711 lines
40 KiB
Fortran
711 lines
40 KiB
Fortran
! Copyright 2012 Max-Planck-Institut für Eisenforschung GmbH
|
|
!
|
|
! This file is part of DAMASK,
|
|
! the Düsseldorf Advanced Material Simulation Kit.
|
|
!
|
|
! DAMASK is free software: you can redistribute it and/or modify
|
|
! it under the terms of the GNU General Public License as published by
|
|
! the Free Software Foundation, either version 3 of the License, or
|
|
! (at your option) any later version.
|
|
!
|
|
! DAMASK is distributed in the hope that it will be useful,
|
|
! but WITHOUT ANY WARRANTY; without even the implied warranty of
|
|
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
|
|
! GNU General Public License for more details.
|
|
!
|
|
! You should have received a copy of the GNU General Public License
|
|
! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
|
|
!
|
|
!##################################################################################################
|
|
!* $Id$
|
|
!##################################################################################################
|
|
! Material subroutine for BVP solution using spectral method
|
|
!
|
|
! Run 'DAMASK_spectral.exe --help' to get usage hints
|
|
!
|
|
! written by P. Eisenlohr,
|
|
! F. Roters,
|
|
! L. Hantcherli,
|
|
! W.A. Counts,
|
|
! D.D. Tjahjanto,
|
|
! C. Kords,
|
|
! M. Diehl,
|
|
! R. Lebensohn
|
|
!
|
|
! MPI fuer Eisenforschung, Duesseldorf
|
|
|
|
#include "spectral_quit.f90"
|
|
|
|
program DAMASK_spectral
|
|
use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
|
|
|
|
use DAMASK_interface, only: &
|
|
DAMASK_interface_init, &
|
|
loadCaseFile, &
|
|
geometryFile, &
|
|
getSolverWorkingDirectoryName, &
|
|
getSolverJobName, &
|
|
appendToOutFile
|
|
|
|
use prec, only: &
|
|
pInt, &
|
|
pReal, &
|
|
DAMASK_NaN
|
|
|
|
use IO, only: &
|
|
IO_isBlank, &
|
|
IO_open_file, &
|
|
IO_stringPos, &
|
|
IO_stringValue, &
|
|
IO_floatValue, &
|
|
IO_intValue, &
|
|
IO_error, &
|
|
IO_lc, &
|
|
IO_read_jobBinaryFile, &
|
|
IO_write_jobBinaryFile
|
|
|
|
use debug, only: &
|
|
debug_level, &
|
|
debug_spectral, &
|
|
debug_levelBasic, &
|
|
debug_spectralDivergence, &
|
|
debug_spectralRestart, &
|
|
debug_spectralFFTW, &
|
|
debug_reset, &
|
|
debug_info
|
|
|
|
use math
|
|
|
|
use mesh, only : &
|
|
mesh_spectral_getResolution, &
|
|
mesh_spectral_getDimension, &
|
|
mesh_spectral_getHomogenization
|
|
|
|
use CPFEM, only: &
|
|
CPFEM_general, &
|
|
CPFEM_initAll
|
|
|
|
use FEsolving, only: &
|
|
restartWrite, &
|
|
restartInc
|
|
|
|
use numerics, only: &
|
|
err_div_tol, &
|
|
err_stress_tolrel, &
|
|
err_stress_tolabs, &
|
|
rotation_tol, &
|
|
itmax,&
|
|
itmin, &
|
|
memory_efficient, &
|
|
divergence_correction, &
|
|
DAMASK_NumThreadsInt, &
|
|
fftw_planner_flag, &
|
|
fftw_timelimit
|
|
|
|
use homogenization, only: &
|
|
materialpoint_sizeResults, &
|
|
materialpoint_results
|
|
|
|
implicit none
|
|
|
|
#ifdef PETSC
|
|
#include <finclude/petscsys.h>
|
|
#include <finclude/petscvec.h>
|
|
#include <finclude/petscsnes.h>
|
|
#include <finclude/petscvec.h90>
|
|
#include <finclude/petscsnes.h90>
|
|
#endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! variables related to information from load case and geom file
|
|
real(pReal), dimension(9) :: &
|
|
temp_valueVector !> temporarily from loadcase file when reading in tensors
|
|
logical, dimension(9) :: &
|
|
temp_maskVector !> temporarily from loadcase file when reading in tensors
|
|
integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
|
|
(1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
|
|
1_pInt, & ! dropguessing
|
|
maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
|
|
myUnit = 234_pInt
|
|
integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
|
|
|
|
integer(pInt) :: &
|
|
N_l = 0_pInt, &
|
|
N_t = 0_pInt, &
|
|
N_n = 0_pInt, &
|
|
N_Fdot = 0_pInt, &
|
|
Npoints,& ! number of Fourier points
|
|
homog, & ! homogenization scheme used
|
|
res1_red ! to store res(1)/2 +1
|
|
|
|
character(len=1024) :: &
|
|
line
|
|
|
|
type bc_type
|
|
real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
|
|
stress = 0.0_pReal, & ! stress BC (if applicable)
|
|
rotation = math_I3 ! rotation of BC (if applicable)
|
|
real(pReal) :: time = 0.0_pReal, & ! length of increment
|
|
temperature = 300.0_pReal ! isothermal starting conditions
|
|
integer(pInt) :: incs = 0_pInt, & ! number of increments
|
|
outputfrequency = 1_pInt, & ! frequency of result writes
|
|
restartfrequency = 0_pInt, & ! frequency of restart writes
|
|
logscale = 0_pInt ! linear/logaritmic time inc flag
|
|
logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
|
|
velGradApplied = .false. ! decide wether velocity gradient or fdot is given
|
|
logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
|
|
maskStress = .false. ! mask of stress boundary conditions
|
|
logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
|
|
end type
|
|
|
|
type(bc_type), allocatable, dimension(:) :: bc
|
|
|
|
|
|
real(pReal) :: wgt
|
|
real(pReal), dimension(3) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal ! physical dimension of volume element per direction
|
|
integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress, stiffness and compliance average etc.
|
|
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 ! stiffness and compliance
|
|
|
|
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
|
|
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
|
|
integer(pInt) :: size_reduced = 0_pInt ! number of stress BCs
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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)
|
|
|
|
real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc
|
|
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
|
|
real(pReal), dimension(:,:,:), allocatable :: temperature
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! loop variables, convergence etc.
|
|
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
|
|
real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
|
|
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
|
|
complex(pReal), dimension(3) :: temp3_Complex
|
|
complex(pReal), dimension(3,3) :: temp33_Complex
|
|
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
|
|
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
|
|
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
|
|
real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
|
|
real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
|
|
err_div_max, err_real_div_max
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! variables for debugging fft using a scalar field
|
|
type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
|
|
plan_scalarField_forth, plan_scalarField_back
|
|
complex(pReal), dimension(:,:,:), pointer :: scalarField_real
|
|
complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
|
|
integer(pInt) :: row, column
|
|
|
|
!##################################################################################################
|
|
! reading of information from load case file and geometry file
|
|
!##################################################################################################
|
|
|
|
subroutine init
|
|
|
|
#ifdef PETSC
|
|
integer :: ierr_psc
|
|
call PetscInitialize(PETSC_NULL_CHARACTER, ierr_psc)
|
|
#endif
|
|
call DAMASK_interface_init
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') ' <<<+- DAMASK_spectral init -+>>>'
|
|
write(6,'(a)') ' $Id$'
|
|
#include "compilation_info.f90"
|
|
write(6,'(a)') ''
|
|
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! debugging parameters
|
|
debugGeneral = iand(debug_level(debug_spectral),debug_levelBasic) /= 0
|
|
debugDivergence = iand(debug_level(debug_spectral),debug_spectralDivergence) /= 0
|
|
debugRestart = iand(debug_level(debug_spectral),debug_spectralRestart) /= 0
|
|
debugFFTW = iand(debug_level(debug_spectral),debug_spectralFFTW) /= 0
|
|
|
|
!##################################################################################################
|
|
! initialization
|
|
!##################################################################################################
|
|
|
|
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
|
|
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
|
|
call c_f_pointer(tensorField, P_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
|
|
call c_f_pointer(tensorField, deltaF_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! creating plans
|
|
plan_stress = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
|
|
P_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
|
|
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
|
|
P_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,fftw_planner_flag)
|
|
|
|
plan_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
|
|
deltaF_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,&
|
|
deltaF_real,[ res(3),res(2) ,res(1)+2_pInt],&
|
|
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! in case of no restart get reference material stiffness and init fields to no deformation
|
|
if (restartInc == 1_pInt) then
|
|
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
|
|
F(i,j,k,1:3,1:3) = math_I3
|
|
F_lastInc(i,j,k,1:3,1:3) = math_I3
|
|
coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) - geomdim/real(2_pInt*res,pReal)
|
|
call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
|
|
0.0_pReal,ielem,1_pInt,sigma,dsde,P_real(i,j,k,1:3,1:3),dPdF)
|
|
C = C + dPdF
|
|
enddo; enddo; enddo
|
|
C = C * wgt
|
|
C_ref = C
|
|
call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
|
|
write (777,rec=1) C_ref
|
|
close(777)
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! restore deformation gradient and stiffness from saved state
|
|
elseif (restartInc > 1_pInt) then ! using old values from file
|
|
if (debugRestart) write(6,'(a,i6,a)') 'Reading values of increment ',&
|
|
restartInc - 1_pInt,' from file'
|
|
call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
|
|
trim(getSolverJobName()),size(F))
|
|
read (777,rec=1) F
|
|
close (777)
|
|
F_lastInc = F
|
|
F_aim = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
F_aim = F_aim + F(i,j,k,1:3,1:3) ! calculating old average deformation
|
|
enddo; enddo; enddo
|
|
F_aim = F_aim * wgt
|
|
F_aim_lastInc = F_aim
|
|
coordinates = 0.0 ! change it later!!!
|
|
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
|
|
read (777,rec=1) C_ref
|
|
close (777)
|
|
call IO_read_jobBinaryFile(777,'C',trim(getSolverJobName()),size(C))
|
|
read (777,rec=1) C
|
|
close (777)
|
|
CPFEM_mode = 2_pInt
|
|
endif
|
|
|
|
end subroutine init
|
|
|
|
|
|
subroutine solution(guessmode, F_aim,F_aimLastInc, BC_stress, mask_stress)
|
|
!--------------------------------------------------------------------------------------------------
|
|
! update local deformation gradient and coordinates
|
|
|
|
deltaF_aim = math_rotate_backward33(deltaF_aim,bc(loadcase)%rotation)
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
temp33_Real = F(i,j,k,1:3,1:3)
|
|
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
|
|
+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
|
|
*timeinc/timeinc_old &
|
|
+ (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
|
|
F_lastInc(i,j,k,1:3,1:3) = temp33_Real
|
|
enddo; enddo; enddo
|
|
call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,bc(loadcase)%rotation),& ! calculate current coordinates
|
|
1.0_pReal,F_lastInc,coordinates)
|
|
|
|
|
|
|
|
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,'/',bc(loadcase)%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,bc(loadcase)%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,bc(loadcase)%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 - bc(loadcase)%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 - bc(loadcase)%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,bc(loadcase)%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))
|
|
deltaF_fourier(i,j,k, 1:3,1:3) = temp33_Complex
|
|
enddo; enddo; enddo
|
|
|
|
endif
|
|
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)
|
|
* real(Npoints,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
|
|
scalarField_fourier(i,j,k) = deltaF_fourier(i,j,k,row,column)
|
|
enddo; enddo; enddo
|
|
do i = 0_pInt, res(1)/2_pInt-2_pInt ! unpack fft data for conj complex symmetric part
|
|
m = 1_pInt
|
|
do k = 1_pInt, res(3)
|
|
n = 1_pInt
|
|
do j = 1_pInt, res(2)
|
|
scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
|
|
if(n == 1_pInt) n = res(2) + 1_pInt
|
|
n = n-1_pInt
|
|
enddo
|
|
if(m == 1_pInt) m = res(3) + 1_pInt
|
|
m = m -1_pInt
|
|
enddo; enddo
|
|
endif
|
|
!--------------------------------------------------------------------------------------------------
|
|
! doing the inverse FT
|
|
call fftw_execute_dft_c2r(plan_correction,deltaF_fourier,deltaF_real) ! back transform of fluct deformation gradient
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! comparing 1 and 3x3 inverse FT results
|
|
if (debugFFTW) then
|
|
write(6,'(a,i1,1x,i1)') 'checking iFT results of compontent ', row, column
|
|
call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
|
|
write(6,'(a,es11.4)') 'max iFT relative error = ',&
|
|
maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
|
|
deltaF_real(1:res(1),1:res(2),1:res(3),row,column))/&
|
|
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate some additional output
|
|
if(debugGeneral) then
|
|
maxCorrectionSkew = 0.0_pReal
|
|
maxCorrectionSym = 0.0_pReal
|
|
temp33_Real = 0.0_pReal
|
|
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
|
|
maxCorrectionSym = max(maxCorrectionSym,&
|
|
maxval(math_symmetric33(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)
|
|
enddo; enddo; enddo
|
|
write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
|
|
maxCorrectionSym*wgt
|
|
write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
|
|
maxCorrectionSkew*wgt
|
|
write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
|
|
maxval(math_symmetric33(temp33_real))/&
|
|
maxval(math_skew33(temp33_real))
|
|
endif
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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
|
|
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
|
|
|