845 lines
47 KiB
Fortran
845 lines
47 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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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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end type solution_t
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type init
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real(pReal), dimension(3,3) :: F_init
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end type init
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type bc_type
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real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
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stress = 0.0_pReal, & ! stress BC (if applicable)
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rotation = math_I3 ! rotation of BC (if applicable)
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real(pReal) :: time = 0.0_pReal, & ! length of increment
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temperature = 300.0_pReal ! isothermal starting conditions
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integer(pInt) :: incs = 0_pInt, & ! number of increments
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outputfrequency = 1_pInt, & ! frequency of result writes
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restartfrequency = 0_pInt, & ! frequency of restart writes
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logscale = 0_pInt ! linear/logaritmic time inc flag
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logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
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velGradApplied = .false. ! decide wether velocity gradient or fdot is given
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logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
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maskStress = .false. ! mask of stress boundary conditions
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logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
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end type
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real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc
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real(pReal), dimension(:,:,:,:), allocatable :: coordinates
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real(pReal), dimension(:,:,:), allocatable :: temperature
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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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complex(pReal), dimension(:,:,:), pointer :: scalarField_real
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complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
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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, plan_correction
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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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contains
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type(init) function solverInit(solver,restartInc,loadcase)
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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 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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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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debug_reset, &
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debug_info
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implicit none
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real(pReal) :: restartInc
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character(len=*) :: solver
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integer(pInt) :: &
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Npoints,& ! number of Fourier points
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homog, & ! homogenization scheme used
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res1_red
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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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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) :: inc, iter, ielem, CPFEM_mode=1_pInt, &
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ierr
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logical :: errmatinv
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real(pReal) :: defgradDet
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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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P_av, &
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F_aim = math_I3, &
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F_aim_lastInc = math_I3, &
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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_ref = 0.0_pReal, &
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C = 0.0_pReal, &
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S_lastInc, &
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C_lastInc
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!--------------------------------------------------------------------------------------------------
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! pointwise data
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type(C_PTR) :: tensorField ! field in real an fourier space
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type(bc_type) :: loadcase ! field in real an fourier space
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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_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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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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real(pReal) :: wgt
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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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!--------------------------------------------------------------------------------------------------
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! pointwise data ! 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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!variables controlling debugging
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logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
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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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if (solver == 'AL') solverInit%F_init=1.0_pReal
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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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! 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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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 (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 = loadcase%temperature) ! 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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!--------------------------------------------------------------------------------------------------
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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_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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! 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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! 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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! 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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!--------------------------------------------------------------------------------------------------
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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, p=1_pInt:3_pInt)&
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gamma_hat(i,j,k, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
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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 function solverInit
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type(solution_t) function solution(solver,load,restartWrite)
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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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!--------------------------------------------------------------------------------------------------
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! arrays for mixed boundary conditions
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logical restartWrite
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character(len=*) :: solver
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type(bc_type) :: load
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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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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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complex(pReal), dimension(3) :: temp3_complex
|
|
complex(pReal), dimension(3,3) :: temp33_complex
|
|
integer(pInt) :: size_reduced = 0_pInt
|
|
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
|
|
real(pReal), dimension(6) :: sigma ! cauchy stress
|
|
real(pReal), dimension(6,6) :: dsde
|
|
real(pReal), dimension(9,9) :: temp99_Real ! compliance and stiffness in matrix notation
|
|
|
|
integer(pInt) :: Npoints
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! pointwise data
|
|
type(C_PTR) :: tensorField ! field in real an fourier space
|
|
real(pReal), dimension(:,:,:,:,:), pointer :: P_real, deltaF_real ! field in real space (pointer)
|
|
|
|
complex(pReal), dimension(:,:,:,:,:), pointer :: P_fourier,deltaF_fourier ! field in fourier space (pointer)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! variables storing information for spectral method and FFTW
|
|
type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
|
|
real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
|
|
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
|
|
real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
|
|
integer(pInt), dimension(3) :: k_s, res
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! loop variables, convergence etc.
|
|
real(pReal) :: time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
|
|
real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
|
|
real(pReal), dimension(3,3) :: temp33_Real
|
|
integer(pInt) :: i, j, k, l, m, n, p, errorID
|
|
integer(pInt) :: N_Loadcases, loadcase = 0_pInt, inc, iter, ielem, CPFEM_mode=1_pInt, &
|
|
ierr, totalIncsCounter = 0_pInt,&
|
|
notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
|
|
logical :: errmatinv
|
|
real(pReal) :: defgradDet
|
|
character(len=6) :: loadcase_string
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!variables controlling debugging
|
|
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!variables for additional output due to general debugging
|
|
real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! variables for additional output of divergence calculations
|
|
type(C_PTR) :: divergence, plan_divergence
|
|
type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
|
|
plan_scalarField_forth, plan_scalarField_back
|
|
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
|
|
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
|
|
real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
|
|
integer(pInt) :: row, column
|
|
real(pReal), dimension(3,3) :: &
|
|
P_av, &
|
|
F_aim = math_I3, &
|
|
F_aim_lastInc = math_I3, &
|
|
mask_stress, &
|
|
mask_defgrad, &
|
|
deltaF_aim, &
|
|
F_aim_lab, &
|
|
F_aim_lab_lastIter, &
|
|
P_av_lab
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
dPdF, &
|
|
C_ref = 0.0_pReal, &
|
|
C = 0.0_pReal, &
|
|
S_lastInc, &
|
|
C_lastInc
|
|
real(pReal), dimension(3) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal
|
|
|
|
integer(pInt) :: &
|
|
res1_red
|
|
real(pReal) :: wgt
|
|
if (solver == 'AL') solution%converged=.true.
|
|
mask_defgrad = merge(ones,zeroes,load%maskDeformation)
|
|
mask_stress = merge(ones,zeroes,load%maskStress)
|
|
size_reduced = int(count(load%maskStressVector), pInt)
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate reduced compliance
|
|
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
|
|
C_lastInc = math_rotate_forward3333(C,load%rotation) ! calculate stiffness from former inc
|
|
temp99_Real = math_Plain3333to99(C_lastInc)
|
|
k = 0_pInt ! build reduced stiffness
|
|
do n = 1_pInt,9_pInt
|
|
if(load%maskStressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(load%maskStressVector(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(load%maskStressVector(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(load%maskStressVector(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
|
|
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
|
|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! report begin of new iteration
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '=================================================================='
|
|
write(6,'(6(a,i6.6))') 'Loadcase ',loadcase,' Inc. ',inc,'/',load%incs,&
|
|
' @ 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'
|
|
F_aim_lab_lastIter = math_rotate_backward33(F_aim,load%rotation)
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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_real(i,j,k,1:3,1:3),dPdF)
|
|
enddo; enddo; enddo
|
|
|
|
P_real = 0.0_pReal ! needed because of the padding for FFTW
|
|
C = 0.0_pReal
|
|
ielem = 0_pInt
|
|
call debug_reset()
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
ielem = ielem + 1_pInt
|
|
call CPFEM_general(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_real(i,j,k,1:3,1:3),dPdF)
|
|
CPFEM_mode = 2_pInt
|
|
C = C + dPdF
|
|
enddo; enddo; enddo
|
|
call debug_info()
|
|
! for test of regridding
|
|
! if( bc(loadcase)%restartFrequency > 0_pInt .and. &
|
|
! mod(inc-1,bc(loadcase)%restartFrequency) == 0_pInt .and. &
|
|
! restartInc/=inc) call quit(-1*(restartInc+1)) ! trigger exit to regrid
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! copy one component of the stress field to to a single FT and check for mismatch
|
|
if (debugFFTW) then
|
|
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
|
|
column = (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(P_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,&
|
|
P_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_stress,P_real,P_fourier)
|
|
|
|
P_av_lab = real(P_fourier(1,1,1,1:3,1:3),pReal)*wgt
|
|
P_av = math_rotate_forward33(P_av_lab,load%rotation)
|
|
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
|
|
math_transpose33(P_av)/1.e6_pReal
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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))-&
|
|
P_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))-&
|
|
P_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
|
|
P_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
P_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) &
|
|
P_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)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress BC handling
|
|
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
|
|
err_stress = maxval(abs(mask_stress * (P_av - load%stress))) ! 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 - load%stress))) ! 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,load%rotation) ! boundary conditions from load frame into lab (Fourier) frame
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! actual spectral method
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... calculating equilibrium with spectral method .................'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
pstress_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av_lab,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
|
|
math_transpose33(P_av_lab)))))
|
|
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(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
|
|
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
|
+sum(aimag(math_mul33x3_complex(P_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(P_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum( real(math_mul33x3_complex(P_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(P_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
|
|
|
|
if (err_div_RMS/pstress_av_L2 > err_div &
|
|
.and. err_stress < err_stress_tol &
|
|
.and. iter >= itmin ) then
|
|
write(6,'(a)') 'Increasing divergence, stopping iterations'
|
|
iter = itmax
|
|
endif
|
|
err_div = err_div_RMS/pstress_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(P_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
|
|
endif
|
|
write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
|
|
' (',err_div,' N/m³)'
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! to the actual spectral method calculation (mechanical equilibrium)
|
|
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
|
|
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
|
|
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
|
|
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
|
|
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
|
|
temp33_Real = math_inv33(temp33_Real)
|
|
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
|
|
gamma_hat(1,1,1, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
|
|
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) *&
|
|
P_fourier(i,j,k,1:3,1:3))
|
|
deltaF_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) *&
|
|
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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!--------------------------------------------------------------------------------------------------
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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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|
! 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)
|
|
maxCorrectionSym = max(maxCorrectionSym,&
|
|
maxval(math_symmetric33(deltaF_real(i,j,k,1:3,1:3))))
|
|
maxCorrectionSkew = max(maxCorrectionSkew,&
|
|
maxval(math_skew33(deltaF_real(i,j,k,1:3,1:3))))
|
|
temp33_Real = temp33_Real + deltaF_real(i,j,k,1:3,1:3)
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|
enddo; enddo; enddo
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|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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
|
|
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
|
|
|
|
|
|
if( load%restartFrequency > 0_pInt .and. &
|
|
mod(inc,load%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
|
|
|
|
|
|
deallocate(c_reduced)
|
|
deallocate(s_reduced)
|
|
end function solution
|
|
|
|
|
|
|
|
end module DAMASK_spectralSolver
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