835 lines
49 KiB
Fortran
835 lines
49 KiB
Fortran
!--------------------------------------------------------------------------------------------------
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! $Id$
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!--------------------------------------------------------------------------------------------------
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!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
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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 DAMASK_spectral_utilities
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use, intrinsic :: iso_c_binding
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use prec, only: &
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pReal, &
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pInt
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implicit none
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logical, public :: cutBack =.false. !< cut back of BVP solver in case convergence is not achieved or a material point is terminally ill
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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real(pReal), public, dimension(:,:,:,:,:), pointer :: field_real !< real representation (some stress or deformation) of field_fourier
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complex(pReal),private, dimension(:,:,:,:,:), pointer :: field_fourier !< field on which the Fourier transform operates
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real(pReal), private, dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat !< gamma operator (field) for spectral method
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real(pReal), private, dimension(:,:,:,:), allocatable :: xi !< wave vector field for divergence and for gamma operator
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real(pReal), private, dimension(3,3,3,3) :: C_ref !< reference stiffness
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!--------------------------------------------------------------------------------------------------
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! debug fftw
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complex(pReal),private, dimension(:,:,:), pointer :: scalarField_real, & !< scalar field real representation for debug of FFTW
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scalarField_fourier !< scalar field complex representation for debug of FFTW
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!--------------------------------------------------------------------------------------------------
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! debug divergence
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real(pReal), private, dimension(:,:,:,:), pointer :: divergence_real !< scalar field real representation for debugging divergence calculation
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complex(pReal),private, dimension(:,:,:,:), pointer :: divergence_fourier !< scalar field real representation for debugging divergence calculation
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real(pReal), private, dimension(:,:,:,:), allocatable :: divergence_post !< data of divergence calculation using function from core modules (serves as a reference)
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!--------------------------------------------------------------------------------------------------
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! plans for FFTW
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type(C_PTR), private :: plan_scalarField_forth, plan_scalarField_back !< plans for FFTW in case of debugging the Fourier transform
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type(C_PTR), private :: plan_forward, plan_backward !< plans for FFTW
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type(C_PTR), private :: plan_divergence !< plan for FFTW in case of debugging divergence calculation
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!--------------------------------------------------------------------------------------------------
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! variables controlling debugging
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logical, public :: &
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debugGeneral, & !< general debugging of spectral solver
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debugDivergence, & !< debugging of divergence calculation (comparison to function used for post processing)
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debugRestart, & !< debbuging of restart features
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debugFFTW !< doing additional FFT on scalar field and compare to results of strided 3D FFT
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!--------------------------------------------------------------------------------------------------
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! derived types
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type tSolutionState !< return type of solution from spectral solver variants
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logical :: converged = .true.
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logical :: regrid = .false.
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logical :: termIll = .false.
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integer(pInt) :: iterationsNeeded = 0_pInt
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end type tSolutionState
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type 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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real(pReal), dimension(3,3) :: maskFloat = 0.0_pReal
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logical, dimension(3,3) :: maskLogical = .false.
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character(len=64) :: myType = 'None'
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end type tBoundaryCondition
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public :: &
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utilities_init, &
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utilities_updateGamma, &
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utilities_FFTforward, &
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utilities_FFTbackward, &
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utilities_fourierConvolution, &
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utilities_divergenceRMS, &
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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_destroy
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private :: &
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utilities_getFilter
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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 biwise coding
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!> provided by the debug module to logicals.
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!> Allocates 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 utilities_init()
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use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
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use IO, only: &
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IO_error
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use numerics, only: &
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DAMASK_NumThreadsInt, &
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fftw_planner_flag, &
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fftw_timelimit, &
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memory_efficient
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use debug, only: &
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debug_level, &
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debug_spectral, &
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debug_levelBasic, &
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debug_spectralDivergence, &
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debug_spectralRestart, &
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debug_spectralFFTW
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use mesh, only: &
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res, &
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res1_red, &
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virt_dim
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use math ! must use the whole module for use of FFTW
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implicit none
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integer(pInt) :: i, j, k
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integer(pInt), dimension(3) :: k_s
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type(C_PTR) :: &
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tensorField, & !< field cotaining data for FFTW in real and fourier space (in place)
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scalarField_realC, & !< field cotaining data for FFTW in real space when debugging FFTW (no in place)
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scalarField_fourierC, & !< field cotaining data for FFTW in fourier space when debugging FFTW (no in place)
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divergence !< field cotaining data for FFTW in real and fourier space when debugging divergence (in place)
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write(6,'(/,a)') ' <<<+- DAMASK_spectral_utilities init -+>>>'
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write(6,'(a)') ' $Id$'
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#include "compilation_info.f90"
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write(6,'(a)') ''
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!--------------------------------------------------------------------------------------------------
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! set debugging parameters
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debugGeneral = iand(debug_level(debug_spectral),debug_levelBasic) /= 0
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debugDivergence = iand(debug_level(debug_spectral),debug_spectralDivergence) /= 0
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debugRestart = iand(debug_level(debug_spectral),debug_spectralRestart) /= 0
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debugFFTW = iand(debug_level(debug_spectral),debug_spectralFFTW) /= 0
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!--------------------------------------------------------------------------------------------------
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! allocation
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allocate (xi(3,res1_red,res(2),res(3)),source = 0.0_pReal) ! frequencies, only half the size for first dimension
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tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate aligned data using a C function, C_SIZE_T is of type integer(8)
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call c_f_pointer(tensorField, field_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
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call c_f_pointer(tensorField, field_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
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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. pInt /= C_INT) call IO_error(error_ID=808_pInt) ! check for correct precision in C
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!$ if(DAMASK_NumThreadsInt > 0_pInt) then
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!$ i = fftw_init_threads() ! returns 0 in case of problem
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!$ if (i == 0_pInt) call IO_error(error_ID = 809_pInt)
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!$ call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
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!$ endif
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call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
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!--------------------------------------------------------------------------------------------------
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! creating plans for the convolution
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plan_forward = fftw_plan_many_dft_r2c(3, [res(3),res(2) ,res(1)], 9,& ! dimensions, logical length in each dimension in reversed order, no. of transforms
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field_real, [res(3),res(2) ,res(1)+2_pInt],& ! input data, physical length in each dimension in reversed order
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1, res(3)*res(2)*(res(1)+2_pInt),& ! striding, product of physical length in the 3 dimensions
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field_fourier, [res(3),res(2) ,res1_red],& ! output data, physical length in each dimension in reversed order
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1, res(3)*res(2)* res1_red, fftw_planner_flag) ! striding, product of physical length in the 3 dimensions, planner precision
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plan_backward = fftw_plan_many_dft_c2r(3, [res(3),res(2) ,res(1)], 9,& ! dimensions, logical length in each dimension in reversed order, no. of transforms
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field_fourier, [res(3),res(2) ,res1_red],& ! input data, physical length in each dimension in reversed order
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1, res(3)*res(2)* res1_red,& ! striding, product of physical length in the 3 dimensions
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field_real, [res(3),res(2) ,res(1)+2_pInt],& ! output data, physical length in each dimension in reversed order
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1, res(3)*res(2)*(res(1)+2_pInt), fftw_planner_flag) ! striding, product of physical length in the 3 dimensions, planner precision
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!--------------------------------------------------------------------------------------------------
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! depending on debug options, allocate more memory and create additional plans
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if (debugDivergence) then
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divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
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call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
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call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
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allocate (divergence_post(res(1),res(2),res(3),3),source = 0.0_pReal)
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plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
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divergence_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,&
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divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
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1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
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endif
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if (debugFFTW) then
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scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! allocate data for real representation (no in place transform)
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scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! allocate data for fourier representation (no in place transform)
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call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)]) ! place a pointer for a real representation
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call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)]) ! place a pointer for a fourier representation
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plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& ! reversed order (C style)
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scalarField_real,scalarField_fourier,-1,fftw_planner_flag) ! input, output, forward FFT(-1), planner precision
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plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& ! reversed order (C style)
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scalarField_fourier,scalarField_real,+1,fftw_planner_flag) ! input, output, backward (1), planner precision
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endif
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if (debugGeneral) write(6,'(a)') 'FFTW initialized'
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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 = 1_pInt, res(3)
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k_s(3) = k - 1_pInt
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if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do j = 1_pInt, res(2)
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k_s(2) = j - 1_pInt
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if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2) ! running from 0,1,...,N/2,N/2+1,-N/2,-N/2+1,...,-1
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do i = 1_pInt, res1_red
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k_s(1) = i - 1_pInt ! symmetry, junst running from 0,1,...,N/2,N/2+1
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xi(1:3,i,j,k) = real(k_s, pReal)/virt_dim ! if divergence_correction is set, frequencies are calculated on unit length
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enddo; enddo; enddo
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if(memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(3,3,3,3,1,1,1), source = 0.0_pReal)
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(3,3,3,3,res1_red ,res(2),res(3)), source =0.0_pReal)
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endif
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end subroutine utilities_init
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!--------------------------------------------------------------------------------------------------
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!> @brief updates references stiffness and potentially precalculated gamma operator
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!> @details Sets 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 a on-the-fly calculation, only the reference stiffness is updated.
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!> The gamma operator is filtered depening on the filter selected in numerics.
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!> Also writes out the current reference stiffness for restart.
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!--------------------------------------------------------------------------------------------------
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subroutine utilities_updateGamma(C,saveReference)
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use IO, only: &
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IO_write_jobBinaryFile
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use numerics, only: &
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memory_efficient
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use math, only: &
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math_inv33
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use mesh, only: &
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res, &
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res1_red
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implicit none
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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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logical , intent(in) :: saveReference !< save reference stiffness to file for restart
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real(pReal), dimension(3,3) :: temp33_Real, xiDyad
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real(pReal) :: filter !< weighting of current component
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integer(pInt) :: &
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i, j, k, &
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l, m, n, o
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C_ref = C
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if (saveReference) then
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write(6,'(a)') 'writing reference stiffness to file'
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call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
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write (777,rec=1) C_ref
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close(777)
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endif
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if(.not. memory_efficient) then
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
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if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
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temp33_Real = math_inv33(temp33_Real)
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filter = utilities_getFilter(xi(1:3,i,j,k)) ! weighting factor computed by getFilter function
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)&
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gamma_hat(l,m,n,o, i,j,k) = filter*temp33_Real(l,n)*xiDyad(m,o)
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endif
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enddo; enddo; enddo
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gamma_hat(1:3,1:3,1:3,1:3, 1,1,1) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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endif
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end subroutine utilities_updateGamma
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!--------------------------------------------------------------------------------------------------
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!> @brief forward FFT of data in field_real to field_fourier with highest freqs. removed
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!> @detailed Does an unweighted FFT transform from real to complex.
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!> In case of debugging the FFT, also one component of the tensor (specified by row and column)
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!> is independetly transformed complex to complex and compared to the whole tensor transform
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!--------------------------------------------------------------------------------------------------
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subroutine utilities_FFTforward(row,column)
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use math
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use mesh, only : &
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virt_dim, &
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res, &
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res1_red
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implicit none
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integer(pInt), intent(in), optional :: row, column !< if debug FFTW, compare 3D array field of row and column
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!--------------------------------------------------------------------------------------------------
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! copy one component of the stress field to to a single FT and check for mismatch
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if (debugFFTW) then
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if (.not. present(row) .or. .not. present(column)) stop
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scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
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cmplx(field_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
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endif
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!--------------------------------------------------------------------------------------------------
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! call function to calculate divergence from math (for post processing) to check results
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if (debugDivergence) &
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divergence_post = math_divergenceFFT(virt_dim,field_real(1:res(1),1:res(2),1:res(3),1:3,1:3)) ! some elements are padded
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!--------------------------------------------------------------------------------------------------
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! doing the FFT
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call fftw_execute_dft_r2c(plan_forward,field_real,field_fourier)
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!--------------------------------------------------------------------------------------------------
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! comparing 1 and 3x3 FT results
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if (debugFFTW) then
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call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
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write(6,'(a,i1,1x,i1)') 'checking FT results of compontent ', row, column
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write(6,'(a,2(es11.4,1x))') 'max FT relative error = ',& ! print real and imaginary part seperately
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maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
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field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
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scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
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maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
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field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
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scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
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endif
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!--------------------------------------------------------------------------------------------------
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! removing highest frequencies
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field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
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= cmplx(0.0_pReal,0.0_pReal,pReal)
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field_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
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= cmplx(0.0_pReal,0.0_pReal,pReal)
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if(res(3)>1_pInt) & ! do not delete the whole slice in case of 2D calculation
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field_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
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= cmplx(0.0_pReal,0.0_pReal,pReal)
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end subroutine utilities_FFTforward
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!--------------------------------------------------------------------------------------------------
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!> @brief backward FFT of data in field_fourier to field_real
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!> @detailed Does an inverse FFT transform from complex to real
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!> In case of debugging the FFT, also one component of the tensor (specified by row and column)
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!> is independetly transformed complex to complex and compared to the whole tensor transform
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!> results is weighted by number of points stored in wgt
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!--------------------------------------------------------------------------------------------------
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subroutine utilities_FFTbackward(row,column)
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use math !< must use the whole module for use of FFTW
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use mesh, only: &
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wgt, &
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res, &
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res1_red
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implicit none
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integer(pInt), intent(in), optional :: row, column !< if debug FFTW, compare 3D array field of row and column
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integer(pInt) :: i, j, k, m, n
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!--------------------------------------------------------------------------------------------------
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! unpack FFT data for conj complex symmetric part. This data is not transformed when using c2r
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if (debugFFTW) then
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scalarField_fourier = field_fourier(1:res1_red,1:res(2),1:res(3),row,column)
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do i = 0_pInt, res(1)/2_pInt-2_pInt
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m = 1_pInt
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do k = 1_pInt, res(3)
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n = 1_pInt
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do j = 1_pInt, res(2)
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scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
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if(n == 1_pInt) n = res(2) + 1_pInt
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n = n-1_pInt
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enddo
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if(m == 1_pInt) m = res(3) + 1_pInt
|
|
m = m -1_pInt
|
|
enddo; enddo
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the iFFT
|
|
call fftw_execute_dft_c2r(plan_backward,field_fourier,field_real) ! back transform of fluct deformation gradient
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
write(6,'(a,i1,1x,i1)') 'checking iFT results of compontent ', row, column
|
|
call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
|
|
write(6,'(a,es11.4)') 'max iFT relative error = ',&
|
|
maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
|
|
field_real(1:res(1),1:res(2),1:res(3),row,column))/&
|
|
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
|
|
endif
|
|
|
|
field_real = field_real * wgt ! normalize the result by number of elements
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate some additional output
|
|
! if(debugGeneral) then
|
|
! maxCorrectionSkew = 0.0_pReal
|
|
! maxCorrectionSym = 0.0_pReal
|
|
! temp33_Real = 0.0_pReal
|
|
! do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
! maxCorrectionSym = max(maxCorrectionSym,&
|
|
! maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
|
|
! maxCorrectionSkew = max(maxCorrectionSkew,&
|
|
! maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
|
|
! temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
|
|
! enddo; enddo; enddo
|
|
! write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
|
|
! maxCorrectionSym*wgt
|
|
! write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
|
|
! maxCorrectionSkew*wgt
|
|
! write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
|
|
! maxval(math_symmetric33(temp33_real))/&
|
|
! maxval(math_skew33(temp33_real))
|
|
! endif
|
|
|
|
|
|
end subroutine utilities_FFTbackward
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief doing convolution gamma_hat * field_real, ensuring that average value = fieldAim
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_fourierConvolution(fieldAim)
|
|
use numerics, only: &
|
|
memory_efficient
|
|
use math, only: &
|
|
math_inv33
|
|
use mesh, only: &
|
|
mesh_NcpElems, &
|
|
res, &
|
|
res1_red
|
|
|
|
implicit none
|
|
real(pReal), intent(in), dimension(3,3) :: fieldAim !< desired average value of the field after convolution
|
|
real(pReal), dimension(3,3) :: xiDyad, temp33_Real
|
|
real(pReal) :: filter !< weighting of current component
|
|
complex(pReal), dimension(3,3) :: temp33_complex
|
|
integer(pInt) :: &
|
|
i, j, k, &
|
|
l, m, n, o
|
|
|
|
write(6,'(/,a)') '... doing convolution .....................................................'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! to the actual spectral method calculation (mechanical equilibrium)
|
|
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
|
|
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
|
|
temp33_Real = math_inv33(temp33_Real)
|
|
filter = utilities_getFilter(xi(1:3,i,j,k)) ! weighting factor computed by getFilter function
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, o=1_pInt:3_pInt)&
|
|
gamma_hat(l,m,n,o, 1,1,1) = filter*temp33_Real(l,n)*xiDyad(m,o)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Complex(l,m) = sum(gamma_hat(l,m,1:3,1:3, 1,1,1) * field_fourier(i,j,k,1:3,1:3))
|
|
field_fourier(i,j,k,1:3,1:3) = temp33_Complex
|
|
endif
|
|
enddo; enddo; enddo
|
|
else ! use precalculated gamma-operator
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
|
|
forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
|
|
temp33_Complex(m,n) = sum(gamma_hat(m,n,1:3,1:3, i,j,k) * field_fourier(i,j,k,1:3,1:3))
|
|
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
|
|
enddo; enddo; enddo
|
|
endif
|
|
field_fourier(1,1,1,1:3,1:3) = cmplx(fieldAim*real(mesh_NcpElems,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
|
|
end subroutine utilities_fourierConvolution
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculate root mean square of divergence of field_fourier
|
|
!--------------------------------------------------------------------------------------------------
|
|
real(pReal) function utilities_divergenceRMS()
|
|
use math !< must use the whole module for use of FFTW
|
|
use mesh, only: &
|
|
wgt, &
|
|
res, &
|
|
res1_red
|
|
|
|
implicit none
|
|
integer(pInt) :: i, j, k
|
|
real(pReal) :: &
|
|
err_div_RMS, & !< RMS of divergence in Fourier space
|
|
err_real_div_RMS, & !< RMS of divergence in real space
|
|
err_post_div_RMS, & !< RMS of divergence in Fourier space, calculated using function for post processing
|
|
err_div_max, & !< maximum value of divergence in Fourier space
|
|
err_real_div_max !< maximum value of divergence in real space
|
|
complex(pReal), dimension(3) :: temp3_complex
|
|
|
|
write(6,'(/,a)') '... calculating divergence ................................................'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
utilities_divergenceRMS = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2)
|
|
do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
|
|
utilities_divergenceRMS = utilities_divergenceRMS &
|
|
+ 2.0_pReal*(sum (real(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
|
|
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
|
+sum(aimag(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),&
|
|
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
|
|
enddo
|
|
utilities_divergenceRMS = utilities_divergenceRMS & ! these two layers (DC and Nyquist) do not have a conjugate complex counterpart
|
|
+ sum( real(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum( real(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
|
|
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
|
|
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
|
|
enddo; enddo
|
|
|
|
utilities_divergenceRMS = sqrt(utilities_divergenceRMS) *wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate additional divergence criteria and report
|
|
if (debugDivergence) then ! calculate divergence again
|
|
err_div_max = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
temp3_Complex = math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
|
|
xi(1:3,i,j,k))*TWOPIIMG
|
|
err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
|
|
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
|
|
enddo; enddo; enddo
|
|
|
|
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
|
|
|
|
err_real_div_RMS = sqrt(wgt*sum(divergence_real**2.0_pReal)) ! RMS in real space
|
|
err_post_div_RMS = sqrt(wgt*sum(divergence_post**2.0_pReal)) ! RMS in real space from funtion in math.f90
|
|
err_real_div_max = sqrt(maxval(sum(divergence_real**2.0_pReal,dim=4))) ! max in real space
|
|
err_div_max = sqrt( err_div_max) ! max in Fourier space
|
|
|
|
write(6,'(1x,a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
|
|
write(6,'(1x,a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
|
|
write(6,'(1x,a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
|
|
write(6,'(1x,a,es11.4)') 'error divergence FT max = ',err_div_max
|
|
write(6,'(1x,a,es11.4)') 'error divergence Real max = ',err_real_div_max
|
|
endif
|
|
|
|
end function utilities_divergenceRMS
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates mask compliance tensor
|
|
!--------------------------------------------------------------------------------------------------
|
|
function utilities_maskedCompliance(rot_BC,mask_stress,C)
|
|
use IO, only: &
|
|
IO_error
|
|
use math, only: &
|
|
math_Plain3333to99, &
|
|
math_plain99to3333, &
|
|
math_rotate_forward3333, &
|
|
math_rotate_forward33, &
|
|
math_invert
|
|
|
|
implicit none
|
|
real(pReal), dimension(3,3,3,3) :: utilities_maskedCompliance !< masked compliance
|
|
real(pReal), intent(in) , dimension(3,3,3,3) :: C !< current average stiffness
|
|
real(pReal), intent(in) , dimension(3,3) :: rot_BC !< rotation of load frame
|
|
logical, intent(in), dimension(3,3) :: mask_stress !< mask of stress BC
|
|
integer(pInt) :: j, k, m, n
|
|
logical, dimension(9) :: mask_stressVector
|
|
real(pReal), dimension(9,9) :: temp99_Real
|
|
integer(pInt) :: size_reduced = 0_pInt
|
|
real(pReal), dimension(:,:), allocatable :: &
|
|
s_reduced, & !< reduced compliance matrix (depending on number of stress BC)
|
|
c_reduced, & !< reduced stiffness (depending on number of stress BC)
|
|
sTimesC !< temp variable to check inversion
|
|
logical :: errmatinv
|
|
character(len=1024):: formatString
|
|
|
|
mask_stressVector = reshape(transpose(mask_stress), [9])
|
|
size_reduced = int(count(mask_stressVector), pInt)
|
|
if(size_reduced > 0_pInt )then
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (sTimesC(size_reduced,size_reduced), source =0.0_pReal)
|
|
|
|
temp99_Real = math_Plain3333to99(math_rotate_forward3333(C,rot_BC))
|
|
if(debugGeneral) &
|
|
write(6,'(a,/,9(9(2x,f12.7,1x)/))',advance='no') 'Stiffness C rotated / GPa =',&
|
|
transpose(temp99_Real)/1.e9_pReal
|
|
k = 0_pInt ! calculate reduced stiffness
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector(m)) then
|
|
j = j + 1_pInt
|
|
c_reduced(k,j) = temp99_Real(n,m)
|
|
endif; enddo; endif; enddo
|
|
call math_invert(size_reduced, c_reduced, s_reduced, errmatinv) ! invert reduced stiffness
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
temp99_Real = 0.0_pReal ! fill up compliance with zeros
|
|
k = 0_pInt
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector(m)) then
|
|
j = j + 1_pInt
|
|
temp99_Real(n,m) = s_reduced(k,j)
|
|
endif; enddo; endif; enddo
|
|
!--------------------------------------------------------------------------------------------------
|
|
! check if inversion was successfull
|
|
sTimesC = matmul(c_reduced,s_reduced)
|
|
do m=1_pInt, size_reduced
|
|
do n=1_pInt, size_reduced
|
|
if(m==n .and. abs(sTimesC(m,n)) > (1.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! diagonal elements of S*C should be 1
|
|
if(m/=n .and. abs(sTimesC(m,n)) > (0.0_pReal + 10.0e-12_pReal)) errmatinv = .true. ! off diagonal elements of S*C should be 0
|
|
enddo
|
|
enddo
|
|
if(debugGeneral .or. errmatinv) then ! report
|
|
write(formatString, '(I16.16)') size_reduced
|
|
formatString = '(a,/,'//trim(formatString)//'('//trim(formatString)//'(2x,es9.2,1x)/))'
|
|
write(6,trim(formatString),advance='no') 'C * S', transpose(matmul(c_reduced,s_reduced))
|
|
write(6,trim(formatString),advance='no') 'S', transpose(s_reduced)
|
|
endif
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
deallocate(c_reduced)
|
|
deallocate(s_reduced)
|
|
deallocate(sTimesC)
|
|
else
|
|
temp99_real = 0.0_pReal
|
|
endif
|
|
if(debugGeneral) & ! report
|
|
write(6,'(a,/,9(9(2x,f12.7,1x)/))',advance='no') 'Masked Compliance * GPa =', &
|
|
transpose(temp99_Real*1.e9_pReal)
|
|
utilities_maskedCompliance = math_Plain99to3333(temp99_Real)
|
|
|
|
end function utilities_maskedCompliance
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates constitutive response
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_constitutiveResponse(coordinates,F_lastInc,F,temperature,timeinc,&
|
|
P,C,P_av,forwardData,rotation_BC)
|
|
use debug, only: &
|
|
debug_reset, &
|
|
debug_info
|
|
use math, only: &
|
|
math_transpose33, &
|
|
math_rotate_forward33
|
|
use FEsolving, only: &
|
|
restartWrite
|
|
use mesh, only: &
|
|
res, &
|
|
wgt
|
|
use CPFEM, only: &
|
|
CPFEM_general
|
|
|
|
implicit none
|
|
real(pReal), intent(inout) :: temperature !< temperature (no field)
|
|
real(pReal), intent(in), dimension(res(1),res(2),res(3),3) :: coordinates !< coordinates field
|
|
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
|
|
F_lastInc, & !< target deformation gradient
|
|
F !< previous deformation gradient
|
|
real(pReal), intent(in) :: timeinc !< loading time
|
|
logical, intent(in) :: forwardData !< age results
|
|
real(pReal), intent(in), dimension(3,3) :: rotation_BC !< rotation of load frame
|
|
|
|
real(pReal),intent(out), dimension(3,3,3,3) :: C !< average stiffness
|
|
real(pReal),intent(out), dimension(3,3) :: P_av !< average PK stress
|
|
real(pReal),intent(out), dimension(3,3,res(1),res(2),res(3)) :: P !< PK stress
|
|
|
|
integer(pInt) :: &
|
|
i, j, k, &
|
|
ielem, &
|
|
calcMode, & !< CPFEM mode for calculation
|
|
collectMode !< CPFEM mode for collection
|
|
real(pReal), dimension(3,3,3,3) :: dPdF !< d P / d F
|
|
real(pReal), dimension(6) :: sigma !< cauchy stress in mandel notation
|
|
real(pReal), dimension(6,6) :: dsde !< d sigma / d Epsilon
|
|
|
|
write(6,'(/,a,/)') '... evaluating constitutive response ......................................'
|
|
if (forwardData) then ! aging results
|
|
calcMode = 1_pInt
|
|
collectMode = 4_pInt
|
|
else ! normal calculation
|
|
calcMode = 2_pInt
|
|
collectMode = 3_pInt
|
|
endif
|
|
if (cutBack) then ! restore saved variables
|
|
calcMode = 2_pInt
|
|
collectMode = 5_pInt
|
|
endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate bounds of det(F) and report
|
|
! if(debugGeneral) then
|
|
! defgradDetMax = -huge(1.0_pReal)
|
|
! defgradDetMin = +huge(1.0_pReal)
|
|
! do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
! defgradDet = math_det33(F(i,j,k,1:3,1:3))
|
|
! defgradDetMax = max(defgradDetMax,defgradDet)
|
|
! defgradDetMin = min(defgradDetMin,defgradDet)
|
|
! enddo; enddo; enddo
|
|
|
|
! write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
|
|
! write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
|
|
! endif
|
|
if (DebugGeneral) write(6,*) 'collect mode: ', collectMode,' calc mode: ', calcMode
|
|
flush(6)
|
|
|
|
ielem = 0_pInt
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
call CPFEM_general(collectMode,& ! collect cycle
|
|
coordinates(i,j,k,1:3), F_lastInc(1:3,1:3,i,j,k),F(1:3,1:3,i,j,k), &
|
|
temperature,timeinc,ielem,1_pInt,sigma,dsde,P(1:3,1:3,i,j,k),dPdF)
|
|
collectMode = 3_pInt
|
|
enddo; enddo; enddo
|
|
|
|
P = 0.0_pReal ! needed because of the padding for FFTW
|
|
C = 0.0_pReal
|
|
ielem = 0_pInt
|
|
call debug_reset()
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
call CPFEM_general(calcMode,& ! first element in first iteration retains CPFEM_mode 1,
|
|
coordinates(i,j,k,1:3),F_lastInc(1:3,1:3,i,j,k), F(1:3,1:3,i,j,k), & ! others get 2 (saves winding forward effort)
|
|
temperature,timeinc,ielem,1_pInt,sigma,dsde,P(1:3,1:3,i,j,k),dPdF)
|
|
calcMode = 2_pInt
|
|
C = C + dPdF
|
|
enddo; enddo; enddo
|
|
C = C * wgt
|
|
call debug_info()
|
|
|
|
P_av = math_rotate_forward33(sum(sum(sum(P,dim=5),dim=4),dim=3) * wgt,rotation_BC) ! average of P rotated
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restartWrite = .false. ! reset restartWrite status
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cutBack = .false. ! reset cutBack status
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|
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write(6,'(a,/,3(3(2x,f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
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math_transpose33(P_av)/1.e6_pReal
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|
end subroutine utilities_constitutiveResponse
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|
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!--------------------------------------------------------------------------------------------------
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!> @brief calculates forward rate, either guessing or just add delta/timeinc
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!--------------------------------------------------------------------------------------------------
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pure function utilities_calculateRate(delta_aim,timeinc,timeinc_old,guess,field_lastInc,field)
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use mesh, only: &
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|
res
|
|
|
|
implicit none
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|
real(pReal), intent(in), dimension(3,3) :: delta_aim !< homogeneous addon
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real(pReal), intent(in) :: &
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|
timeinc, & !< timeinc of current step
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|
timeinc_old !< timeinc of last step
|
|
logical, intent(in) :: &
|
|
guess !< guess along former trajectory
|
|
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
|
|
field_lastInc, & !< data of previous step
|
|
field !< data of current step
|
|
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: utilities_calculateRate
|
|
|
|
if(guess) then
|
|
utilities_calculateRate = (field-field_lastInc) / timeinc_old
|
|
else
|
|
utilities_calculateRate = spread(spread(spread(delta_aim,3,res(1)),4,res(2)),5,res(3))/timeinc
|
|
endif
|
|
|
|
end function utilities_calculateRate
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief forwards a field with a pointwise given rate, ensures that the average matches the aim
|
|
!--------------------------------------------------------------------------------------------------
|
|
pure function utilities_forwardField(timeinc,aim,field_lastInc,rate)
|
|
use mesh, only: &
|
|
res, &
|
|
wgt
|
|
|
|
implicit none
|
|
real(pReal), intent(in) :: timeinc !< timeinc of current step
|
|
real(pReal), intent(in), dimension(3,3) :: aim !< average field value aim
|
|
real(pReal), intent(in), dimension(3,3,res(1),res(2),res(3)) :: &
|
|
field_lastInc,& !< initial field
|
|
rate !< rate by which to forward
|
|
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: utilities_forwardField
|
|
real(pReal), dimension(3,3) :: fieldDiff !< <a + adot*t> - aim
|
|
|
|
utilities_forwardField = field_lastInc + rate*timeinc
|
|
fieldDiff = sum(sum(sum(utilities_forwardField,dim=5),dim=4),dim=3)*wgt - aim
|
|
utilities_forwardField = utilities_forwardField - &
|
|
spread(spread(spread(fieldDiff,3,res(1)),4,res(2)),5,res(3))
|
|
|
|
end function utilities_forwardField
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief calculates filter for fourier convolution depending on type given in numerics.config
|
|
!--------------------------------------------------------------------------------------------------
|
|
real(pReal) function utilities_getFilter(k)
|
|
use IO, only: &
|
|
IO_error
|
|
use numerics, only: &
|
|
myfilter
|
|
use mesh, only: &
|
|
res
|
|
use math, only: &
|
|
PI
|
|
|
|
implicit none
|
|
real(pReal),intent(in), dimension(3) :: k !< indices of frequency
|
|
|
|
select case (myfilter)
|
|
case ('none')
|
|
utilities_getFilter = 1.0_pReal
|
|
case ('cosine') !< cosine curve with 1 for avg and zero for highest freq
|
|
utilities_getFilter = (1.0_pReal + cos(PI*k(3)/res(3))) &
|
|
*(1.0_pReal + cos(PI*k(2)/res(2))) &
|
|
*(1.0_pReal + cos(PI*k(1)/res(1)))/8.0_pReal
|
|
case default
|
|
call IO_error(error_ID = 892_pInt, ext_msg = trim(myfilter))
|
|
end select
|
|
|
|
end function utilities_getFilter
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!> @brief cleans up
|
|
!--------------------------------------------------------------------------------------------------
|
|
subroutine utilities_destroy()
|
|
use math
|
|
implicit none
|
|
if (debugDivergence) call fftw_destroy_plan(plan_divergence)
|
|
|
|
if (debugFFTW) call fftw_destroy_plan(plan_scalarField_forth)
|
|
if (debugFFTW) call fftw_destroy_plan(plan_scalarField_back)
|
|
|
|
call fftw_destroy_plan(plan_forward)
|
|
call fftw_destroy_plan(plan_backward)
|
|
|
|
end subroutine utilities_destroy
|
|
|
|
|
|
end module DAMASK_spectral_utilities
|