1188 lines
64 KiB
Fortran
1188 lines
64 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
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!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
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!> @brief Utilities used by the different spectral solver variants
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!--------------------------------------------------------------------------------------------------
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module spectral_utilities
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#include <petsc/finclude/petscsys.h>
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use PETScSys
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#if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY)
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use MPI_f08
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#endif
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use FFTW3
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use prec
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use CLI
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use parallelization
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use math
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use rotations
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use IO
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use config
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use discretization_grid
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use discretization
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use homogenization
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#if (PETSC_VERSION_MAJOR==3 && PETSC_VERSION_MINOR>14) && !defined(PETSC_HAVE_MPI_F90MODULE_VISIBILITY)
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implicit none(type,external)
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#else
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implicit none
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#endif
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private
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!--------------------------------------------------------------------------------------------------
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! grid related information
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real(pREAL), protected, public :: wgt !< weighting factor 1/Nelems
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real(pREAL), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence
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integer :: &
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cells1Red, & !< cells(1)/2+1
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cells2, & !< (local) cells in 2nd direction
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cells2Offset !< (local) cells offset in 2nd direction
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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real(C_DOUBLE), dimension(:,:,:,:,:), pointer :: tensorField_real !< tensor field in real space
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real(C_DOUBLE), dimension(:,:,:,:), pointer :: vectorField_real !< vector field in real space
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real(C_DOUBLE), dimension(:,:,:), pointer :: scalarField_real !< scalar field in real space
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complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:,:), pointer :: tensorField_fourier !< tensor field in Fourier space
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complex(C_DOUBLE_COMPLEX), dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field in Fourier space
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complex(C_DOUBLE_COMPLEX), dimension(:,:,:), pointer :: scalarField_fourier !< scalar field in Fourier space
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complex(pREAL), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
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complex(pREAL), dimension(:,:,:,:), allocatable :: xi1st !< wave vector field for first derivatives
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complex(pREAL), dimension(:,:,:,:), allocatable :: xi2nd !< wave vector field for second derivatives
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real(pREAL), dimension(3,3,3,3) :: C_ref !< mechanic reference stiffness
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!--------------------------------------------------------------------------------------------------
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! plans for FFTW
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type(C_PTR) :: &
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planTensorForth, & !< FFTW MPI plan P(x) to P(k)
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planTensorBack, & !< FFTW MPI plan F(k) to F(x)
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planVectorForth, & !< FFTW MPI plan v(x) to v(k)
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planVectorBack, & !< FFTW MPI plan v(k) to v(x)
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planScalarForth, & !< FFTW MPI plan s(x) to s(k)
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planScalarBack !< FFTW MPI plan s(k) to s(x)
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!--------------------------------------------------------------------------------------------------
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! derived types
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type, public :: tSolutionState !< return type of solution from spectral solver variants
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integer :: &
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iterationsNeeded = 0
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logical :: &
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converged = .true., &
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stagConverged = .true., &
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termIll = .false.
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end type tSolutionState
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type, public :: tBoundaryCondition !< set of parameters defining a boundary condition
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real(pREAL), dimension(3,3) :: values = 0.0_pREAL
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logical, dimension(3,3) :: mask = .true.
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character(len=:), allocatable :: myType
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end type tBoundaryCondition
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type, public :: tSolutionParams
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real(pREAL), dimension(3,3) :: stress_BC
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logical, dimension(3,3) :: stress_mask
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type(tRotation) :: rotation_BC
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real(pREAL) :: Delta_t
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end type tSolutionParams
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type :: tNumerics
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integer :: &
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divergence_correction !< scale divergence/curl calculation: [0: no correction, 1: size scaled to 1, 2: size scaled to Npoints]
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logical :: &
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memory_efficient !< calculate gamma operator on the fly
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end type tNumerics
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type(tNumerics) :: num ! numerics parameters. Better name?
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enum, bind(c); enumerator :: &
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DERIVATIVE_CONTINUOUS_ID, &
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DERIVATIVE_CENTRAL_DIFF_ID, &
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DERIVATIVE_FWBW_DIFF_ID, &
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DIVERGENCE_CORRECTION_NONE_ID, &
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DIVERGENCE_CORRECTION_SIZE_ID, &
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DIVERGENCE_CORRECTION_SIZE_GRID_ID
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end enum
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integer(kind(DERIVATIVE_CONTINUOUS_ID)) :: &
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spectral_derivative_ID
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integer(kind(DIVERGENCE_CORRECTION_NONE_ID)) :: &
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divergence_correction_ID
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public :: &
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spectral_utilities_init, &
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utilities_updateGamma, &
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utilities_GammaConvolution, &
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utilities_GreenConvolution, &
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utilities_divergenceRMS, &
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utilities_curlRMS, &
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utilities_scalarGradient, &
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utilities_vectorDivergence, &
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utilities_maskedCompliance, &
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utilities_constitutiveResponse, &
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utilities_calculateRate, &
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utilities_forwardTensorField, &
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utilities_updateCoords
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief Allocate all neccessary fields and create plans for FFTW.
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!--------------------------------------------------------------------------------------------------
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subroutine spectral_utilities_init()
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PetscErrorCode :: err_PETSc
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integer :: i, j, k, &
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FFTW_planner_flag
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integer, dimension(3) :: k_s
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type(C_PTR) :: &
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tensorField, & !< tensor data for FFTW in real and Fourier space (in-place)
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vectorField, & !< vector data for FFTW in real and Fourier space (in-place)
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scalarField !< scalar data for FFTW in real and Fourier space (in-place)
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integer(C_INTPTR_T), dimension(3) :: cellsFFTW
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integer(C_INTPTR_T) :: N, &
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cells3FFTW, & !< # of cells in 3. dim on current process in real space
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cells3_offset, & !< offset for cells in 3. dim on current process in real space
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cells2FFTW, & !< # of cells in 2. dim on current process in Fourier space
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cells2_offset !< offset for cells in 2. dim on curren process in Fourier space
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integer(C_INTPTR_T), parameter :: &
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vectorSize = 3_C_INTPTR_T, &
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tensorSize = 9_C_INTPTR_T
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type(tDict) , pointer :: &
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num_solver, &
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num_grid, &
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num_grid_fft
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print'(/,1x,a)', '<<<+- spectral_utilities init -+>>>'
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print'(/,1x,a)', 'M. Diehl, Diploma Thesis TU München, 2010'
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print'( 1x,a)', 'https://doi.org/10.13140/2.1.3234.3840'//IO_EOL
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print'( 1x,a)', 'P. Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013'
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print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2012.09.012'//IO_EOL
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print'( 1x,a)', 'P. Shanthraj et al., International Journal of Plasticity 66:31–45, 2015'
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print'( 1x,a)', 'https://doi.org/10.1016/j.ijplas.2014.02.006'//IO_EOL
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print'( 1x,a)', 'P. Shanthraj et al., Handbook of Mechanics of Materials, 2019'
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print'( 1x,a)', 'https://doi.org/10.1007/978-981-10-6855-3_80'
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num_solver => config_numerics%get_dict('solver',defaultVal=emptyDict)
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num_grid => num_solver%get_dict('grid',defaultVal=emptyDict)
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num_grid_fft => num_grid%get_dict('FFT',defaultVal=emptyDict)
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call PetscOptionsClear(PETSC_NULL_OPTIONS,err_PETSc)
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CHKERRQ(err_PETSc)
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call PetscOptionsInsertString(PETSC_NULL_OPTIONS,&
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num_grid%get_asStr('PETSc_options',defaultVal=''),err_PETSc)
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CHKERRQ(err_PETSc)
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cells1Red = cells(1)/2 + 1
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wgt = real(product(cells),pREAL)**(-1)
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num%memory_efficient = num_grid_fft%get_asBool('memory_efficient', defaultVal=.true.)
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select case (num_grid_fft%get_asStr('divergence_correction',defaultVal='grid+size'))
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case ('none')
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divergence_correction_ID = DIVERGENCE_CORRECTION_NONE_ID
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case ('size')
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divergence_correction_ID = DIVERGENCE_CORRECTION_SIZE_ID
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case ('grid+size', 'size+grid')
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divergence_correction_ID = DIVERGENCE_CORRECTION_SIZE_GRID_ID
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case default
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call IO_error(301,ext_msg=trim(num_grid_fft%get_asStr('divergence_correction')))
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end select
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select case (num_grid_fft%get_asStr('derivative',defaultVal='continuous'))
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case ('continuous')
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spectral_derivative_ID = DERIVATIVE_CONTINUOUS_ID
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case ('central_difference')
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spectral_derivative_ID = DERIVATIVE_CENTRAL_DIFF_ID
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case ('FWBW_difference')
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spectral_derivative_ID = DERIVATIVE_FWBW_DIFF_ID
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case default
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call IO_error(892,ext_msg=trim(num_grid_fft%get_asStr('derivative')))
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end select
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!--------------------------------------------------------------------------------------------------
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! scale dimension to calculate either uncorrected, dimension-independent, or dimension- and
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! resolution-independent divergence
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if (divergence_correction_ID == DIVERGENCE_CORRECTION_NONE_ID) then
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do j = 1, 3
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if (j /= minloc(geomSize,1) .and. j /= maxloc(geomSize,1)) &
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scaledGeomSize = geomSize/geomSize(j)
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end do
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elseif (divergence_correction_ID == DIVERGENCE_CORRECTION_SIZE_GRID_ID) then
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do j = 1, 3
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if ( j /= int(minloc(geomSize/real(cells,pREAL),1)) &
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.and. j /= int(maxloc(geomSize/real(cells,pREAL),1))) &
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scaledGeomSize = geomSize/geomSize(j)*real(cells(j),pREAL)
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end do
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else
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scaledGeomSize = geomSize
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end if
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select case(IO_lc(num_grid_fft%get_asStr('FFTW_plan_mode',defaultVal='FFTW_MEASURE')))
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case('fftw_estimate', 'FFTW_ESTIMATE') ! ordered from slow execution (but fast plan creation) to fast execution
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FFTW_planner_flag = FFTW_ESTIMATE
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case('fftw_measure', 'FFTW_MEASURE')
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FFTW_planner_flag = FFTW_MEASURE
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case('fftw_patient', 'FFTW_PATIENT')
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FFTW_planner_flag = FFTW_PATIENT
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case('fftw_exhaustive', 'FFTW_EXHAUSTIVE')
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FFTW_planner_flag = FFTW_EXHAUSTIVE
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case default
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call IO_warning(47,'using default FFTW_MEASURE instead of "'//trim(num_grid_fft%get_asStr('plan_mode'))//'"')
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FFTW_planner_flag = FFTW_MEASURE
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end select
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!--------------------------------------------------------------------------------------------------
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! general initialization of FFTW (see manual on fftw.org for more details)
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if (pREAL /= C_DOUBLE .or. kind(1) /= C_INT) error stop 'C and Fortran datatypes do not match'
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call fftw_set_timelimit(num_grid_fft%get_asReal('FFTW_timelimit',defaultVal=300.0_pREAL))
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print'(/,1x,a)', 'FFTW initialized'; flush(IO_STDOUT)
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cellsFFTW = int(cells,C_INTPTR_T)
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N = fftw_mpi_local_size_many_transposed(3,[cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T)], &
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tensorSize,FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK,PETSC_COMM_WORLD, &
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cells3FFTW,cells3_offset,cells2FFTW,cells2_offset)
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cells2 = int(cells2FFTW)
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cells2Offset = int(cells2_offset)
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if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (tensor, real space)'
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tensorField = fftw_alloc_complex(N)
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call c_f_pointer(tensorField,tensorField_real, &
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[3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
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call c_f_pointer(tensorField,tensorField_fourier, &
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[3_C_INTPTR_T,3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
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N = fftw_mpi_local_size_many_transposed(3,[cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T)], &
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vectorSize,FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK,PETSC_COMM_WORLD, &
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cells3FFTW,cells3_offset,cells2FFTW,cells2_offset)
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if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (vector, real space)'
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if (int(cells2FFTW) /= cells2) error stop 'domain decomposition mismatch (vector, Fourier space)'
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vectorField = fftw_alloc_complex(N)
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call c_f_pointer(vectorField,vectorField_real, &
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[3_C_INTPTR_T,int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
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call c_f_pointer(vectorField,vectorField_fourier, &
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[3_C_INTPTR_T,int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
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N = fftw_mpi_local_size_3d_transposed(cellsFFTW(3),cellsFFTW(2),int(cells1Red,C_INTPTR_T), &
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PETSC_COMM_WORLD,cells3FFTW,cells3_offset,cells2FFTW,cells2_offset)
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if (int(cells3FFTW) /= cells3) error stop 'domain decomposition mismatch (scalar, real space)'
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if (int(cells2FFTW) /= cells2) error stop 'domain decomposition mismatch (scalar, Fourier space)'
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scalarField = fftw_alloc_complex(N)
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call c_f_pointer(scalarField,scalarField_real, &
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[int(cells1Red*2,C_INTPTR_T),cellsFFTW(2),cells3FFTW])
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call c_f_pointer(scalarField,scalarField_fourier, &
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[int(cells1Red, C_INTPTR_T),cellsFFTW(3),cells2FFTW])
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!--------------------------------------------------------------------------------------------------
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! allocation
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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
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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
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!--------------------------------------------------------------------------------------------------
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! tensor MPI fftw plans
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planTensorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),tensorSize, &
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FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
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tensorField_real,tensorField_fourier, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
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if (.not. c_associated(planTensorForth)) error stop 'FFTW error r2c tensor'
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planTensorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),tensorSize, &
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FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
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tensorField_fourier,tensorField_real, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
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if (.not. c_associated(planTensorBack)) error stop 'FFTW error c2r tensor'
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!--------------------------------------------------------------------------------------------------
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! vector MPI fftw plans
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planVectorForth = fftw_mpi_plan_many_dft_r2c(3,cellsFFTW(3:1:-1),vectorSize, &
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FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
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vectorField_real,vectorField_fourier, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
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if (.not. c_associated(planVectorForth)) error stop 'FFTW error r2c vector'
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planVectorBack = fftw_mpi_plan_many_dft_c2r(3,cellsFFTW(3:1:-1),vectorSize, &
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FFTW_MPI_DEFAULT_BLOCK,FFTW_MPI_DEFAULT_BLOCK, &
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vectorField_fourier,vectorField_real, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
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if (.not. c_associated(planVectorBack)) error stop 'FFTW error c2r vector'
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!--------------------------------------------------------------------------------------------------
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! scalar MPI fftw plans
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planScalarForth = fftw_mpi_plan_dft_r2c_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), &
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scalarField_real,scalarField_fourier, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_OUT)
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if (.not. c_associated(planScalarForth)) error stop 'FFTW error r2c scalar'
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planScalarBack = fftw_mpi_plan_dft_c2r_3d(cellsFFTW(3),cellsFFTW(2),cellsFFTW(1), &
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scalarField_fourier,scalarField_real, &
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PETSC_COMM_WORLD,FFTW_planner_flag+FFTW_MPI_TRANSPOSED_IN)
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if (.not. c_associated(planScalarBack)) error stop 'FFTW error c2r scalar'
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!--------------------------------------------------------------------------------------------------
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! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
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do j = cells2Offset+1, cells2Offset+cells2
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k_s(2) = j - 1
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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
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do k = 1, cells(3)
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k_s(3) = k - 1
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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
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do i = 1, cells1Red
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k_s(1) = i - 1 ! symmetry, junst running from 0,1,...,N/2,N/2+1
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xi2nd(1:3,i,k,j-cells2Offset) = utilities_getFreqDerivative(k_s)
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where(mod(cells,2)==0 .and. [i,j,k] == cells/2+1 .and. &
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spectral_derivative_ID == DERIVATIVE_CONTINUOUS_ID) ! for even grids, set the Nyquist Freq component to 0.0
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xi1st(1:3,i,k,j-cells2Offset) = cmplx(0.0_pREAL,0.0_pREAL,pREAL)
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elsewhere
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xi1st(1:3,i,k,j-cells2Offset) = xi2nd(1:3,i,k,j-cells2Offset)
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endwhere
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end do; end do; end do
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if (num%memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pREAL,0.0_pREAL,pREAL))
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(3,3,3,3,cells1Red,cells(3),cells2), source = cmplx(0.0_pREAL,0.0_pREAL,pREAL))
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end if
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call selfTest()
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end subroutine spectral_utilities_init
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!---------------------------------------------------------------------------------------------------
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!> @brief Update reference stiffness and potentially precalculated gamma operator.
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!> @details Set the current reference stiffness to the stiffness given as an argument.
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!> If the gamma operator is precalculated, it is calculated with this stiffness.
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!> In case of an on-the-fly calculation, only the reference stiffness is updated.
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||
!---------------------------------------------------------------------------------------------------
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subroutine utilities_updateGamma(C)
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real(pREAL), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness
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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 Calculate gamma_hat * field_real (convolution).
|
||
!> @details The average value equals the given aim.
|
||
!--------------------------------------------------------------------------------------------------
|
||
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=pSTRLEN):: 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), 'C (load) ', transpose(c_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 Calculate forward rate, either as local guess or as homogeneous add on.
|
||
!--------------------------------------------------------------------------------------------------
|
||
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_forwardTensorField(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_forwardTensorField
|
||
real(pREAL), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
|
||
integer(MPI_INTEGER_KIND) :: err_MPI
|
||
|
||
|
||
utilities_forwardTensorField = field_lastInc + rate*Delta_t
|
||
if (present(aim)) then !< correct to match average
|
||
fieldDiff = sum(sum(sum(utilities_forwardTensorField,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_forwardTensorField = utilities_forwardTensorField &
|
||
- spread(spread(spread(fieldDiff,3,cells(1)),4,cells(2)),5,cells3)
|
||
end if
|
||
|
||
end function utilities_forwardTensorField
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @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
|