = fftw_alloc_complex(N) call c_f_pointer(scalarField,scalarField_real, & [int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW]) call c_f_pointer(scalarField,scalarField_fourier, & [int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW]) !-------------------------------------------------------------------------------------------------- ! allocation allocate (xi1st (3,cells1Red,cells(3),cells2),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, only half the size for first dimension allocate (xi2nd (3,cells1Red,cells(3),cells2),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for second derivatives, only half the size for first dimension !-------------------------------------------------------------------------------------------------- ! tensor MPI fftw plans planTensorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),tensorSize, & FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, & tensorField_real,tensorField_fourier, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT) if (.not. c_associated(planTensorForth)) error stop 'FFTW error r2c tensor' planTensorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),tensorSize, & FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, & tensorField_fourier,tensorField_real, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN) if (.not. c_associated(planTensorBack)) error stop 'FFTW error c2r tensor' !-------------------------------------------------------------------------------------------------- ! vector MPI fftw plans planVectorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),vectorSize, & FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, & vectorField_real,vectorField_fourier, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT) if (.not. c_associated(planVectorForth)) error stop 'FFTW error r2c vector' planVectorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),vectorSize, & FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, & vectorField_fourier,vectorField_real, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN) if (.not. c_associated(planVectorBack)) error stop 'FFTW error c2r vector' !-------------------------------------------------------------------------------------------------- ! scalar MPI fftw plans planScalarForth = fftw_mpi_plan_dft_r2c_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), & scalarField_real,scalarField_fourier, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT) if (.not. c_associated(planScalarForth)) error stop 'FFTW error r2c scalar' planScalarBack = fftw_mpi_plan_dft_c2r_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), & scalarField_fourier,scalarField_real, & PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN) if (.not. c_associated(planScalarBack)) error stop 'FFTW error c2r scalar' !-------------------------------------------------------------------------------------------------- ! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) do j = cells2Offset+1, cells2Offset+cells2 k_s(2) = j - 1 if (j > cells(2)/2 + 1) k_s(2) = k_s(2) - cells(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1 do k = 1, cells(3) k_s(3) = k - 1 if (k > cells(3)/2 + 1) k_s(3) = k_s(3) - cells(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1 do i = 1, cells1Red k_s(1) = i - 1 ! symmetry, junst running from 0,1,...,N/2,N/2+1 xi2nd(1:3,i,k,j-cells2Offset) = utilities_getFreqDerivative(k_s) where(mod(cells,2)==0 .and. [i,j,k] == cells/2+1 .and. & spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) ! for even grids, set the Nyquist Freq component to 0.0 xi1st(1:3,i,k,j-cells2Offset) = cmplx(0.0_pReal,0.0_pReal,pReal) elsewhere xi1st(1:3,i,k,j-cells2Offset) = xi2nd(1:3,i,k,j-cells2Offset) endwhere end do; end do; end do 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,cells1Red,cells(3),cells2), source = cmplx(0.0_pReal,0.0_pReal,pReal)) end if call selfTest() 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_cmplx, xiDyad_cmplx real(pReal), dimension(6,6) :: A, A_inv integer :: & i, j, k, & l, m, n, o logical :: err C_ref = C/wgt 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 !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err) do j = cells2Offset+1, cells2Offset+cells2; do k = 1, cells(3); do i = 1, cells1Red if (any([i,j,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 #ifndef __INTEL_COMPILER do concurrent(l = 1:3, m = 1:3) xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j-cells2Offset))*xi1st(m,i,k,j-cells2Offset) end do do concurrent(l = 1:3, m = 1:3) temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx) end do #else forall(l = 1:3, m = 1:3) & xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j-cells2Offset))*xi1st(m,i,k,j-cells2Offset) forall(l = 1:3, m = 1:3) & temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx) #endif A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) = temp33_cmplx%re A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im if (abs(math_det33(A(1:3,1:3))) > 1.e-16_pReal) then call math_invert(A_inv, err, A) temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal) #ifndef __INTEL_COMPILER do concurrent(l=1:3, m=1:3, n=1:3, o=1:3) gamma_hat(l,m,n,o,i,k,j-cells2Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m) end do #else forall(l=1:3, m=1:3, n=1:3, o=1:3) & gamma_hat(l,m,n,o,i,k,j-cells2Offset) = temp33_cmplx(l,n) * xiDyad_cmplx(o,m) #endif end if end if end do; end do; end do !$OMP END PARALLEL DO end if end subroutine utilities_updateGamma !-------------------------------------------------------------------------------------------------- !> @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 !-------------------------------------------------------------------------------------------------- function utilities_GammaConvolution(field, fieldAim) result(gammaField) real(pReal), intent(in), dimension(3,3,cells(1),cells(2),cells3) :: field real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution real(pReal), dimension(3,3,cells(1),cells(2),cells3) :: gammaField complex(pReal), dimension(3,3) :: temp33_cmplx, xiDyad_cmplx real(pReal), dimension(6,6) :: A, A_inv integer :: & i, j, k, & l, m, n, o logical :: err print'(/,1x,a)', '... doing gamma convolution ...............................................' flush(IO_STDOUT) tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal tensorField_real(1:3,1:3,1:cells(1), 1:cells(2),1:cells3) = field call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) memoryEfficient: if (num%memory_efficient) then !$OMP PARALLEL DO PRIVATE(l,m,n,o,temp33_cmplx,xiDyad_cmplx,A,A_inv,err,gamma_hat) do j = 1, cells2; do k = 1, cells(3); do i = 1, cells1Red if (any([i,j+cells2Offset,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 #ifndef __INTEL_COMPILER do concurrent(l = 1:3, m = 1:3) xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j))*xi1st(m,i,k,j) end do do concurrent(l = 1:3, m = 1:3) temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx) end do #else forall(l = 1:3, m = 1:3) & xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,k,j))*xi1st(m,i,k,j) forall(l = 1:3, m = 1:3) & temp33_cmplx(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal,pReal)*xiDyad_cmplx) #endif A(1:3,1:3) = temp33_cmplx%re; A(4:6,4:6) = temp33_cmplx%re A(1:3,4:6) = temp33_cmplx%im; A(4:6,1:3) = -temp33_cmplx%im if (abs(math_det33(A(1:3,1:3))) > 1.e-16_pReal) then call math_invert(A_inv, err, A) temp33_cmplx = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal) #ifndef __INTEL_COMPILER do concurrent(l=1:3, m=1:3, n=1:3, o=1:3) gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m) end do do concurrent(l = 1:3, m = 1:3) temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,k,j)) end do #else forall(l=1:3, m=1:3, n=1:3, o=1:3) & gamma_hat(l,m,n,o,1,1,1) = temp33_cmplx(l,n)*xiDyad_cmplx(o,m) forall(l = 1:3, m = 1:3) & temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,k,j)) #endif tensorField_fourier(1:3,1:3,i,k,j) = temp33_cmplx else tensorField_fourier(1:3,1:3,i,k,j) = cmplx(0.0_pReal,0.0_pReal,pReal) end if end if end do; end do; end do !$OMP END PARALLEL DO else memoryEfficient !$OMP PARALLEL DO PRIVATE(l,m,temp33_cmplx) do j = 1, cells2; do k = 1, cells(3); do i = 1,cells1Red #ifndef __INTEL_COMPILER do concurrent(l = 1:3, m = 1:3) temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,k,j)*tensorField_fourier(1:3,1:3,i,k,j)) end do #else forall(l = 1:3, m = 1:3) & temp33_cmplx(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,k,j)*tensorField_fourier(1:3,1:3,i,k,j)) #endif tensorField_fourier(1:3,1:3,i,k,j) = temp33_cmplx end do; end do; end do !$OMP END PARALLEL DO end if memoryEfficient if (cells3Offset == 0) tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim,0.0_pReal,pReal) call fftw_mpi_execute_dft_c2r(planTensorBack,tensorField_fourier,tensorField_real) gammaField = tensorField_real(1:3,1:3,1:cells(1),1:cells(2),1:cells3) end function utilities_GammaConvolution !-------------------------------------------------------------------------------------------------- !> @brief Convolution of Greens' operator for damage/thermal. !-------------------------------------------------------------------------------------------------- function utilities_GreenConvolution(field, D_ref, mu_ref, Delta_t) result(greenField) real(pReal), intent(in), dimension(cells(1),cells(2),cells3) :: field real(pReal), dimension(3,3), intent(in) :: D_ref real(pReal), intent(in) :: mu_ref, Delta_t real(pReal), dimension(cells(1),cells(2),cells3) :: greenField complex(pReal) :: GreenOp_hat integer :: i, j, k scalarField_real(cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal scalarField_real(1:cells(1), 1:cells(2),1:cells3) = field call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier) !$OMP PARALLEL DO PRIVATE(GreenOp_hat) do j = 1, cells2; do k = 1, cells(3); do i = 1, cells1Red GreenOp_hat = cmplx(wgt,0.0_pReal,pReal) & / (cmplx(mu_ref,0.0_pReal,pReal) + cmplx(Delta_t,0.0_pReal,pReal) & * sum(conjg(xi1st(1:3,i,k,j))* matmul(cmplx(D_ref,0.0_pReal,pReal),xi1st(1:3,i,k,j)))) scalarField_fourier(i,k,j) = scalarField_fourier(i,k,j)*GreenOp_hat end do; end do; end do !$OMP END PARALLEL DO call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real) greenField = scalarField_real(1:cells(1),1:cells(2),1:cells3) end function utilities_GreenConvolution !-------------------------------------------------------------------------------------------------- !> @brief Calculate root mean square of divergence. !-------------------------------------------------------------------------------------------------- real(pReal) function utilities_divergenceRMS(tensorField) real(pReal), dimension(3,3,cells(1),cells(2),cells3), intent(in) :: tensorField integer :: i, j, k integer(MPI_INTEGER_KIND) :: err_MPI complex(pReal), dimension(3) :: rescaledGeom tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal tensorField_real(1:3,1:3,1:cells(1), 1:cells(2),1:cells3) = tensorField call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal,pReal) !-------------------------------------------------------------------------------------------------- ! calculating RMS divergence criterion in Fourier space utilities_divergenceRMS = 0.0_pReal do j = 1, cells2; do k = 1, cells(3) do i = 2, cells1Red -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,k,j), & ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2, i.e. do not take square root and square again conjg(-xi1st(1:3,i,k,j))*rescaledGeom))**2) & ! --> sum squared L_2 norm of vector +sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,k,j),& conjg(-xi1st(1:3,i,k,j))*rescaledGeom))**2)) end do utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if cells(1) /= 1) + sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,k,j), & conjg(-xi1st(1:3,1,k,j))*rescaledGeom))**2) & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,k,j), & conjg(-xi1st(1:3,1,k,j))*rescaledGeom))**2) & + sum( real(matmul(tensorField_fourier(1:3,1:3,cells1Red,k,j), & conjg(-xi1st(1:3,cells1Red,k,j))*rescaledGeom))**2) & + sum(aimag(matmul(tensorField_fourier(1:3,1:3,cells1Red,k,j), & conjg(-xi1st(1:3,cells1Red,k,j))*rescaledGeom))**2) end do; end do call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space if (cells(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of cells(1) == 1 end function utilities_divergenceRMS !-------------------------------------------------------------------------------------------------- !> @brief Calculate root mean square of curl. !-------------------------------------------------------------------------------------------------- real(pReal) function utilities_curlRMS(tensorField) real(pReal), dimension(3,3,cells(1),cells(2),cells3), intent(in) :: tensorField integer :: i, j, k, l integer(MPI_INTEGER_KIND) :: err_MPI complex(pReal), dimension(3,3) :: curl_fourier complex(pReal), dimension(3) :: rescaledGeom tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal tensorField_real(1:3,1:3,1:cells(1), 1:cells(2),1:cells3) = tensorField call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal,pReal) !-------------------------------------------------------------------------------------------------- ! calculating max curl criterion in Fourier space utilities_curlRMS = 0.0_pReal do j = 1, cells2; do k = 1, cells(3); do i = 2, cells1Red - 1 do l = 1, 3 curl_fourier(l,1) = (+tensorField_fourier(l,3,i,k,j)*xi1st(2,i,k,j)*rescaledGeom(2) & -tensorField_fourier(l,2,i,k,j)*xi1st(3,i,k,j)*rescaledGeom(3)) curl_fourier(l,2) = (+tensorField_fourier(l,1,i,k,j)*xi1st(3,i,k,j)*rescaledGeom(3) & -tensorField_fourier(l,3,i,k,j)*xi1st(1,i,k,j)*rescaledGeom(1)) curl_fourier(l,3) = (+tensorField_fourier(l,2,i,k,j)*xi1st(1,i,k,j)*rescaledGeom(1) & -tensorField_fourier(l,1,i,k,j)*xi1st(2,i,k,j)*rescaledGeom(2)) end do utilities_curlRMS = utilities_curlRMS & +2.0_pReal*sum(curl_fourier%re**2+curl_fourier%im**2) ! Has somewhere a conj. complex counterpart. Therefore count it twice. end do do l = 1, 3 curl_fourier = (+tensorField_fourier(l,3,1,k,j)*xi1st(2,1,k,j)*rescaledGeom(2) & -tensorField_fourier(l,2,1,k,j)*xi1st(3,1,k,j)*rescaledGeom(3)) curl_fourier = (+tensorField_fourier(l,1,1,k,j)*xi1st(3,1,k,j)*rescaledGeom(3) & -tensorField_fourier(l,3,1,k,j)*xi1st(1,1,k,j)*rescaledGeom(1)) curl_fourier = (+tensorField_fourier(l,2,1,k,j)*xi1st(1,1,k,j)*rescaledGeom(1) & -tensorField_fourier(l,1,1,k,j)*xi1st(2,1,k,j)*rescaledGeom(2)) end do utilities_curlRMS = utilities_curlRMS & + sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (DC) does not have a conjugate complex counterpart (if cells(1) /= 1) do l = 1, 3 curl_fourier = (+tensorField_fourier(l,3,cells1Red,k,j)*xi1st(2,cells1Red,k,j)*rescaledGeom(2) & -tensorField_fourier(l,2,cells1Red,k,j)*xi1st(3,cells1Red,k,j)*rescaledGeom(3)) curl_fourier = (+tensorField_fourier(l,1,cells1Red,k,j)*xi1st(3,cells1Red,k,j)*rescaledGeom(3) & -tensorField_fourier(l,3,cells1Red,k,j)*xi1st(1,cells1Red,k,j)*rescaledGeom(1)) curl_fourier = (+tensorField_fourier(l,2,cells1Red,k,j)*xi1st(1,cells1Red,k,j)*rescaledGeom(1) & -tensorField_fourier(l,1,cells1Red,k,j)*xi1st(2,cells1Red,k,j)*rescaledGeom(2)) end do utilities_curlRMS = utilities_curlRMS & + sum(curl_fourier%re**2 + curl_fourier%im**2) ! this layer (Nyquist) does not have a conjugate complex counterpart (if cells(1) /= 1) end do; end do call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' utilities_curlRMS = sqrt(utilities_curlRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space if (cells(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of cells(1) == 1 end function utilities_curlRMS !-------------------------------------------------------------------------------------------------- !> @brief Calculate masked 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(tRotation), 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 = .not. reshape(transpose(mask_stress), [9]) size_reduced = count(mask_stressVector) if (size_reduced > 0) then temp99_real = math_3333to99(rot_BC%rotate(C)) do i = 1,9; do j = 1,9 mask(i,j) = mask_stressVector(i) .and. mask_stressVector(j) end do; end do 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. !-------------------------------------------------------------------------------------------------- ! check if inversion was successful sTimesC = matmul(c_reduced,s_reduced) errmatinv = errmatinv .or. any(dNeq(sTimesC,math_eye(size_reduced),1.0e-12_pReal)) if (errmatinv) then write(formatString, '(i2)') size_reduced formatString = '(/,1x,a,/,'//trim(formatString)//'('//trim(formatString)//'(2x,es9.2,1x)/))' print trim(formatString), 'C * S (load) ', transpose(matmul(c_reduced,s_reduced)) print trim(formatString), 'S (load) ', transpose(s_reduced) if (errmatinv) error stop 'matrix inversion error' end if temp99_real = reshape(unpack(reshape(s_reduced,[size_reduced**2]),reshape(mask,[81]),0.0_pReal),[9,9]) else temp99_real = 0.0_pReal end if utilities_maskedCompliance = math_99to3333(temp99_Real) end function utilities_maskedCompliance !-------------------------------------------------------------------------------------------------- !> @brief Calculate gradient of scalar field. !-------------------------------------------------------------------------------------------------- function utilities_scalarGradient(field) result(grad) real(pReal), intent(in), dimension( cells(1),cells(2),cells3) :: field real(pReal), dimension(3,cells(1),cells(2),cells3) :: grad integer :: i, j, k scalarField_real(cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal scalarField_real(1:cells(1), 1:cells(2),1:cells3) = field call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier) do j = 1, cells2; do k = 1, cells(3); do i = 1,cells1Red vectorField_fourier(1:3,i,k,j) = scalarField_fourier(i,k,j)*xi1st(1:3,i,k,j) end do; end do; end do call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real) grad = vectorField_real(1:3,1:cells(1),1:cells(2),1:cells3)*wgt end function utilities_scalarGradient !-------------------------------------------------------------------------------------------------- !> @brief Calculate divergence of vector field. !-------------------------------------------------------------------------------------------------- function utilities_vectorDivergence(field) result(div) real(pReal), intent(in), dimension(3,cells(1),cells(2),cells3) :: field real(pReal), dimension( cells(1),cells(2),cells3) :: div vectorField_real(1:3,cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal vectorField_real(1:3,1:cells(1), 1:cells(2),1:cells3) = field call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier) scalarField_fourier(1:cells1Red,1:cells(3),1:cells2) = sum(vectorField_fourier(1:3,1:cells1Red,1:cells(3),1:cells2) & *conjg(-xi1st),1) ! ToDo: use "xi1st" instead of "conjg(-xi1st)"? call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real) div = scalarField_real(1:cells(1),1:cells(2),1:cells3)*wgt end function utilities_vectorDivergence !-------------------------------------------------------------------------------------------------- !> @brief calculate constitutive response from homogenization_F0 to F during Delta_t !-------------------------------------------------------------------------------------------------- subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,& F,Delta_t,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,cells(1),cells(2),cells3) :: P !< PK stress real(pReal), intent(in), dimension(3,3,cells(1),cells(2),cells3) :: F !< deformation gradient target real(pReal), intent(in) :: Delta_t !< loading time type(tRotation), intent(in), optional :: rotation_BC !< rotation of load frame integer :: i integer(MPI_INTEGER_KIND) :: err_MPI 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 print'(/,1x,a)', '... evaluating constitutive response ......................................' flush(IO_STDOUT) homogenization_F = reshape(F,[3,3,product(cells(1:2))*cells3]) ! set materialpoint target F to estimated field call homogenization_mechanical_response(Delta_t,1,product(cells(1:2))*cells3) ! calculate P field if (.not. terminallyIll) & call homogenization_thermal_response(Delta_t,1,product(cells(1:2))*cells3) if (.not. terminallyIll) & call homogenization_mechanical_response2(Delta_t,[1,1],[1,product(cells(1:2))*cells3]) P = reshape(homogenization_P, [3,3,cells(1),cells(2),cells3]) P_av = sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt call MPI_Allreduce(MPI_IN_PLACE,P_av,9_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' if (present(rotation_BC)) then if (any(dNeq(rotation_BC%asQuaternion(), real([1.0, 0.0, 0.0, 0.0],pReal)))) & print'(/,1x,a,/,2(3(2x,f12.4,1x)/),3(2x,f12.4,1x))', & 'Piola--Kirchhoff stress (lab) / MPa =', transpose(P_av)*1.e-6_pReal P_av = rotation_BC%rotate(P_av) end if print'(/,1x,a,/,2(3(2x,f12.4,1x)/),3(2x,f12.4,1x))', & 'Piola--Kirchhoff stress / MPa =', transpose(P_av)*1.e-6_pReal flush(IO_STDOUT) 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(cells(1:2))*cells3 if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then dPdF_max = homogenization_dPdF(1:3,1:3,1:3,1:3,i) dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2) end if if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2)) then dPdF_min = homogenization_dPdF(1:3,1:3,1:3,1:3,i) dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,i)**2) end if end do valueAndRank = [dPdF_norm_max,real(worldrank,pReal)] call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1_MPI_INTEGER_KIND,MPI_2DOUBLE_PRECISION,MPI_MAXLOC,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' call MPI_Bcast(dPdF_max,81_MPI_INTEGER_KIND,MPI_DOUBLE,int(valueAndRank(2),MPI_INTEGER_KIND),MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' valueAndRank = [dPdF_norm_min,real(worldrank,pReal)] call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1_MPI_INTEGER_KIND,MPI_2DOUBLE_PRECISION,MPI_MINLOC,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' call MPI_Bcast(dPdF_min,81_MPI_INTEGER_KIND,MPI_DOUBLE,int(valueAndRank(2),MPI_INTEGER_KIND),MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' C_minmaxAvg = 0.5_pReal*(dPdF_max + dPdF_min) C_volAvg = sum(homogenization_dPdF,dim=5) call MPI_Allreduce(MPI_IN_PLACE,C_volAvg,81_MPI_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' C_volAvg = C_volAvg * wgt end subroutine utilities_constitutiveResponse !-------------------------------------------------------------------------------------------------- !> @brief calculates forward rate, either guessing or just add delta/Delta_t !-------------------------------------------------------------------------------------------------- pure function utilities_calculateRate(heterogeneous,field0,field,dt,avRate) real(pReal), intent(in), dimension(3,3) :: & avRate !< homogeneous addon real(pReal), intent(in) :: & dt !< Delta_t between field0 and field logical, intent(in) :: & heterogeneous !< calculate field of rates real(pReal), intent(in), dimension(3,3,cells(1),cells(2),cells3) :: & field0, & !< data of previous step field !< data of current step real(pReal), dimension(3,3,cells(1),cells(2),cells3) :: & utilities_calculateRate utilities_calculateRate = merge((field-field0) / dt, & spread(spread(spread(avRate,3,cells(1)),4,cells(2)),5,cells3), & heterogeneous) 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(Delta_t,field_lastInc,rate,aim) real(pReal), intent(in) :: & Delta_t !< Delta_t of current step real(pReal), intent(in), dimension(3,3,cells(1),cells(2),cells3) :: & 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,cells(1),cells(2),cells3) :: & utilities_forwardField real(pReal), dimension(3,3) :: fieldDiff !< - aim integer(MPI_INTEGER_KIND) :: err_MPI utilities_forwardField = field_lastInc + rate*Delta_t 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_INTEGER_KIND,MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' fieldDiff = fieldDiff - aim utilities_forwardField = utilities_forwardField & - spread(spread(spread(fieldDiff,3,cells(1)),4,cells(2)),5,cells3) end if end function utilities_forwardField !-------------------------------------------------------------------------------------------------- !> @brief Calculate Filter for Fourier convolution. !> @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, TAU*real(k_s,pReal)/geomSize,pReal) case (DERIVATIVE_CENTRAL_DIFF_ID) utilities_getFreqDerivative = cmplx(0.0_pReal, sin(TAU*real(k_s,pReal)/real(cells,pReal)), pReal)/ & cmplx(2.0_pReal*geomSize/real(cells,pReal), 0.0_pReal, pReal) case (DERIVATIVE_FWBW_DIFF_ID) utilities_getFreqDerivative(1) = & cmplx(cos(TAU*real(k_s(1),pReal)/real(cells(1),pReal)) - 1.0_pReal, & sin(TAU*real(k_s(1),pReal)/real(cells(1),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(2),pReal)/real(cells(2),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(2),pReal)/real(cells(2),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(3),pReal)/real(cells(3),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(3),pReal)/real(cells(3),pReal)), pReal)/ & cmplx(4.0_pReal*geomSize(1)/real(cells(1),pReal), 0.0_pReal, pReal) utilities_getFreqDerivative(2) = & cmplx(cos(TAU*real(k_s(1),pReal)/real(cells(1),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(1),pReal)/real(cells(1),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(2),pReal)/real(cells(2),pReal)) - 1.0_pReal, & sin(TAU*real(k_s(2),pReal)/real(cells(2),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(3),pReal)/real(cells(3),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(3),pReal)/real(cells(3),pReal)), pReal)/ & cmplx(4.0_pReal*geomSize(2)/real(cells(2),pReal), 0.0_pReal, pReal) utilities_getFreqDerivative(3) = & cmplx(cos(TAU*real(k_s(1),pReal)/real(cells(1),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(1),pReal)/real(cells(1),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(2),pReal)/real(cells(2),pReal)) + 1.0_pReal, & sin(TAU*real(k_s(2),pReal)/real(cells(2),pReal)), pReal)* & cmplx(cos(TAU*real(k_s(3),pReal)/real(cells(3),pReal)) - 1.0_pReal, & sin(TAU*real(k_s(3),pReal)/real(cells(3),pReal)), pReal)/ & cmplx(4.0_pReal*geomSize(3)/real(cells(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. !-------------------------------------------------------------------------------------------------- subroutine utilities_updateCoords(F) real(pReal), dimension(3,3,cells(1),cells(2),cells3), intent(in) :: F real(pReal), dimension(3, cells(1),cells(2),cells3) :: x_p !< Point/cell center coordinates real(pReal), dimension(3, cells(1),cells(2),0:cells3+1) :: u_tilde_p_padded !< Fluctuation of cell center displacement (padded along z for MPI) real(pReal), dimension(3, cells(1)+1,cells(2)+1,cells3+1) :: x_n !< Node coordinates integer :: & i,j,k,n, & c integer(MPI_INTEGER_KIND) :: & rank_t, rank_b integer(MPI_INTEGER_KIND) :: err_MPI #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY) type(MPI_Request), dimension(4) :: request type(MPI_Status), dimension(4) :: status #else integer, dimension(4) :: request integer, dimension(MPI_STATUS_SIZE,4) :: status #endif 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(cells, pReal) tensorField_real(1:3,1:3,1:cells(1), 1:cells(2),1:cells3) = F tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,1:cells(2),1:cells3) = 0.0_pReal call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) !-------------------------------------------------------------------------------------------------- ! average F if (cells3Offset == 0) Favg = tensorField_fourier(1:3,1:3,1,1,1)%re*wgt call MPI_Bcast(Favg,9_MPI_INTEGER_KIND,MPI_DOUBLE,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' !-------------------------------------------------------------------------------------------------- ! integration in Fourier space to get fluctuations of cell center displacements !$OMP PARALLEL DO do j = 1, cells2; do k = 1, cells(3); do i = 1, cells1Red if (any([i,j+cells2Offset,k] /= 1)) then vectorField_fourier(1:3,i,k,j) = matmul(tensorField_fourier(1:3,1:3,i,k,j),xi2nd(1:3,i,k,j)) & / sum(conjg(-xi2nd(1:3,i,k,j))*xi2nd(1:3,i,k,j)) else vectorField_fourier(1:3,i,k,j) = cmplx(0.0,0.0,pReal) end if end do; end do; end do !$OMP END PARALLEL DO call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real) u_tilde_p_padded(1:3,1:cells(1),1:cells(2),1:cells3) = vectorField_real(1:3,1:cells(1),1:cells(2),1:cells3) * wgt !-------------------------------------------------------------------------------------------------- ! pad cell center fluctuations along z-direction (needed when running MPI simulation) c = product(shape(u_tilde_p_padded(:,:,:,1))) !< amount of data to transfer rank_t = modulo(worldrank+1_MPI_INTEGER_KIND,worldsize) rank_b = modulo(worldrank-1_MPI_INTEGER_KIND,worldsize) ! send bottom layer to process below call MPI_Isend(u_tilde_p_padded(:,:,:,1), c,MPI_DOUBLE,rank_b,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(1),err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' call MPI_Irecv(u_tilde_p_padded(:,:,:,cells3+1),c,MPI_DOUBLE,rank_t,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(2),err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' ! send top layer to process above call MPI_Isend(u_tilde_p_padded(:,:,:,cells3) ,c,MPI_DOUBLE,rank_t,1_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(3),err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' call MPI_Irecv(u_tilde_p_padded(:,:,:,0), c,MPI_DOUBLE,rank_b,1_MPI_INTEGER_KIND,MPI_COMM_WORLD,request(4),err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' call MPI_Waitall(4,request,status,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' #if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY) ! ToDo #else if (any(status(MPI_ERROR,:) /= 0)) error stop 'MPI error' #endif !-------------------------------------------------------------------------------------------------- ! calculate nodal positions x_n = 0.0_pReal do j = 0,cells(2); do k = 0,cells3; do i = 0,cells(1) x_n(1:3,i+1,j+1,k+1) = matmul(Favg,step*(real([i,j,k+cells3Offset],pReal))) averageFluct: do n = 1,8 me = [i+neighbor(1,n),j+neighbor(2,n),k+neighbor(3,n)] x_n(1:3,i+1,j+1,k+1) = x_n(1:3,i+1,j+1,k+1) & + u_tilde_p_padded(1:3,modulo(me(1)-1,cells(1))+1,modulo(me(2)-1,cells(2))+1,me(3))*0.125_pReal end do averageFluct end do; end do; end do !-------------------------------------------------------------------------------------------------- ! calculate cell center/point positions do k = 1,cells3; do j = 1,cells(2); do i = 1,cells(1) x_p(1:3,i,j,k) = u_tilde_p_padded(1:3,i,j,k) & + matmul(Favg,step*(real([i,j,k+cells3Offset],pReal)-0.5_pReal)) end do; end do; end do call discretization_setNodeCoords(reshape(x_n,[3,(cells(1)+1)*(cells(2)+1)*(cells3+1)])) call discretization_setIPcoords (reshape(x_p,[3,cells(1)*cells(2)*cells3])) end subroutine utilities_updateCoords !-------------------------------------------------------------------------------------------------- !> @brief Check correctness of forward-backward transform. !-------------------------------------------------------------------------------------------------- subroutine selfTest() real(pReal), allocatable, dimension(:,:,:,:,:) :: tensorField_real_ real(pReal), allocatable, dimension(:,:,:,:) :: vectorField_real_ real(pReal), allocatable, dimension(:,:,:) :: scalarField_real_ real(pReal), dimension(3,3) :: tensorSum real(pReal), dimension(3) :: vectorSum real(pReal) :: scalarSum real(pReal), dimension(3,3) :: r integer(MPI_INTEGER_KIND) :: err_MPI call random_number(tensorField_real) tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal tensorField_real_ = tensorField_real call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier) call MPI_Allreduce(sum(sum(sum(tensorField_real_,dim=5),dim=4),dim=3),tensorSum,9_MPI_INTEGER_KIND, & MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' if (worldrank==0) then if (any(dNeq(tensorSum/tensorField_fourier(:,:,1,1,1)%re,1.0_pReal,1.0e-12_pReal))) & error stop 'mismatch avg tensorField FFT <-> real' end if call fftw_mpi_execute_dft_c2r(planTensorBack,tensorField_fourier,tensorField_real) tensorField_real(1:3,1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal if (maxval(abs(tensorField_real_ - tensorField_real*wgt))>5.0e-15_pReal) & error stop 'mismatch tensorField FFT/invFFT <-> real' call random_number(vectorField_real) vectorField_real(1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal vectorField_real_ = vectorField_real call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier) call MPI_Allreduce(sum(sum(sum(vectorField_real_,dim=4),dim=3),dim=2),vectorSum,3_MPI_INTEGER_KIND, & MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' if (worldrank==0) then if (any(dNeq(vectorSum/vectorField_fourier(:,1,1,1)%re,1.0_pReal,1.0e-12_pReal))) & error stop 'mismatch avg vectorField FFT <-> real' end if call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real) vectorField_real(1:3,cells(1)+1:cells1Red*2,:,:) = 0.0_pReal if (maxval(abs(vectorField_real_ - vectorField_real*wgt))>5.0e-15_pReal) & error stop 'mismatch vectorField FFT/invFFT <-> real' call random_number(scalarField_real) scalarField_real(cells(1)+1:cells1Red*2,:,:) = 0.0_pReal scalarField_real_ = scalarField_real call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier) call MPI_Allreduce(sum(sum(sum(scalarField_real_,dim=3),dim=2),dim=1),scalarSum,1_MPI_INTEGER_KIND, & MPI_DOUBLE,MPI_SUM,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' if (worldrank==0) then if (dNeq(scalarSum/scalarField_fourier(1,1,1)%re,1.0_pReal,1.0e-12_pReal)) & error stop 'mismatch avg scalarField FFT <-> real' end if call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real) scalarField_real(cells(1)+1:cells1Red*2,:,:) = 0.0_pReal if (maxval(abs(scalarField_real_ - scalarField_real*wgt))>5.0e-15_pReal) & error stop 'mismatch scalarField FFT/invFFT <-> real' call random_number(r) call MPI_Bcast(r,9_MPI_INTEGER_KIND,MPI_DOUBLE,0_MPI_INTEGER_KIND,MPI_COMM_WORLD,err_MPI) if (err_MPI /= 0_MPI_INTEGER_KIND) error stop 'MPI error' scalarField_real_ = r(1,1) if (maxval(abs(utilities_scalarGradient(scalarField_real_)))>5.0e-9_pReal) error stop 'non-zero grad(const)' vectorField_real_ = spread(spread(spread(r(1,:),2,cells(1)),3,cells(2)),4,cells3) if (maxval(abs(utilities_vectorDivergence(vectorField_real_)))>5.0e-9_pReal) error stop 'non-zero div(const)' tensorField_real_ = spread(spread(spread(r,3,cells(1)),4,cells(2)),5,cells3) if (utilities_divergenceRMS(tensorField_real_)>5.0e-14_pReal) error stop 'non-zero RMS div(const)' if (utilities_curlRMS(tensorField_real_)>5.0e-14_pReal) error stop 'non-zero RMS curl(const)' if (cells(1) > 2 .and. spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) then scalarField_real_ = spread(spread(planeCosine(cells(1)),2,cells(2)),3,cells3) vectorField_real_ = utilities_scalarGradient(scalarField_real_)/TAU*geomSize(1) scalarField_real_ = -spread(spread(planeSine (cells(1)),2,cells(2)),3,cells3) if (maxval(abs(vectorField_real_(1,:,:,:) - scalarField_real_))>5.0e-12_pReal) error stop 'grad cosine' scalarField_real_ = spread(spread(planeSine (cells(1)),2,cells(2)),3,cells3) vectorField_real_ = utilities_scalarGradient(scalarField_real_)/TAU*geomSize(1) scalarField_real_ = spread(spread(planeCosine(cells(1)),2,cells(2)),3,cells3) if (maxval(abs(vectorField_real_(1,:,:,:) - scalarField_real_))>5.0e-12_pReal) error stop 'grad sine' vectorField_real_(2:3,:,:,:) = 0.0_pReal vectorField_real_(1,:,:,:) = spread(spread(planeCosine(cells(1)),2,cells(2)),3,cells3) scalarField_real_ = utilities_vectorDivergence(vectorField_real_)/TAU*geomSize(1) vectorField_real_(1,:,:,:) =-spread(spread(planeSine( cells(1)),2,cells(2)),3,cells3) if (maxval(abs(vectorField_real_(1,:,:,:) - scalarField_real_))>5.0e-12_pReal) error stop 'div cosine' vectorField_real_(2:3,:,:,:) = 0.0_pReal vectorField_real_(1,:,:,:) = spread(spread(planeSine( cells(1)),2,cells(2)),3,cells3) scalarField_real_ = utilities_vectorDivergence(vectorField_real_)/TAU*geomSize(1) vectorField_real_(1,:,:,:) = spread(spread(planeCosine(cells(1)),2,cells(2)),3,cells3) if (maxval(abs(vectorField_real_(1,:,:,:) - scalarField_real_))>5.0e-12_pReal) error stop 'div sine' end if contains function planeCosine(n) integer, intent(in) :: n real(pReal), dimension(n) :: planeCosine planeCosine = cos(real(math_range(n),pReal)/real(n,pReal)*TAU-TAU/real(n*2,pReal)) end function planeCosine function planeSine(n) integer, intent(in) :: n real(pReal), dimension(n) :: planeSine planeSine = sin(real(math_range(n),pReal)/real(n,pReal)*TAU-TAU/real(n*2,pReal)) end function planeSine end subroutine selfTest end module spectral_utilities