613 lines
34 KiB
Fortran
613 lines
34 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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#include "spectral_quit.f90"
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program DAMASK_spectral
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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 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 prec, only: &
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pInt, &
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pReal, &
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DAMASK_NaN
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use IO, only: &
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IO_isBlank, &
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IO_open_file, &
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IO_stringPos, &
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IO_stringValue, &
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IO_floatValue, &
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IO_intValue, &
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IO_error, &
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IO_lc, &
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IO_read_jobBinaryFile, &
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IO_write_jobBinaryFile
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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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debug_reset, &
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debug_info
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use math
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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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mesh_spectral_getHomogenization
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use CPFEM, only: &
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CPFEM_general, &
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CPFEM_initAll
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use FEsolving, only: &
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restartWrite, &
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restartInc
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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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memory_efficient, &
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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 homogenization, only: &
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materialpoint_sizeResults, &
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materialpoint_results
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implicit none
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! field in real an fourier space
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real(pReal), dimension(:,:,:,:,:), pointer :: P_real, deltaF_real ! field in real space (pointer)
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complex(pReal), dimension(:,:,:,:,:), pointer :: P_fourier,deltaF_fourier ! field in fourier space (pointer)
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!--------------------------------------------------------------------------------------------------
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! loop variables, convergence etc.
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real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! 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), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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complex(pReal), dimension(3) :: temp3_Complex
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complex(pReal), dimension(3,3) :: temp33_Complex
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real(pReal), dimension(3,3) :: temp33_Real
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integer(pInt) :: i, j, k, l, m, n, p, errorID
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integer(pInt) :: N_Loadcases, loadcase = 0_pInt, inc, iter, ielem, CPFEM_mode=1_pInt, &
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ierr, totalIncsCounter = 0_pInt,&
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notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
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logical :: errmatinv
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real(pReal) :: defgradDet
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character(len=6) :: loadcase_string
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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 for additional output due to general debugging
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real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
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!--------------------------------------------------------------------------------------------------
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! variables for additional output of divergence calculations
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type(C_PTR) :: divergence, 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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real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
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err_div_max, err_real_div_max
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!--------------------------------------------------------------------------------------------------
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! variables for debugging fft using a scalar field
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type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
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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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integer(pInt) :: row, column
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!##################################################################################################
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! reading of information from load case file and geometry file
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!##################################################################################################
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subroutine init
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#ifdef PETSC
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integer :: ierr_psc
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call PetscInitialize(PETSC_NULL_CHARACTER, ierr_psc)
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#endif
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call DAMASK_interface_init
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write(6,'(a)') ''
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write(6,'(a)') ' <<<+- DAMASK_spectral 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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! 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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call c_f_pointer(tensorField, P_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, deltaF_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, P_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
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call c_f_pointer(tensorField, deltaF_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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! creating plans
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plan_stress = 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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P_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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P_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_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
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deltaF_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,&
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deltaF_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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! 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_real(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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CPFEM_mode = 2_pInt
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endif
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end subroutine init
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subroutine solution(guessmode, F_aim,F_aimLastInc, BC_stress, mask_stress)
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!--------------------------------------------------------------------------------------------------
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! update local deformation gradient and coordinates
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deltaF_aim = math_rotate_backward33(deltaF_aim,bc(loadcase)%rotation)
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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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temp33_Real = F(i,j,k,1:3,1:3)
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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
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+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
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*timeinc/timeinc_old &
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+ (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
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F_lastInc(i,j,k,1:3,1:3) = temp33_Real
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enddo; enddo; enddo
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call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,bc(loadcase)%rotation),& ! calculate current coordinates
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1.0_pReal,F_lastInc,coordinates)
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guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
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iter = 0_pInt
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err_div = huge(err_div_tol) ! go into loop
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!##################################################################################################
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! convergence loop (looping over iterations)
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!##################################################################################################
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do while((iter < itmax .and. (err_div > err_div_tol .or. err_stress > err_stress_tol))&
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.or. iter < itmin)
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iter = iter + 1_pInt
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!--------------------------------------------------------------------------------------------------
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! report begin of new iteration
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write(6,'(a)') ''
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write(6,'(a)') '=================================================================='
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write(6,'(6(a,i6.6))') 'Loadcase ',loadcase,' Inc. ',inc,'/',bc(loadcase)%incs,&
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' @ Iter. ',itmin,' < ',iter,' < ',itmax
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write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
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math_transpose33(F_aim)
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write(6,'(a)') ''
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write(6,'(a)') '... update stress field P(F) .....................................'
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if (restartWrite) write(6,'(a)') 'writing restart info for last increment'
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F_aim_lab_lastIter = math_rotate_backward33(F_aim,bc(loadcase)%rotation)
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!--------------------------------------------------------------------------------------------------
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! evaluate constitutive response
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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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call CPFEM_general(3_pInt,& ! collect cycle
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coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),F(i,j,k,1:3,1:3), &
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temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde,&
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P_real(i,j,k,1:3,1:3),dPdF)
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enddo; enddo; enddo
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P_real = 0.0_pReal ! needed because of the padding for FFTW
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C = 0.0_pReal
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ielem = 0_pInt
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call debug_reset()
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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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call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
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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)
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temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde, &
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P_real(i,j,k,1:3,1:3),dPdF)
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CPFEM_mode = 2_pInt
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C = C + dPdF
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enddo; enddo; enddo
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call debug_info()
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! for test of regridding
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! if( bc(loadcase)%restartFrequency > 0_pInt .and. &
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! mod(inc-1,bc(loadcase)%restartFrequency) == 0_pInt .and. &
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! restartInc/=inc) call quit(-1*(restartInc+1)) ! trigger exit to regrid
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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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row = (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
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column = (mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
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scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
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cmplx(P_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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call divergence_fft(res,virt_dim,3_pInt,&
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P_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
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!--------------------------------------------------------------------------------------------------
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! doing the FT because it simplifies calculation of average stress in real space also
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call fftw_execute_dft_r2c(plan_stress,P_real,P_fourier)
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P_av_lab = real(P_fourier(1,1,1,1:3,1:3),pReal)*wgt
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P_av = math_rotate_forward33(P_av_lab,bc(loadcase)%rotation)
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write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
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math_transpose33(P_av)/1.e6_pReal
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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 = ',&
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maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
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P_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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P_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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P_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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P_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) &
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P_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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!--------------------------------------------------------------------------------------------------
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! stress BC handling
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if(size_reduced > 0_pInt) then ! calculate stress BC if applied
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err_stress = maxval(abs(mask_stress * (P_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable)
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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
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write(6,'(a)') ''
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write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
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write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
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' (',err_stress,' Pa)'
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F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - bc(loadcase)%stress))) ! residual on given stress components
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write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
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else
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err_stress_tol = +huge(1.0_pReal)
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endif
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F_aim_lab = math_rotate_backward33(F_aim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
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!--------------------------------------------------------------------------------------------------
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! actual spectral method
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write(6,'(a)') ''
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write(6,'(a)') '... calculating equilibrium with spectral method .................'
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!--------------------------------------------------------------------------------------------------
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! calculating RMS divergence criterion in Fourier space
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pstress_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av_lab,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
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math_transpose33(P_av_lab)))))
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err_div_RMS = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2)
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do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
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err_div_RMS = err_div_RMS &
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+ 2.0_pReal*(sum (real(math_mul33x3_complex(P_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
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xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
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+sum(aimag(math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3),&
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xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
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enddo
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err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
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+ sum( real(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
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xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
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+ sum(aimag(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
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xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
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+ sum( real(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
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xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
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+ sum(aimag(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
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xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
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enddo; enddo
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err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
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if (err_div_RMS/pstress_av_L2 > err_div &
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.and. err_stress < err_stress_tol &
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.and. iter >= itmin ) then
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write(6,'(a)') 'Increasing divergence, stopping iterations'
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iter = itmax
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endif
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err_div = err_div_RMS/pstress_av_L2 ! criterion to stop iterations
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!--------------------------------------------------------------------------------------------------
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! calculate additional divergence criteria and report
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if (debugDivergence) then ! calculate divergence again
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err_div_max = 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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temp3_Complex = math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
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xi(1:3,i,j,k))*TWOPIIMG
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err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
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divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
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enddo; enddo; enddo
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call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
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err_real_div_RMS = 0.0_pReal
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err_post_div_RMS = 0.0_pReal
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err_real_div_max = 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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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
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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
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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
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enddo; enddo; enddo
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err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
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err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
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err_real_div_max = sqrt( err_real_div_max) ! max in real space
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err_div_max = sqrt( err_div_max) ! max in Fourier space
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write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
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write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
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write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
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write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
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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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!--------------------------------------------------------------------------------------------------
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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
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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, p=1_pInt:3_pInt)&
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gamma_hat(1,1,1, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
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temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
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P_fourier(i,j,k,1:3,1:3))
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deltaF_fourier(i,j,k,1:3,1:3) = temp33_Complex
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endif
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enddo; enddo; enddo
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else ! use precalculated gamma-operator
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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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forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
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temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
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P_fourier(i,j,k,1:3,1:3))
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deltaF_fourier(i,j,k, 1:3,1:3) = temp33_Complex
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enddo; enddo; enddo
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endif
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deltaF_fourier(1,1,1,1:3,1:3) = cmplx((F_aim_lab_lastIter - F_aim_lab) & ! assign (negative) average deformation gradient change to zero frequency (real part)
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* real(Npoints,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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!--------------------------------------------------------------------------------------------------
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! comparing 1 and 3x3 inverse FT results
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if (debugFFTW) 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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scalarField_fourier(i,j,k) = deltaF_fourier(i,j,k,row,column)
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enddo; enddo; enddo
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do i = 0_pInt, res(1)/2_pInt-2_pInt ! unpack fft data for conj complex symmetric part
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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
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m = m -1_pInt
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enddo; enddo
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endif
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!--------------------------------------------------------------------------------------------------
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! doing the inverse FT
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call fftw_execute_dft_c2r(plan_correction,deltaF_fourier,deltaF_real) ! back transform of fluct deformation gradient
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!--------------------------------------------------------------------------------------------------
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! comparing 1 and 3x3 inverse FT results
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|
if (debugFFTW) then
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write(6,'(a,i1,1x,i1)') 'checking iFT results of compontent ', row, column
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call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
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write(6,'(a,es11.4)') 'max iFT relative error = ',&
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maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
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deltaF_real(1:res(1),1:res(2),1:res(3),row,column))/&
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real(scalarField_real(1:res(1),1:res(2),1:res(3))))
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endif
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|
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!--------------------------------------------------------------------------------------------------
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|
! calculate some additional output
|
|
if(debugGeneral) then
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|
maxCorrectionSkew = 0.0_pReal
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maxCorrectionSym = 0.0_pReal
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temp33_Real = 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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|
maxCorrectionSym = max(maxCorrectionSym,&
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|
maxval(math_symmetric33(deltaF_real(i,j,k,1:3,1:3))))
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|
maxCorrectionSkew = max(maxCorrectionSkew,&
|
|
maxval(math_skew33(deltaF_real(i,j,k,1:3,1:3))))
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|
temp33_Real = temp33_Real + deltaF_real(i,j,k,1:3,1:3)
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|
enddo; enddo; enddo
|
|
write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
|
|
maxCorrectionSym*wgt
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|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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) - deltaF_real(i,j,k,1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
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|
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
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '=================================================================='
|
|
if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
|
|
write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' NOT converged'
|
|
notConvergedCounter = notConvergedCounter + 1_pInt
|
|
else
|
|
convergedCounter = convergedCounter + 1_pInt
|
|
write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' converged'
|
|
endif
|
|
|
|
if (mod(inc,bc(loadcase)%outputFrequency) == 0_pInt) then ! at output frequency
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... writing results to file ......................................'
|
|
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
|
|
flush(538)
|
|
endif
|
|
|
|
if( bc(loadcase)%restartFrequency > 0_pInt .and. &
|
|
mod(inc,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
|
|
restartInc=totalIncsCounter
|
|
restartWrite = .true.
|
|
write(6,'(a)') 'writing converged results for restart'
|
|
call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F)) ! writing deformation gradient field to file
|
|
write (777,rec=1) F
|
|
close (777)
|
|
call IO_write_jobBinaryFile(777,'C',size(C))
|
|
write (777,rec=1) C
|
|
close(777)
|
|
endif
|
|
|
|
endif ! end calculation/forwarding
|
|
enddo ! end looping over incs in current loadcase
|
|
|