840 lines
46 KiB
Fortran
840 lines
46 KiB
Fortran
! Copyright 2012 Max-Planck-Institut für Eisenforschung GmbH
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!
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! This file is part of DAMASK,
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! the Düsseldorf Advanced Material Simulation Kit.
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!
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! DAMASK is free software: you can redistribute it and/or modify
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! it under the terms of the GNU General Public License as published by
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! the Free Software Foundation, either version 3 of the License, or
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! (at your option) any later version.
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!
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! DAMASK is distributed in the hope that it will be useful,
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! but WITHOUT ANY WARRANTY; without even the implied warranty of
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! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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! GNU General Public License for more details.
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!
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! You should have received a copy of the GNU General Public License
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! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
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!
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!##################################################################################################
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!* $Id$
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!##################################################################################################
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! Material subroutine for BVP solution using spectral method
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!
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! Run 'DAMASK_spectral.exe --help' to get usage hints
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!
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! written by P. Eisenlohr,
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! F. Roters,
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! L. Hantcherli,
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! W.A. Counts,
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! D.D. Tjahjanto,
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! C. Kords,
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! M. Diehl,
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! R. Lebensohn
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!
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! MPI fuer Eisenforschung, Duesseldorf
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module DAMASK_spectralSolver
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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 prec, only: pReal, pInt
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use math
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use DAMASK_interface, only: &
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DAMASK_interface_init, &
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loadCaseFile, &
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geometryFile, &
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getSolverWorkingDirectoryName, &
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getSolverJobName, &
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appendToOutFile
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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_spectralRestart, &
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debug_spectralFFTW
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use IO
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use CPFEM, only: &
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CPFEM_general
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use numerics, only: &
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memory_efficient
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implicit none
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type solution_t ! mask of stress boundary conditions
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logical :: converged = .false.
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logical :: regrid = .false.
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logical :: term_ill = .false.
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end type solution_t
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character(len=5) :: solverType, parameter = 'basic'
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real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc,P
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real(pReal), dimension(:,:,:,:), allocatable :: coordinates
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real(pReal), dimension(:,:,:), allocatable :: temperature
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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type(C_PTR) :: plan_forward, plan_backward ! plans for fftw
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real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
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real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
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real(pReal), dimension(:,:,:,:,:), pointer :: field_real
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complex(pReal), dimension(:,:,:,:,:), pointer :: field_fourier
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!--------------------------------------------------------------------------------------------------
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! debug fftw
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type(C_PTR) :: plan_scalarField_forth, plan_scalarField_back
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complex(pReal), dimension(:,:,:), pointer :: scalarField_real
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complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
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!--------------------------------------------------------------------------------------------------
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! debug divergence
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type(C_PTR) :: plan_divergence
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real(pReal), dimension(:,:,:,:), pointer :: divergence_real
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complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
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real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
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!--------------------------------------------------------------------------------------------------
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!variables controlling debugging
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logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
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!--------------------------------------------------------------------------------------------------
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! variables storing information for spectral method and FFTW
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type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
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!--------------------------------------------------------------------------------------------------
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! stress, stiffness and compliance average etc.
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real(pReal), dimension(3,3) :: &
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F_aim = math_I3, &
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F_aim_lastInc = math_I3
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real(pReal), dimension(3,3,3,3) :: &
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C_ref = 0.0_pReal, &
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C = 0.0_pReal
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real(pReal), dimension(3) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal ! physical dimension of volume element per direction
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integer(pInt), dimension(3) :: res = 1_pInt
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real(pReal) :: wgt
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integer(pInt) :: res1_red, Npoints
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contains
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subroutine Solver_Init()
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use mesh, only : &
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mesh_spectral_getResolution, &
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mesh_spectral_getDimension
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use numerics, only: &
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divergence_correction, &
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DAMASK_NumThreadsInt, &
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fftw_planner_flag, &
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fftw_timelimit
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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 FEsolving, only: &
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restartInc
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implicit none
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!--------------------------------------------------------------------------------------------------
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! loop variables, convergence etc.
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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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real(pReal), dimension(3,3) :: temp33_Real
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integer(pInt) :: i, j, k, l, m, n, q, ielem
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real(pReal), dimension(3,3,3,3) :: dPdF
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type(C_PTR) :: tensorField ! field in real and fourier space
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type(C_PTR) :: scalarField_realC, scalarField_fourierC
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type(C_PTR) :: divergence
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integer(pInt), dimension(3) :: k_s
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real(pReal), dimension(6) :: sigma ! cauchy stress
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real(pReal), dimension(6,6) :: dsde
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integer(pInt) :: ierr
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write(6,'(a)') ''
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write(6,'(a)') ' <<<+- DAMASK_spectralSolver 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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! initialization
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!##################################################################################################
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res = mesh_spectral_getResolution()
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geomdim = mesh_spectral_getDimension()
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res1_red = res(1)/2_pInt + 1_pInt
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Npoints = res(1)*res(2)*res(3)
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wgt = 1.0/real(Npoints,pReal)
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allocate (F ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
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allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
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allocate (P ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
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allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
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allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
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allocate (temperature( res(1), res(2),res(3)), source = 0.0_pReal) ! start out isothermally
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tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous 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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!$ ierr = fftw_init_threads()
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!$ if (ierr == 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
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plan_forward = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
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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 lenght in the 3 dimensions
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field_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,fftw_planner_flag)
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plan_backward =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
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field_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,&
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field_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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!--------------------------------------------------------------------------------------------------
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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)); divergence_post = 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)) ! do not do an inplace transform
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scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T))
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call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)])
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call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)])
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plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
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scalarField_real,scalarField_fourier,-1,fftw_planner_flag)
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plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
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scalarField_fourier,scalarField_real,+1,fftw_planner_flag)
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endif
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if (debugGeneral) write(6,'(a)') 'FFTW initialized'
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!--------------------------------------------------------------------------------------------------
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! in case of no restart get reference material stiffness and init fields to no deformation
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if (restartInc == 1_pInt) then
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ielem = 0_pInt
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
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ielem = ielem + 1_pInt
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F(i,j,k,1:3,1:3) = math_I3
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F_lastInc(i,j,k,1:3,1:3) = math_I3
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coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) - geomdim/real(2_pInt*res,pReal)
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call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
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0.0_pReal,ielem,1_pInt,sigma,dsde,P(i,j,k,1:3,1:3),dPdF)
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C = C + dPdF
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enddo; enddo; enddo
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C = C * wgt
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C_ref = C
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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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!--------------------------------------------------------------------------------------------------
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! restore deformation gradient and stiffness from saved state
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elseif (restartInc > 1_pInt) then ! using old values from file
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if (debugRestart) write(6,'(a,i6,a)') 'Reading values of increment ',&
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restartInc - 1_pInt,' from file'
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call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
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trim(getSolverJobName()),size(F))
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read (777,rec=1) F
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close (777)
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F_lastInc = F
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F_aim = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
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F_aim = F_aim + F(i,j,k,1:3,1:3) ! calculating old average deformation
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enddo; enddo; enddo
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F_aim = F_aim * wgt
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F_aim_lastInc = F_aim
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coordinates = 0.0 ! change it later!!!
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call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
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read (777,rec=1) C_ref
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close (777)
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call IO_read_jobBinaryFile(777,'C',trim(getSolverJobName()),size(C))
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read (777,rec=1) C
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close (777)
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endif
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!--------------------------------------------------------------------------------------------------
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! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
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if (divergence_correction) then
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do i = 1_pInt, 3_pInt
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if (i /= minloc(geomdim,1) .and. i /= maxloc(geomdim,1)) virt_dim = geomdim/geomdim(i)
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enddo
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else
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virt_dim = geomdim
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endif
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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)
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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)
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do i = 1_pInt, res1_red
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k_s(1) = i - 1_pInt
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xi(1:3,i,j,k) = real(k_s, pReal)/virt_dim
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enddo; enddo; enddo
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!--------------------------------------------------------------------------------------------------
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! calculate the gamma operator
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if(memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source = 0.0_pReal)
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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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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
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gamma_hat(i,j,k, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
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endif
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enddo; enddo; enddo
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gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 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 Solver_Init
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type(solution_t) function solution(guessmode,timeinc,timeinc_old,P_BC,F_BC,mask_stressVector,velgrad,rotation_BC)
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use numerics, only: &
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err_div_tol, &
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err_stress_tolrel, &
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err_stress_tolabs, &
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rotation_tol, &
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itmax,&
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itmin, &
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divergence_correction, &
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DAMASK_NumThreadsInt, &
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fftw_planner_flag, &
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fftw_timelimit
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use debug, only: &
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debug_reset, &
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debug_info
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!--------------------------------------------------------------------------------------------------
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! arrays for mixed boundary conditions
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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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integer(pInt) :: size_reduced = 0_pInt
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real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
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real(pReal), dimension(6) :: sigma ! cauchy stress
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real(pReal), dimension(6,6) :: dsde
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real(pReal), dimension(9,9) :: temp99_Real ! compliance and stiffness in matrix notation
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real(pReal), dimension(3,3,3,3) :: &
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C_lastInc
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integer(pInt) :: iter, ielem
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!--------------------------------------------------------------------------------------------------
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! loop variables, convergence etc.
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real(pReal) :: timeinc, timeinc_old ! elapsed time, begin of interval, time interval
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real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
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real(pReal), dimension(3,3) :: temp33_Real
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integer(pInt) :: i, j, k, m, n
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integer(pInt) :: CPFEM_mode=1_pInt
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logical :: errmatinv, restartWrite
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real(pReal) :: defgradDet
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!--------------------------------------------------------------------------------------------------
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! variables for additional output of divergence calculations
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real(pReal), dimension(3,3) :: &
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P_av, &
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mask_stress, &
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mask_defgrad, &
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deltaF_aim, &
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F_aim_lab, &
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F_aim_lab_lastIter, &
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P_av_lab
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real(pReal), dimension(3,3,3,3) :: &
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dPdF, &
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C = 0.0_pReal, &
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S_lastInc
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logical :: velgrad
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real(pReal), dimension(3,3) :: P_BC,F_BC,rotation_BC
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logical, dimension(9) :: mask_stressVector
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real(pReal) :: defgradDetMax, defgradDetMin
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mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3]))
|
|
mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3]))
|
|
size_reduced = int(count(mask_stressVector), pInt)
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
|
|
|
|
if (velgrad) then ! calculate deltaF_aim from given L and current F
|
|
deltaF_aim = timeinc * mask_defgrad * math_mul33x33(F_BC, F_aim)
|
|
else ! deltaF_aim = fDot *timeinc where applicable
|
|
deltaF_aim = timeinc * mask_defgrad * F_BC
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! winding forward of deformation aim in loadcase system
|
|
temp33_Real = F_aim
|
|
F_aim = F_aim &
|
|
+ guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
|
|
+ deltaF_aim
|
|
F_aim_lastInc = temp33_Real
|
|
!--------------------------------------------------------------------------------------------------
|
|
! winding forward of deformation aim in loadcase system
|
|
temp33_Real = F_aim
|
|
F_aim = F_aim &
|
|
+ guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
|
|
+ deltaF_aim
|
|
F_aim_lastInc = temp33_Real
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! update local deformation gradient and coordinates
|
|
deltaF_aim = math_rotate_backward33(deltaF_aim,rotation_BC)
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
temp33_Real = F(i,j,k,1:3,1:3)
|
|
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
|
|
+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
|
|
*timeinc/timeinc_old &
|
|
+ (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
|
|
F_lastInc(i,j,k,1:3,1:3) = temp33_Real
|
|
enddo; enddo; enddo
|
|
call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,rotation_BC),& ! calculate current coordinates
|
|
1.0_pReal,F_lastInc,coordinates)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate reduced compliance
|
|
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
|
|
C_lastInc = math_rotate_forward3333(C,rotation_BC) ! calculate stiffness from former inc
|
|
temp99_Real = math_Plain3333to99(C_lastInc)
|
|
k = 0_pInt ! build 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, i, errmatinv) ! invert reduced stiffness
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
temp99_Real = 0.0_pReal ! build full compliance
|
|
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
|
|
S_lastInc = (math_Plain99to3333(temp99_Real))
|
|
endif
|
|
|
|
iter = 0_pInt
|
|
err_div = huge(err_div_tol) ! go into loop
|
|
|
|
!##################################################################################################
|
|
! convergence loop (looping over iterations)
|
|
!##################################################################################################
|
|
|
|
do while((iter < itmax .and. (err_div > err_div_tol .or. err_stress > err_stress_tol))&
|
|
.or. iter < itmin)
|
|
iter = iter + 1_pInt
|
|
|
|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
P_av = math_rotate_forward33(P_av_lab,rotation_BC)
|
|
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
|
|
math_transpose33(P_av)/1.e6_pReal
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress BC handling
|
|
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
|
|
err_stress = maxval(abs(mask_stress * (P_av - P_BC))) ! maximum deviaton (tensor norm not applicable)
|
|
err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
|
|
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
|
|
' (',err_stress,' Pa)'
|
|
F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - P_BC))) ! residual on given stress components
|
|
write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
|
|
else
|
|
err_stress_tol = +huge(1.0_pReal)
|
|
endif
|
|
|
|
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame
|
|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
!--------------------------------------------------------------------------------------------------
|
|
! report begin of new iteration
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '=================================================================='
|
|
write(6,'(3(a,i6.6))') ' @ Iter. ',itmin,' < ',iter,' < ',itmax
|
|
write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
|
|
math_transpose33(F_aim)
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... update stress field P(F) .....................................'
|
|
if (restartWrite) write(6,'(a)') 'writing restart info for last increment'
|
|
if(restartWrite) then
|
|
write(6,'(a)') 'writing converged results for restart'
|
|
call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F_lastInc)) ! writing deformation gradient field to file
|
|
write (777,rec=1) F_LastInc
|
|
close (777)
|
|
call IO_write_jobBinaryFile(777,'C',size(C))
|
|
write (777,rec=1) C
|
|
close(777)
|
|
endif
|
|
F_aim_lab_lastIter = math_rotate_backward33(F_aim,rotation_BC)
|
|
!--------------------------------------------------------------------------------------------------
|
|
! evaluate constitutive response
|
|
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(3_pInt,& ! collect cycle
|
|
coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),F(i,j,k,1:3,1:3), &
|
|
temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde,&
|
|
P(i,j,k,1:3,1:3),dPdF)
|
|
enddo; enddo; enddo
|
|
|
|
P = 0.0_pReal ! needed because of the padding for FFTW
|
|
C = 0.0_pReal
|
|
P_av_lab = 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(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
|
|
coordinates(i,j,k,1:3),F_lastInc(i,j,k,1:3,1:3), F(i,j,k,1:3,1:3), & ! others get 2 (saves winding forward effort)
|
|
temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde, &
|
|
P(i,j,k,1:3,1:3),dPdF)
|
|
CPFEM_mode = 2_pInt
|
|
C = C + dPdF
|
|
P_av_lab = P_av_lab + P(i,j,k,1:3,1:3)
|
|
enddo; enddo; enddo
|
|
call debug_info()
|
|
restartWrite = .false.
|
|
P_av_lab = P_av_lab * wgt
|
|
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
|
|
|
|
P_av = math_rotate_forward33(P_av_lab,rotation_BC)
|
|
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
|
|
math_transpose33(P_av)/1.e6_pReal
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress BC handling
|
|
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
|
|
err_stress = maxval(abs(mask_stress * (P_av - P_BC))) ! maximum deviaton (tensor norm not applicable)
|
|
err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
|
|
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
|
|
' (',err_stress,' Pa)'
|
|
F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - P_BC))) ! residual on given stress components
|
|
write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
|
|
else
|
|
err_stress_tol = +huge(1.0_pReal)
|
|
endif
|
|
|
|
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC)
|
|
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = P
|
|
call convolution(.True.,F_aim_lab_lastIter - F_aim_lab)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! updated deformation gradient
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - field_real(i,j,k,1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
|
|
enddo; enddo; enddo
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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
|
|
|
|
enddo ! end looping when convergency is achieved
|
|
|
|
CPFEM_mode = 1_pInt ! winding forward
|
|
C = C * wgt
|
|
|
|
deallocate(c_reduced)
|
|
deallocate(s_reduced)
|
|
end function solution
|
|
|
|
subroutine convolution(calcDivergence, field_aim)
|
|
real(pReal) :: err_div
|
|
real(pReal), dimension(3,3) :: temp33_Real
|
|
integer(pInt) :: i, j, k, l, m, n, q
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!variables for additional output due to general debugging
|
|
real(pReal) :: maxCorrectionSym, maxCorrectionSkew
|
|
logical :: calcDivergence
|
|
real(pReal), dimension(3,3) :: field_avg, field_aim
|
|
integer(pInt) :: row, column
|
|
real(pReal) :: field_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
|
|
err_div_max, err_real_div_max
|
|
complex(pReal), dimension(3) :: temp3_complex
|
|
complex(pReal), dimension(3,3) :: temp33_complex
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! actual spectral method
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... doing convolution .................'
|
|
!--------------------------------------------------------------------------------------------------
|
|
! copy one component of the stress field to to a single FT and check for mismatch
|
|
if (debugFFTW) then
|
|
row = 3 ! (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
|
|
column = 3 !(mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
|
|
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
|
|
cmplx(field_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! call function to calculate divergence from math (for post processing) to check results
|
|
if (debugDivergence) &
|
|
call divergence_fft(res,virt_dim,3_pInt,&
|
|
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the FT because it simplifies calculation of average stress in real space also
|
|
call fftw_execute_dft_r2c(plan_forward,field_real,field_fourier)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 FT results
|
|
if (debugFFTW) then
|
|
call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
|
|
write(6,'(a,i1,1x,i1)') 'checking FT results of compontent ', row, column
|
|
write(6,'(a,2(es11.4,1x))') 'max FT relative error = ',&
|
|
maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
|
|
field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
|
|
scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
|
|
maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
|
|
field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
|
|
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! removing highest frequencies
|
|
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
field_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
if(res(3)>1_pInt) &
|
|
field_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
if( calcDivergence) then
|
|
field_avg = real(field_fourier(1,1,1,1:3,1:3),pReal)*wgt
|
|
|
|
field_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(field_avg,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
|
|
math_transpose33(field_avg)))))
|
|
err_div_RMS = 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.
|
|
err_div_RMS = err_div_RMS &
|
|
+ 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
|
|
err_div_RMS = err_div_RMS & ! Those 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
|
|
|
|
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
|
|
err_div = err_div_RMS/field_av_L2 ! criterion to stop iterations
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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 = 0.0_pReal
|
|
err_post_div_RMS = 0.0_pReal
|
|
err_real_div_max = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
|
|
err_post_div_RMS = err_post_div_RMS + sum(divergence_post(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
|
|
err_real_div_max = max(err_real_div_max,sum(divergence_real(i,j,k,1:3)**2.0_pReal)) ! max of squared L_2 norm of div(stress) in real space
|
|
enddo; enddo; enddo
|
|
|
|
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
|
|
err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
|
|
err_real_div_max = sqrt( err_real_div_max) ! max in real space
|
|
err_div_max = sqrt( err_div_max) ! max in Fourier space
|
|
|
|
write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
|
|
write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
|
|
write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
|
|
write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
|
|
write(6,'(a,es11.4)') 'error divergence Real max = ',err_real_div_max
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endif
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! write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
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! ' (',err_div,' N/m³)'
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|
end if
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|
!--------------------------------------------------------------------------------------------------
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|
! to the actual spectral method calculation (mechanical equilibrium)
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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
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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
|
|
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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|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
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|
gamma_hat(1,1,1, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
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|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
|
|
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(i,j,k, m,n, 1:3,1:3) *&
|
|
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(field_aim,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
scalarField_fourier(i,j,k) = field_fourier(i,j,k,row,column)
|
|
enddo; enddo; enddo
|
|
do i = 0_pInt, res(1)/2_pInt-2_pInt ! unpack fft data for conj complex symmetric part
|
|
m = 1_pInt
|
|
do k = 1_pInt, res(3)
|
|
n = 1_pInt
|
|
do j = 1_pInt, res(2)
|
|
scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
|
|
if(n == 1_pInt) n = res(2) + 1_pInt
|
|
n = n-1_pInt
|
|
enddo
|
|
if(m == 1_pInt) m = res(3) + 1_pInt
|
|
m = m -1_pInt
|
|
enddo; enddo
|
|
endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the inverse FT
|
|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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 convolution
|
|
|
|
|
|
end module DAMASK_spectralSolver
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