1108 lines
62 KiB
Fortran
1108 lines
62 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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use, intrinsic :: iso_c_binding
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#include <petsc/finclude/petscsys.h>
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use PETScSys
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use prec
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use DAMASK_interface
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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 discretization_grid
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use discretization
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use homogenization
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implicit none
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private
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include 'fftw3-mpi.f03'
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!--------------------------------------------------------------------------------------------------
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! field labels information
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enum, bind(c); enumerator :: &
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FIELD_UNDEFINED_ID, &
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FIELD_MECH_ID, &
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FIELD_THERMAL_ID, &
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FIELD_DAMAGE_ID
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end enum
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!--------------------------------------------------------------------------------------------------
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! grid related information information
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real(pReal), protected, public :: wgt !< weighting factor 1/Nelems
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integer, protected, public :: grid1Red !< grid(1)/2
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real(pReal), protected, public, dimension(3) :: scaledGeomSize !< scaled geometry size for calculation of divergence
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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real (C_DOUBLE), public, dimension(:,:,:,:,:), pointer :: tensorField_real !< real representation (some stress or deformation) of field_fourier
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:,:), pointer :: tensorField_fourier !< field on which the Fourier transform operates
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real(C_DOUBLE), public, dimension(:,:,:,:), pointer :: vectorField_real !< vector field real representation for fftw
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:,:), pointer :: vectorField_fourier !< vector field fourier representation for fftw
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real(C_DOUBLE), public, dimension(:,:,:), pointer :: scalarField_real !< scalar field real representation for fftw
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complex(C_DOUBLE_COMPLEX),public, dimension(:,:,:), pointer :: scalarField_fourier !< scalar field fourier representation for fftw
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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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! variables controlling debugging
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logical :: &
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debugGeneral, & !< general debugging of spectral solver
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debugRotation, & !< also printing out results in lab frame
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debugPETSc !< use some in debug defined options for more verbose PETSc solution
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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 = .false.
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character(len=:), allocatable :: myType
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end type tBoundaryCondition
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type, public :: tLoadCase
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type(rotation) :: rot !< rotation of BC
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type(tBoundaryCondition) :: stress, & !< stress BC
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deformation !< deformation BC (dot_F, F, or L)
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real(pReal) :: time !< length of increment
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integer :: incs, & !< number of increments
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outputfrequency, & !< frequency of result writes
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restartfrequency !< frequency of restart writes
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logical :: followFormerTrajectory, & !< follow trajectory of former loadcase
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logscale !< logarithmic time inc flag
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integer(kind(FIELD_UNDEFINED_ID)), allocatable :: ID(:)
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end type tLoadCase
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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(rotation) :: rotation_BC
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real(pReal) :: timeinc, timeincOld
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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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end enum
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integer(kind(DERIVATIVE_CONTINUOUS_ID)) :: &
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spectral_derivative_ID
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public :: &
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spectral_utilities_init, &
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utilities_updateGamma, &
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utilities_FFTtensorForward, &
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utilities_FFTtensorBackward, &
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utilities_FFTvectorForward, &
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utilities_FFTvectorBackward, &
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utilities_FFTscalarForward, &
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utilities_FFTscalarBackward, &
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utilities_fourierGammaConvolution, &
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utilities_fourierGreenConvolution, &
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utilities_divergenceRMS, &
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utilities_curlRMS, &
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utilities_fourierScalarGradient, &
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utilities_fourierVectorDivergence, &
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utilities_fourierVectorGradient, &
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utilities_fourierTensorDivergence, &
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utilities_maskedCompliance, &
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utilities_constitutiveResponse, &
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utilities_calculateRate, &
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utilities_forwardField, &
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utilities_updateCoords, &
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utilities_saveReferenceStiffness, &
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FIELD_UNDEFINED_ID, &
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FIELD_MECH_ID, &
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FIELD_THERMAL_ID, &
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FIELD_DAMAGE_ID
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contains
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!--------------------------------------------------------------------------------------------------
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!> @brief allocates all neccessary fields, sets debug flags, create plans for FFTW
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!> @details Sets the debug levels for general, divergence, restart, and FFTW from the bitwise coding
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!> provided by the debug module to logicals.
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!> Allocate all fields used by FFTW and create the corresponding plans depending on the debug
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!> level chosen.
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!> Initializes FFTW.
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!--------------------------------------------------------------------------------------------------
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subroutine spectral_utilities_init
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PetscErrorCode :: ierr
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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, & !< field containing data for FFTW in real and fourier space (in place)
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vectorField, & !< field containing data for FFTW in real space when debugging FFTW (no in place)
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scalarField !< field containing data for FFTW in real space when debugging FFTW (no in place)
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integer(C_INTPTR_T), dimension(3) :: gridFFTW
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integer(C_INTPTR_T) :: alloc_local, local_K, local_K_offset
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integer(C_INTPTR_T), parameter :: &
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scalarSize = 1_C_INTPTR_T, &
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vecSize = 3_C_INTPTR_T, &
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tensorSize = 9_C_INTPTR_T
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character(len=*), parameter :: &
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PETSCDEBUG = ' -snes_view -snes_monitor '
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class(tNode) , pointer :: &
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num_grid, &
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debug_grid ! pointer to grid debug options
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print'(/,a)', ' <<<+- spectral_utilities init -+>>>'
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print*, 'Diehl, Diploma Thesis TU München, 2010'
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print*, 'https://doi.org/10.13140/2.1.3234.3840'//IO_EOL
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print*, 'Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013'
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print*, 'https://doi.org/10.1016/j.ijplas.2012.09.012'//IO_EOL
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print*, 'Shanthraj et al., International Journal of Plasticity 66:31–45, 2015'
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print*, 'https://doi.org/10.1016/j.ijplas.2014.02.006'//IO_EOL
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print*, 'Shanthraj et al., Handbook of Mechanics of Materials, 2019'
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print*, 'https://doi.org/10.1007/978-981-10-6855-3_80'
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!--------------------------------------------------------------------------------------------------
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! set debugging parameters
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debug_grid => config_debug%get('grid',defaultVal=emptyList)
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debugGeneral = debug_grid%contains('basic')
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debugRotation = debug_grid%contains('rotation')
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debugPETSc = debug_grid%contains('petsc')
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if(debugPETSc) print'(3(/,a),/)', &
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' Initializing PETSc with debug options: ', &
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trim(PETScDebug), &
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' add more using the PETSc_Options keyword in numerics.yaml '; flush(IO_STDOUT)
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num_grid => config_numerics%get('grid',defaultVal=emptyDict)
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call PETScOptionsClear(PETSC_NULL_OPTIONS,ierr)
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CHKERRQ(ierr)
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if(debugPETSc) call PETScOptionsInsertString(PETSC_NULL_OPTIONS,trim(PETSCDEBUG),ierr)
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CHKERRQ(ierr)
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call PETScOptionsInsertString(PETSC_NULL_OPTIONS,&
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num_grid%get_asString('petsc_options',defaultVal=''),ierr)
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CHKERRQ(ierr)
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grid1Red = grid(1)/2 + 1
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wgt = 1.0/real(product(grid),pReal)
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num%memory_efficient = num_grid%get_asInt('memory_efficient', defaultVal=1) > 0 ! ToDo: should be logical in YAML file
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num%divergence_correction = num_grid%get_asInt('divergence_correction', defaultVal=2)
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if (num%divergence_correction < 0 .or. num%divergence_correction > 2) &
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call IO_error(301,ext_msg='divergence_correction')
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select case (num_grid%get_asString('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%get_asString('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 (num%divergence_correction == 1) 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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enddo
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elseif (num%divergence_correction == 2) then
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do j = 1, 3
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if ( j /= int(minloc(geomSize/real(grid,pReal),1)) &
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.and. j /= int(maxloc(geomSize/real(grid,pReal),1))) &
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scaledGeomSize = geomSize/geomSize(j)*real(grid(j),pReal)
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enddo
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else
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scaledGeomSize = geomSize
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endif
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select case(IO_lc(num_grid%get_asString('fftw_plan_mode',defaultVal='FFTW_MEASURE')))
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case('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')
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FFTW_planner_flag = FFTW_MEASURE
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case('fftw_patient')
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FFTW_planner_flag = FFTW_PATIENT
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case('fftw_exhaustive')
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FFTW_planner_flag = FFTW_EXHAUSTIVE
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case default
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call IO_warning(warning_ID=47,ext_msg=trim(IO_lc(num_grid%get_asString('fftw_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%get_asFloat('fftw_timelimit',defaultVal=-1.0_pReal))
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print*, 'FFTW initialized'; flush(IO_STDOUT)
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!--------------------------------------------------------------------------------------------------
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! MPI allocation
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gridFFTW = int(grid,C_INTPTR_T)
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alloc_local = fftw_mpi_local_size_3d(gridFFTW(3), gridFFTW(2), gridFFTW(1)/2 +1, &
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PETSC_COMM_WORLD, local_K, local_K_offset)
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allocate (xi1st (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for first derivatives, only half the size for first dimension
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allocate (xi2nd (3,grid1Red,grid(2),grid3),source = cmplx(0.0_pReal,0.0_pReal,pReal)) ! frequencies for second derivatives, only half the size for first dimension
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tensorField = fftw_alloc_complex(tensorSize*alloc_local)
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call c_f_pointer(tensorField, tensorField_real, [3_C_INTPTR_T,3_C_INTPTR_T, &
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2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T),gridFFTW(2),local_K]) ! place a pointer for a real tensor representation
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call c_f_pointer(tensorField, tensorField_fourier, [3_C_INTPTR_T,3_C_INTPTR_T, &
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gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T , gridFFTW(2),local_K]) ! place a pointer for a fourier tensor representation
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vectorField = fftw_alloc_complex(vecSize*alloc_local)
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call c_f_pointer(vectorField, vectorField_real, [3_C_INTPTR_T,&
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2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T),gridFFTW(2),local_K]) ! place a pointer for a real vector representation
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call c_f_pointer(vectorField, vectorField_fourier,[3_C_INTPTR_T,&
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gridFFTW(1)/2_C_INTPTR_T + 1_C_INTPTR_T, gridFFTW(2),local_K]) ! place a pointer for a fourier vector representation
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scalarField = fftw_alloc_complex(scalarSize*alloc_local) ! allocate data for real representation (no in place transform)
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call c_f_pointer(scalarField, scalarField_real, &
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[2_C_INTPTR_T*(gridFFTW(1)/2_C_INTPTR_T + 1),gridFFTW(2),local_K]) ! place a pointer for a real scalar representation
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call c_f_pointer(scalarField, scalarField_fourier, &
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[ gridFFTW(1)/2_C_INTPTR_T + 1 ,gridFFTW(2),local_K]) ! place a pointer for a fourier scarlar representation
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!--------------------------------------------------------------------------------------------------
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! tensor MPI fftw plans
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planTensorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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tensorField_real, tensorField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planTensorForth)) call IO_error(810, ext_msg='planTensorForth')
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planTensorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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tensorSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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tensorField_fourier,tensorField_real, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! all processors, planer precision
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if (.not. C_ASSOCIATED(planTensorBack)) call IO_error(810, ext_msg='planTensorBack')
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!--------------------------------------------------------------------------------------------------
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! vector MPI fftw plans
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planVectorForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK,&! no. of transforms, default iblock and oblock
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vectorField_real, vectorField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planVectorForth)) call IO_error(810, ext_msg='planVectorForth')
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planVectorBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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vecSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, & ! no. of transforms, default iblock and oblock
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vectorField_fourier,vectorField_real, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! all processors, planer precision
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if (.not. C_ASSOCIATED(planVectorBack)) call IO_error(810, ext_msg='planVectorBack')
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!--------------------------------------------------------------------------------------------------
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! scalar MPI fftw plans
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planScalarForth = fftw_mpi_plan_many_dft_r2c(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order
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scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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scalarField_real, scalarField_fourier, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planScalarForth)) call IO_error(810, ext_msg='planScalarForth')
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planScalarBack = fftw_mpi_plan_many_dft_c2r(3, [gridFFTW(3),gridFFTW(2),gridFFTW(1)], & ! dimension, logical length in each dimension in reversed order, no. of transforms
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scalarSize, FFTW_MPI_DEFAULT_BLOCK, FFTW_MPI_DEFAULT_BLOCK, &! no. of transforms, default iblock and oblock
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scalarField_fourier,scalarField_real, & ! input data, output data
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PETSC_COMM_WORLD, FFTW_planner_flag) ! use all processors, planer precision
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if (.not. C_ASSOCIATED(planScalarBack)) call IO_error(810, ext_msg='planScalarBack')
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!--------------------------------------------------------------------------------------------------
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! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
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do k = grid3Offset+1, grid3Offset+grid3
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k_s(3) = k - 1
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if(k > grid(3)/2 + 1) k_s(3) = k_s(3) - grid(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do j = 1, grid(2)
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k_s(2) = j - 1
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if(j > grid(2)/2 + 1) k_s(2) = k_s(2) - grid(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do i = 1, grid1Red
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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,j,k-grid3Offset) = utilities_getFreqDerivative(k_s)
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where(mod(grid,2)==0 .and. [i,j,k] == grid/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,j,k-grid3Offset) = cmplx(0.0_pReal,0.0_pReal,pReal)
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elsewhere
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xi1st(1:3,i,j,k-grid3Offset) = xi2nd(1:3,i,j,k-grid3Offset)
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endwhere
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enddo; enddo; enddo
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if(num%memory_efficient) then ! allocate just single fourth order tensor
|
||
allocate (gamma_hat(3,3,3,3,1,1,1), source = cmplx(0.0_pReal,0.0_pReal,pReal))
|
||
else ! precalculation of gamma_hat field
|
||
allocate (gamma_hat(3,3,3,3,grid1Red,grid(2),grid3), source = cmplx(0.0_pReal,0.0_pReal,pReal))
|
||
endif
|
||
|
||
end subroutine spectral_utilities_init
|
||
|
||
|
||
!---------------------------------------------------------------------------------------------------
|
||
!> @brief updates reference stiffness and potentially precalculated gamma operator
|
||
!> @details Sets the current reference stiffness to the stiffness given as an argument.
|
||
!> If the gamma operator is precalculated, it is calculated with this stiffness.
|
||
!> In case of an on-the-fly calculation, only the reference stiffness is updated.
|
||
!---------------------------------------------------------------------------------------------------
|
||
subroutine utilities_updateGamma(C)
|
||
|
||
real(pReal), intent(in), dimension(3,3,3,3) :: C !< input stiffness to store as reference stiffness
|
||
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
|
||
real(pReal), dimension(6,6) :: A, A_inv
|
||
integer :: &
|
||
i, j, k, &
|
||
l, m, n, o
|
||
logical :: err
|
||
|
||
C_ref = C
|
||
|
||
if(.not. num%memory_efficient) then
|
||
gamma_hat = cmplx(0.0_pReal,0.0_pReal,pReal) ! for the singular point and any non invertible A
|
||
do k = grid3Offset+1, grid3Offset+grid3; do j = 1, grid(2); do i = 1, grid1Red
|
||
if (any([i,j,k] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
||
forall(l = 1:3, m = 1:3) &
|
||
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
|
||
forall(l = 1:3, m = 1:3) &
|
||
temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
|
||
A(1:3,1:3) = real(temp33_complex); A(4:6,4:6) = real(temp33_complex)
|
||
A(1:3,4:6) = aimag(temp33_complex); A(4:6,1:3) = -aimag(temp33_complex)
|
||
if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
|
||
call math_invert(A_inv, err, A)
|
||
temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
|
||
forall(l=1:3, m=1:3, n=1:3, o=1:3) &
|
||
gamma_hat(l,m,n,o,i,j,k-grid3Offset) = temp33_complex(l,n)* &
|
||
conjg(-xi1st(o,i,j,k-grid3Offset))*xi1st(m,i,j,k-grid3Offset)
|
||
endif
|
||
endif
|
||
enddo; enddo; enddo
|
||
endif
|
||
|
||
end subroutine utilities_updateGamma
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief forward FFT of data in field_real to field_fourier
|
||
!> @details Does an unweighted FFT transform from real to complex. Extra padding entries are set
|
||
! to 0.0
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTtensorForward
|
||
|
||
tensorField_real(1:3,1:3,grid(1)+1:grid1Red*2,:,:) = 0.0_pReal
|
||
call fftw_mpi_execute_dft_r2c(planTensorForth,tensorField_real,tensorField_fourier)
|
||
|
||
end subroutine utilities_FFTtensorForward
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief backward FFT of data in field_fourier to field_real
|
||
!> @details Does an weighted inverse FFT transform from complex to real
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTtensorBackward
|
||
|
||
call fftw_mpi_execute_dft_c2r(planTensorBack,tensorField_fourier,tensorField_real)
|
||
tensorField_real = tensorField_real * wgt ! normalize the result by number of elements
|
||
|
||
end subroutine utilities_FFTtensorBackward
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief forward FFT of data in scalarField_real to scalarField_fourier
|
||
!> @details Does an unweighted FFT transform from real to complex. Extra padding entries are set
|
||
! to 0.0
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTscalarForward
|
||
|
||
scalarField_real(grid(1)+1:grid1Red*2,:,:) = 0.0_pReal
|
||
call fftw_mpi_execute_dft_r2c(planScalarForth,scalarField_real,scalarField_fourier)
|
||
|
||
end subroutine utilities_FFTscalarForward
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief backward FFT of data in scalarField_fourier to scalarField_real
|
||
!> @details Does an weighted inverse FFT transform from complex to real
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTscalarBackward
|
||
|
||
call fftw_mpi_execute_dft_c2r(planScalarBack,scalarField_fourier,scalarField_real)
|
||
scalarField_real = scalarField_real * wgt ! normalize the result by number of elements
|
||
|
||
end subroutine utilities_FFTscalarBackward
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
|
||
!> @details Does an unweighted FFT transform from real to complex. Extra padding entries are set
|
||
! to 0.0
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTvectorForward
|
||
|
||
vectorField_real(1:3,grid(1)+1:grid1Red*2,:,:) = 0.0_pReal
|
||
call fftw_mpi_execute_dft_r2c(planVectorForth,vectorField_real,vectorField_fourier)
|
||
|
||
end subroutine utilities_FFTvectorForward
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief backward FFT of data in field_fourier to field_real
|
||
!> @details Does an weighted inverse FFT transform from complex to real
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_FFTvectorBackward
|
||
|
||
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
|
||
vectorField_real = vectorField_real * wgt ! normalize the result by number of elements
|
||
|
||
end subroutine utilities_FFTvectorBackward
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief doing convolution gamma_hat * field_real, ensuring that average value = fieldAim
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierGammaConvolution(fieldAim)
|
||
|
||
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
|
||
complex(pReal), dimension(3,3) :: temp33_complex, xiDyad_cmplx
|
||
real(pReal), dimension(6,6) :: A, A_inv
|
||
|
||
integer :: &
|
||
i, j, k, &
|
||
l, m, n, o
|
||
logical :: err
|
||
|
||
|
||
print'(/,a)', ' ... doing gamma convolution ...............................................'
|
||
flush(IO_STDOUT)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! do the actual spectral method calculation (mechanical equilibrium)
|
||
memoryEfficient: if(num%memory_efficient) then
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1, grid1Red
|
||
if (any([i,j,k+grid3Offset] /= 1)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
||
forall(l = 1:3, m = 1:3) &
|
||
xiDyad_cmplx(l,m) = conjg(-xi1st(l,i,j,k))*xi1st(m,i,j,k)
|
||
forall(l = 1:3, m = 1:3) &
|
||
temp33_complex(l,m) = sum(cmplx(C_ref(l,1:3,m,1:3),0.0_pReal)*xiDyad_cmplx)
|
||
A(1:3,1:3) = real(temp33_complex); A(4:6,4:6) = real(temp33_complex)
|
||
A(1:3,4:6) = aimag(temp33_complex); A(4:6,1:3) = -aimag(temp33_complex)
|
||
if (abs(math_det33(A(1:3,1:3))) > 1e-16) then
|
||
call math_invert(A_inv, err, A)
|
||
temp33_complex = cmplx(A_inv(1:3,1:3),A_inv(1:3,4:6),pReal)
|
||
forall(l=1:3, m=1:3, n=1:3, o=1:3) &
|
||
gamma_hat(l,m,n,o,1,1,1) = temp33_complex(l,n)*conjg(-xi1st(o,i,j,k))*xi1st(m,i,j,k)
|
||
else
|
||
gamma_hat(1:3,1:3,1:3,1:3,1,1,1) = cmplx(0.0_pReal,0.0_pReal,pReal)
|
||
endif
|
||
forall(l = 1:3, m = 1:3) &
|
||
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,1,1,1)*tensorField_fourier(1:3,1:3,i,j,k))
|
||
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
|
||
endif
|
||
enddo; enddo; enddo
|
||
else memoryEfficient
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red
|
||
forall(l = 1:3, m = 1:3) &
|
||
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3,i,j,k) * tensorField_fourier(1:3,1:3,i,j,k))
|
||
tensorField_fourier(1:3,1:3,i,j,k) = temp33_Complex
|
||
enddo; enddo; enddo
|
||
endif memoryEfficient
|
||
|
||
if (grid3Offset == 0) tensorField_fourier(1:3,1:3,1,1,1) = cmplx(fieldAim/wgt,0.0_pReal,pReal)
|
||
|
||
end subroutine utilities_fourierGammaConvolution
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief doing convolution DamageGreenOp_hat * field_real
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierGreenConvolution(D_ref, mobility_ref, deltaT)
|
||
|
||
real(pReal), dimension(3,3), intent(in) :: D_ref
|
||
real(pReal), intent(in) :: mobility_ref, deltaT
|
||
complex(pReal) :: GreenOp_hat
|
||
integer :: i, j, k
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! do the actual spectral method calculation
|
||
do k = 1, grid3; do j = 1, grid(2) ;do i = 1, grid1Red
|
||
GreenOp_hat = cmplx(1.0_pReal,0.0_pReal,pReal)/ &
|
||
(cmplx(mobility_ref,0.0_pReal,pReal) + cmplx(deltaT,0.0_pReal)*&
|
||
sum(conjg(xi1st(1:3,i,j,k))* matmul(cmplx(D_ref,0.0_pReal),xi1st(1:3,i,j,k))))
|
||
scalarField_fourier(i,j,k) = scalarField_fourier(i,j,k)*GreenOp_hat
|
||
enddo; enddo; enddo
|
||
|
||
end subroutine utilities_fourierGreenConvolution
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate root mean square of divergence of field_fourier
|
||
!--------------------------------------------------------------------------------------------------
|
||
real(pReal) function utilities_divergenceRMS()
|
||
|
||
integer :: i, j, k, ierr
|
||
complex(pReal), dimension(3) :: rescaledGeom
|
||
|
||
print'(/,a)', ' ... calculating divergence ................................................'
|
||
flush(IO_STDOUT)
|
||
|
||
rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! calculating RMS divergence criterion in Fourier space
|
||
utilities_divergenceRMS = 0.0_pReal
|
||
do k = 1, grid3; do j = 1, grid(2)
|
||
do i = 2, grid1Red -1 ! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
||
utilities_divergenceRMS = utilities_divergenceRMS &
|
||
+ 2.0_pReal*(sum (real(matmul(tensorField_fourier(1:3,1:3,i,j,k),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
|
||
conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
||
+sum(aimag(matmul(tensorField_fourier(1:3,1:3,i,j,k),&
|
||
conjg(-xi1st(1:3,i,j,k))*rescaledGeom))**2.0_pReal))
|
||
enddo
|
||
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart (if grid(1) /= 1)
|
||
+ sum( real(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
|
||
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,1 ,j,k), &
|
||
conjg(-xi1st(1:3,1,j,k))*rescaledGeom))**2.0_pReal) &
|
||
+ sum( real(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal) &
|
||
+ sum(aimag(matmul(tensorField_fourier(1:3,1:3,grid1Red,j,k), &
|
||
conjg(-xi1st(1:3,grid1Red,j,k))*rescaledGeom))**2.0_pReal)
|
||
enddo; enddo
|
||
if(grid(1) == 1) utilities_divergenceRMS = utilities_divergenceRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
|
||
call MPI_Allreduce(MPI_IN_PLACE,utilities_divergenceRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='utilities_divergenceRMS')
|
||
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) * wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
|
||
|
||
|
||
end function utilities_divergenceRMS
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate max of curl of field_fourier
|
||
!--------------------------------------------------------------------------------------------------
|
||
real(pReal) function utilities_curlRMS()
|
||
|
||
integer :: i, j, k, l, ierr
|
||
complex(pReal), dimension(3,3) :: curl_fourier
|
||
complex(pReal), dimension(3) :: rescaledGeom
|
||
|
||
print'(/,a)', ' ... calculating curl ......................................................'
|
||
flush(IO_STDOUT)
|
||
|
||
rescaledGeom = cmplx(geomSize/scaledGeomSize,0.0_pReal)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! calculating max curl criterion in Fourier space
|
||
utilities_curlRMS = 0.0_pReal
|
||
|
||
do k = 1, grid3; do j = 1, grid(2);
|
||
do i = 2, grid1Red - 1
|
||
do l = 1, 3
|
||
curl_fourier(l,1) = (+tensorField_fourier(l,3,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2) &
|
||
-tensorField_fourier(l,2,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3))
|
||
curl_fourier(l,2) = (+tensorField_fourier(l,1,i,j,k)*xi1st(3,i,j,k)*rescaledGeom(3) &
|
||
-tensorField_fourier(l,3,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1))
|
||
curl_fourier(l,3) = (+tensorField_fourier(l,2,i,j,k)*xi1st(1,i,j,k)*rescaledGeom(1) &
|
||
-tensorField_fourier(l,1,i,j,k)*xi1st(2,i,j,k)*rescaledGeom(2))
|
||
enddo
|
||
utilities_curlRMS = utilities_curlRMS &
|
||
+2.0_pReal*sum(real(curl_fourier)**2.0_pReal+aimag(curl_fourier)**2.0_pReal)! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
||
enddo
|
||
do l = 1, 3
|
||
curl_fourier = (+tensorField_fourier(l,3,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2) &
|
||
-tensorField_fourier(l,2,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3))
|
||
curl_fourier = (+tensorField_fourier(l,1,1,j,k)*xi1st(3,1,j,k)*rescaledGeom(3) &
|
||
-tensorField_fourier(l,3,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1))
|
||
curl_fourier = (+tensorField_fourier(l,2,1,j,k)*xi1st(1,1,j,k)*rescaledGeom(1) &
|
||
-tensorField_fourier(l,1,1,j,k)*xi1st(2,1,j,k)*rescaledGeom(2))
|
||
enddo
|
||
utilities_curlRMS = utilities_curlRMS &
|
||
+ sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal) ! this layer (DC) does not have a conjugate complex counterpart (if grid(1) /= 1)
|
||
do l = 1, 3
|
||
curl_fourier = (+tensorField_fourier(l,3,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2) &
|
||
-tensorField_fourier(l,2,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3))
|
||
curl_fourier = (+tensorField_fourier(l,1,grid1Red,j,k)*xi1st(3,grid1Red,j,k)*rescaledGeom(3) &
|
||
-tensorField_fourier(l,3,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1))
|
||
curl_fourier = (+tensorField_fourier(l,2,grid1Red,j,k)*xi1st(1,grid1Red,j,k)*rescaledGeom(1) &
|
||
-tensorField_fourier(l,1,grid1Red,j,k)*xi1st(2,grid1Red,j,k)*rescaledGeom(2))
|
||
enddo
|
||
utilities_curlRMS = utilities_curlRMS &
|
||
+ sum(real(curl_fourier)**2.0_pReal + aimag(curl_fourier)**2.0_pReal) ! this layer (Nyquist) does not have a conjugate complex counterpart (if grid(1) /= 1)
|
||
enddo; enddo
|
||
|
||
call MPI_Allreduce(MPI_IN_PLACE,utilities_curlRMS,1,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='utilities_curlRMS')
|
||
utilities_curlRMS = sqrt(utilities_curlRMS) * wgt
|
||
if(grid(1) == 1) utilities_curlRMS = utilities_curlRMS * 0.5_pReal ! counted twice in case of grid(1) == 1
|
||
|
||
end function utilities_curlRMS
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates mask compliance tensor used to adjust F to fullfill stress BC
|
||
!--------------------------------------------------------------------------------------------------
|
||
function utilities_maskedCompliance(rot_BC,mask_stress,C)
|
||
|
||
real(pReal), dimension(3,3,3,3) :: utilities_maskedCompliance !< masked compliance
|
||
real(pReal), intent(in), dimension(3,3,3,3) :: C !< current average stiffness
|
||
type(rotation), intent(in) :: rot_BC !< rotation of load frame
|
||
logical, intent(in), dimension(3,3) :: mask_stress !< mask of stress BC
|
||
|
||
integer :: i, j
|
||
logical, dimension(9) :: mask_stressVector
|
||
logical, dimension(9,9) :: mask
|
||
real(pReal), dimension(9,9) :: temp99_real
|
||
integer :: size_reduced = 0
|
||
real(pReal), dimension(:,:), allocatable :: &
|
||
s_reduced, & !< reduced compliance matrix (depending on number of stress BC)
|
||
c_reduced, & !< reduced stiffness (depending on number of stress BC)
|
||
sTimesC !< temp variable to check inversion
|
||
logical :: errmatinv
|
||
character(len=pStringLen):: formatString
|
||
|
||
mask_stressVector = reshape(transpose(mask_stress), [9])
|
||
size_reduced = count(mask_stressVector)
|
||
if(size_reduced > 0) then
|
||
temp99_real = math_3333to99(rot_BC%rotate(C))
|
||
|
||
if(debugGeneral) then
|
||
print'(/,a)', ' ... updating masked compliance ............................................'
|
||
write(IO_STDOUT,'(/,a,/,9(9(2x,f12.7,1x)/))',advance='no') ' Stiffness C (load) / GPa =',&
|
||
transpose(temp99_Real)*1.0e-9_pReal
|
||
flush(IO_STDOUT)
|
||
endif
|
||
|
||
do i = 1,9; do j = 1,9
|
||
mask(i,j) = mask_stressVector(i) .and. mask_stressVector(j)
|
||
enddo; enddo
|
||
c_reduced = reshape(pack(temp99_Real,mask),[size_reduced,size_reduced])
|
||
|
||
allocate(s_reduced,mold = c_reduced)
|
||
call math_invert(s_reduced, errmatinv, c_reduced) ! invert reduced stiffness
|
||
if (any(IEEE_is_NaN(s_reduced))) errmatinv = .true.
|
||
if (errmatinv) call IO_error(error_ID=400,ext_msg='utilities_maskedCompliance')
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! check if inversion was successful
|
||
sTimesC = matmul(c_reduced,s_reduced)
|
||
errmatinv = errmatinv .or. any(dNeq(sTimesC,math_eye(size_reduced),1.0e-12_pReal))
|
||
if (debugGeneral .or. errmatinv) then
|
||
write(formatString, '(i2)') size_reduced
|
||
formatString = '(/,a,/,'//trim(formatString)//'('//trim(formatString)//'(2x,es9.2,1x)/))'
|
||
write(IO_STDOUT,trim(formatString),advance='no') ' C * S (load) ', &
|
||
transpose(matmul(c_reduced,s_reduced))
|
||
write(IO_STDOUT,trim(formatString),advance='no') ' S (load) ', transpose(s_reduced)
|
||
if(errmatinv) call IO_error(error_ID=400,ext_msg='utilities_maskedCompliance')
|
||
endif
|
||
temp99_real = reshape(unpack(reshape(s_reduced,[size_reduced**2]),reshape(mask,[81]),0.0_pReal),[9,9])
|
||
else
|
||
temp99_real = 0.0_pReal
|
||
endif
|
||
|
||
utilities_maskedCompliance = math_99to3333(temp99_Real)
|
||
|
||
if(debugGeneral) then
|
||
write(IO_STDOUT,'(/,a,/,9(9(2x,f10.5,1x)/),/)',advance='no') &
|
||
' Masked Compliance (load) * GPa =', transpose(temp99_Real)*1.0e9_pReal
|
||
flush(IO_STDOUT)
|
||
endif
|
||
|
||
end function utilities_maskedCompliance
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate scalar gradient in fourier field
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierScalarGradient()
|
||
|
||
integer :: i, j, k
|
||
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red
|
||
vectorField_fourier(1:3,i,j,k) = scalarField_fourier(i,j,k)*xi1st(1:3,i,j,k) ! ToDo: no -conjg?
|
||
enddo; enddo; enddo
|
||
|
||
end subroutine utilities_fourierScalarGradient
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate vector divergence in fourier field
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierVectorDivergence()
|
||
|
||
integer :: i, j, k
|
||
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red
|
||
scalarField_fourier(i,j,k) = sum(vectorField_fourier(1:3,i,j,k)*conjg(-xi1st(1:3,i,j,k)))
|
||
enddo; enddo; enddo
|
||
|
||
end subroutine utilities_fourierVectorDivergence
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate vector gradient in fourier field
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierVectorGradient()
|
||
|
||
integer :: i, j, k, m, n
|
||
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red
|
||
do m = 1, 3; do n = 1, 3
|
||
tensorField_fourier(m,n,i,j,k) = vectorField_fourier(m,i,j,k)*xi1st(n,i,j,k)
|
||
enddo; enddo
|
||
enddo; enddo; enddo
|
||
|
||
end subroutine utilities_fourierVectorGradient
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate tensor divergence in fourier field
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_fourierTensorDivergence()
|
||
|
||
integer :: i, j, k
|
||
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1,grid1Red
|
||
vectorField_fourier(:,i,j,k) = matmul(tensorField_fourier(:,:,i,j,k),conjg(-xi1st(:,i,j,k)))
|
||
enddo; enddo; enddo
|
||
|
||
end subroutine utilities_fourierTensorDivergence
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate constitutive response from homogenization_F0 to F during timeinc
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_constitutiveResponse(P,P_av,C_volAvg,C_minmaxAvg,&
|
||
F,timeinc,rotation_BC)
|
||
|
||
real(pReal), intent(out), dimension(3,3,3,3) :: C_volAvg, C_minmaxAvg !< average stiffness
|
||
real(pReal), intent(out), dimension(3,3) :: P_av !< average PK stress
|
||
real(pReal), intent(out), dimension(3,3,grid(1),grid(2),grid3) :: P !< PK stress
|
||
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: F !< deformation gradient target
|
||
real(pReal), intent(in) :: timeinc !< loading time
|
||
type(rotation), intent(in), optional :: rotation_BC !< rotation of load frame
|
||
|
||
|
||
integer :: &
|
||
i,ierr
|
||
real(pReal), dimension(3,3,3,3) :: dPdF_max, dPdF_min
|
||
real(pReal) :: dPdF_norm_max, dPdF_norm_min
|
||
real(pReal), dimension(2) :: valueAndRank !< pair of min/max norm of dPdF to synchronize min/max of dPdF
|
||
|
||
print'(/,a)', ' ... evaluating constitutive response ......................................'
|
||
flush(IO_STDOUT)
|
||
|
||
homogenization_F = reshape(F,[3,3,1,product(grid(1:2))*grid3]) ! set materialpoint target F to estimated field
|
||
|
||
call materialpoint_stressAndItsTangent(timeinc) ! calculate P field
|
||
|
||
P = reshape(homogenization_P, [3,3,grid(1),grid(2),grid3])
|
||
P_av = sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt ! average of P
|
||
call MPI_Allreduce(MPI_IN_PLACE,P_av,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||
if (debugRotation) &
|
||
write(IO_STDOUT,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' Piola--Kirchhoff stress (lab) / MPa =',&
|
||
transpose(P_av)*1.e-6_pReal
|
||
if(present(rotation_BC)) &
|
||
P_av = rotation_BC%rotate(P_av)
|
||
write(IO_STDOUT,'(/,a,/,3(3(2x,f12.4,1x)/))',advance='no') ' 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(grid(1:2))*grid3
|
||
if (dPdF_norm_max < sum(homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)) then
|
||
dPdF_max = homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)
|
||
dPdF_norm_max = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)
|
||
endif
|
||
if (dPdF_norm_min > sum(homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)) then
|
||
dPdF_min = homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)
|
||
dPdF_norm_min = sum(homogenization_dPdF(1:3,1:3,1:3,1:3,1,i)**2.0_pReal)
|
||
endif
|
||
end do
|
||
|
||
valueAndRank = [dPdF_norm_max,real(worldrank,pReal)]
|
||
call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1, MPI_2DOUBLE_PRECISION, MPI_MAXLOC, PETSC_COMM_WORLD, ierr)
|
||
if (ierr /= 0) call IO_error(894, ext_msg='MPI_Allreduce max')
|
||
call MPI_Bcast(dPdF_max,81,MPI_DOUBLE,int(valueAndRank(2)),PETSC_COMM_WORLD, ierr)
|
||
if (ierr /= 0) call IO_error(894, ext_msg='MPI_Bcast max')
|
||
|
||
valueAndRank = [dPdF_norm_min,real(worldrank,pReal)]
|
||
call MPI_Allreduce(MPI_IN_PLACE,valueAndRank,1, MPI_2DOUBLE_PRECISION, MPI_MINLOC, PETSC_COMM_WORLD, ierr)
|
||
if (ierr /= 0) call IO_error(894, ext_msg='MPI_Allreduce min')
|
||
call MPI_Bcast(dPdF_min,81,MPI_DOUBLE,int(valueAndRank(2)),PETSC_COMM_WORLD, ierr)
|
||
if (ierr /= 0) call IO_error(894, ext_msg='MPI_Bcast min')
|
||
|
||
C_minmaxAvg = 0.5_pReal*(dPdF_max + dPdF_min)
|
||
|
||
C_volAvg = sum(sum(homogenization_dPdF,dim=6),dim=5)
|
||
call MPI_Allreduce(MPI_IN_PLACE,C_volAvg,81,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||
C_volAvg = C_volAvg * wgt
|
||
|
||
|
||
end subroutine utilities_constitutiveResponse
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates forward rate, either guessing or just add delta/timeinc
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function utilities_calculateRate(heterogeneous,field0,field,dt,avRate)
|
||
|
||
real(pReal), intent(in), dimension(3,3) :: &
|
||
avRate !< homogeneous addon
|
||
real(pReal), intent(in) :: &
|
||
dt !< timeinc between field0 and field
|
||
logical, intent(in) :: &
|
||
heterogeneous !< calculate field of rates
|
||
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
|
||
field0, & !< data of previous step
|
||
field !< data of current step
|
||
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: &
|
||
utilities_calculateRate
|
||
|
||
if (heterogeneous) then
|
||
utilities_calculateRate = (field-field0) / dt
|
||
else
|
||
utilities_calculateRate = spread(spread(spread(avRate,3,grid(1)),4,grid(2)),5,grid3)
|
||
endif
|
||
|
||
end function utilities_calculateRate
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief forwards a field with a pointwise given rate, if aim is given,
|
||
!> ensures that the average matches the aim
|
||
!--------------------------------------------------------------------------------------------------
|
||
function utilities_forwardField(timeinc,field_lastInc,rate,aim)
|
||
|
||
real(pReal), intent(in) :: &
|
||
timeinc !< timeinc of current step
|
||
real(pReal), intent(in), dimension(3,3,grid(1),grid(2),grid3) :: &
|
||
field_lastInc, & !< initial field
|
||
rate !< rate by which to forward
|
||
real(pReal), intent(in), optional, dimension(3,3) :: &
|
||
aim !< average field value aim
|
||
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: &
|
||
utilities_forwardField
|
||
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
|
||
PetscErrorCode :: ierr
|
||
|
||
utilities_forwardField = field_lastInc + rate*timeinc
|
||
if (present(aim)) then !< correct to match average
|
||
fieldDiff = sum(sum(sum(utilities_forwardField,dim=5),dim=4),dim=3)*wgt
|
||
call MPI_Allreduce(MPI_IN_PLACE,fieldDiff,9,MPI_DOUBLE,MPI_SUM,PETSC_COMM_WORLD,ierr)
|
||
fieldDiff = fieldDiff - aim
|
||
utilities_forwardField = utilities_forwardField - &
|
||
spread(spread(spread(fieldDiff,3,grid(1)),4,grid(2)),5,grid3)
|
||
endif
|
||
|
||
end function utilities_forwardField
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
|
||
!> @details this is the full operator to calculate derivatives, i.e. 2 \pi i k for the
|
||
! standard approach
|
||
!--------------------------------------------------------------------------------------------------
|
||
pure function utilities_getFreqDerivative(k_s)
|
||
|
||
integer, intent(in), dimension(3) :: k_s !< indices of frequency
|
||
complex(pReal), dimension(3) :: utilities_getFreqDerivative
|
||
|
||
select case (spectral_derivative_ID)
|
||
case (DERIVATIVE_CONTINUOUS_ID)
|
||
utilities_getFreqDerivative = cmplx(0.0_pReal, 2.0_pReal*PI*real(k_s,pReal)/geomSize,pReal)
|
||
|
||
case (DERIVATIVE_CENTRAL_DIFF_ID)
|
||
utilities_getFreqDerivative = cmplx(0.0_pReal, sin(2.0_pReal*PI*real(k_s,pReal)/real(grid,pReal)), pReal)/ &
|
||
cmplx(2.0_pReal*geomSize/real(grid,pReal), 0.0_pReal, pReal)
|
||
|
||
case (DERIVATIVE_FWBW_DIFF_ID)
|
||
utilities_getFreqDerivative(1) = &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) - 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||
cmplx(4.0_pReal*geomSize(1)/real(grid(1),pReal), 0.0_pReal, pReal)
|
||
utilities_getFreqDerivative(2) = &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) - 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||
cmplx(4.0_pReal*geomSize(2)/real(grid(2),pReal), 0.0_pReal, pReal)
|
||
utilities_getFreqDerivative(3) = &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(1),pReal)/real(grid(1),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)) + 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(2),pReal)/real(grid(2),pReal)), pReal)* &
|
||
cmplx(cos(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)) - 1.0_pReal, &
|
||
sin(2.0_pReal*PI*real(k_s(3),pReal)/real(grid(3),pReal)), pReal)/ &
|
||
cmplx(4.0_pReal*geomSize(3)/real(grid(3),pReal), 0.0_pReal, pReal)
|
||
end select
|
||
|
||
end function utilities_getFreqDerivative
|
||
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
!> @brief calculate coordinates in current configuration for given defgrad field
|
||
! using integration in Fourier space. Similar as in mesh.f90, but using data already defined for
|
||
! convolution
|
||
!--------------------------------------------------------------------------------------------------
|
||
subroutine utilities_updateCoords(F)
|
||
|
||
real(pReal), dimension(3,3,grid(1),grid(2),grid3), intent(in) :: F
|
||
real(pReal), dimension(3, grid(1),grid(2),grid3) :: IPcoords
|
||
real(pReal), dimension(3, grid(1),grid(2),grid3+2) :: IPfluct_padded ! Fluctuations of cell center displacement (padded along z for MPI)
|
||
real(pReal), dimension(3, grid(1)+1,grid(2)+1,grid3+1) :: nodeCoords
|
||
integer :: &
|
||
i,j,k,n, &
|
||
rank_t, &
|
||
rank_b, &
|
||
c, r, &
|
||
ierr
|
||
integer, dimension(MPI_STATUS_SIZE) :: &
|
||
s
|
||
real(pReal), dimension(3) :: step
|
||
real(pReal), dimension(3,3) :: Favg
|
||
integer, dimension(3) :: me
|
||
integer, dimension(3,8) :: &
|
||
neighbor = reshape([ &
|
||
0, 0, 0, &
|
||
1, 0, 0, &
|
||
1, 1, 0, &
|
||
0, 1, 0, &
|
||
0, 0, 1, &
|
||
1, 0, 1, &
|
||
1, 1, 1, &
|
||
0, 1, 1 ], [3,8])
|
||
|
||
step = geomSize/real(grid, pReal)
|
||
!--------------------------------------------------------------------------------------------------
|
||
! integration in Fourier space to get fluctuations of cell center discplacements
|
||
tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = F
|
||
call utilities_FFTtensorForward()
|
||
|
||
do k = 1, grid3; do j = 1, grid(2); do i = 1, grid1Red
|
||
if(any([i,j,k+grid3Offset] /= 1)) then
|
||
vectorField_fourier(1:3,i,j,k) = matmul(tensorField_fourier(1:3,1:3,i,j,k),xi2nd(1:3,i,j,k)) &
|
||
/ sum(conjg(-xi2nd(1:3,i,j,k))*xi2nd(1:3,i,j,k)) * cmplx(wgt,0.0,pReal)
|
||
else
|
||
vectorField_fourier(1:3,i,j,k) = cmplx(0.0,0.0,pReal)
|
||
endif
|
||
enddo; enddo; enddo
|
||
|
||
call fftw_mpi_execute_dft_c2r(planVectorBack,vectorField_fourier,vectorField_real)
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! average F
|
||
if (grid3Offset == 0) Favg = real(tensorField_fourier(1:3,1:3,1,1,1),pReal)*wgt
|
||
call MPI_Bcast(Favg,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Bcast')
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! pad cell center fluctuations along z-direction (needed when running MPI simulation)
|
||
IPfluct_padded(1:3,1:grid(1),1:grid(2),2:grid3+1) = vectorField_real(1:3,1:grid(1),1:grid(2),1:grid3)
|
||
c = product(shape(IPfluct_padded(:,:,:,1))) !< amount of data to transfer
|
||
rank_t = modulo(worldrank+1,worldsize)
|
||
rank_b = modulo(worldrank-1,worldsize)
|
||
|
||
! send bottom layer to process below
|
||
call MPI_Isend(IPfluct_padded(:,:,:,2), c,MPI_DOUBLE,rank_b,0,PETSC_COMM_WORLD,r,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Isend')
|
||
call MPI_Irecv(IPfluct_padded(:,:,:,grid3+2),c,MPI_DOUBLE,rank_t,0,PETSC_COMM_WORLD,r,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Irecv')
|
||
call MPI_Wait(r,s,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Wait')
|
||
|
||
! send top layer to process above
|
||
call MPI_Isend(IPfluct_padded(:,:,:,grid3+1),c,MPI_DOUBLE,rank_t,0,PETSC_COMM_WORLD,r,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Isend')
|
||
call MPI_Irecv(IPfluct_padded(:,:,:,1), c,MPI_DOUBLE,rank_b,0,PETSC_COMM_WORLD,r,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Irecv')
|
||
call MPI_Wait(r,s,ierr)
|
||
if(ierr /=0) call IO_error(894, ext_msg='update_IPcoords/MPI_Wait')
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! calculate nodal displacements
|
||
nodeCoords = 0.0_pReal
|
||
do k = 0,grid3; do j = 0,grid(2); do i = 0,grid(1)
|
||
nodeCoords(1:3,i+1,j+1,k+1) = matmul(Favg,step*(real([i,j,k+grid3Offset],pReal)))
|
||
averageFluct: do n = 1,8
|
||
me = [i+neighbor(1,n),j+neighbor(2,n),k+neighbor(3,n)]
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||
nodeCoords(1:3,i+1,j+1,k+1) = nodeCoords(1:3,i+1,j+1,k+1) &
|
||
+ IPfluct_padded(1:3,modulo(me(1)-1,grid(1))+1,modulo(me(2)-1,grid(2))+1,me(3)+1)*0.125_pReal
|
||
enddo averageFluct
|
||
enddo; enddo; enddo
|
||
|
||
!--------------------------------------------------------------------------------------------------
|
||
! calculate cell center displacements
|
||
do k = 1,grid3; do j = 1,grid(2); do i = 1,grid(1)
|
||
IPcoords(1:3,i,j,k) = vectorField_real(1:3,i,j,k) &
|
||
+ matmul(Favg,step*(real([i,j,k+grid3Offset],pReal)-0.5_pReal))
|
||
enddo; enddo; enddo
|
||
|
||
call discretization_setNodeCoords(reshape(NodeCoords,[3,(grid(1)+1)*(grid(2)+1)*(grid3+1)]))
|
||
call discretization_setIPcoords (reshape(IPcoords, [3,grid(1)*grid(2)*grid3]))
|
||
|
||
end subroutine utilities_updateCoords
|
||
|
||
|
||
!---------------------------------------------------------------------------------------------------
|
||
!> @brief Write out the current reference stiffness for restart.
|
||
!---------------------------------------------------------------------------------------------------
|
||
subroutine utilities_saveReferenceStiffness
|
||
|
||
integer :: &
|
||
fileUnit,ierr
|
||
|
||
if (worldrank == 0) then
|
||
print'(a)', ' writing reference stiffness data required for restart to file'; flush(IO_STDOUT)
|
||
open(newunit=fileUnit, file=getSolverJobName()//'.C_ref',&
|
||
status='replace',access='stream',action='write',iostat=ierr)
|
||
if(ierr /=0) call IO_error(100,ext_msg='could not open file '//getSolverJobName()//'.C_ref')
|
||
write(fileUnit) C_ref
|
||
close(fileUnit)
|
||
endif
|
||
|
||
end subroutine utilities_saveReferenceStiffness
|
||
|
||
end module spectral_utilities
|