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DAMASK_EICMD/code/DAMASK_spectralSolver.f90

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removed old standalone AL solver and introduced new structure for solver zoo
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! 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
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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
use math
use DAMASK_interface, only: &
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DAMASK_interface_init, &
loadCaseFile, &
geometryFile, &
getSolverWorkingDirectoryName, &
getSolverJobName, &
appendToOutFile
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use debug, only: &
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debug_level, &
debug_spectral, &
debug_levelBasic, &
debug_spectralRestart, &
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debug_spectralFFTW
use IO
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implicit none
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type solution_t ! mask of stress boundary conditions
logical :: converged = .false.
logical :: regrid = .false.
end type solution_t
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type init
real(pReal), dimension(3,3) :: F_init
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
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
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real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
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)
complex(pReal), dimension(:,:,:), pointer :: scalarField_real
complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
!--------------------------------------------------------------------------------------------------
! variables for additional output of divergence calculations
type(C_PTR) :: divergence, plan_divergence, plan_correction
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
contains
type(init) function solverInit(solver,restartInc,loadcase)
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use mesh, only : &
mesh_spectral_getResolution, &
mesh_spectral_getDimension
use CPFEM, only: &
CPFEM_general
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use numerics, only: &
memory_efficient, &
divergence_correction, &
DAMASK_NumThreadsInt, &
fftw_planner_flag, &
fftw_timelimit
use debug, only: &
debug_level, &
debug_spectral, &
debug_levelBasic, &
debug_spectralDivergence, &
debug_spectralRestart, &
debug_spectralFFTW, &
debug_reset, &
debug_info
implicit none
real(pReal) :: restartInc
character(len=*) :: solver
integer(pInt) :: &
Npoints,& ! number of Fourier points
homog, & ! homogenization scheme used
res1_red
!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
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) :: inc, iter, ielem, CPFEM_mode=1_pInt, &
ierr
logical :: errmatinv
real(pReal) :: defgradDet
!--------------------------------------------------------------------------------------------------
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! 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, &
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C_lastInc
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!--------------------------------------------------------------------------------------------------
! pointwise data
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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!--------------------------------------------------------------------------------------------------
! 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
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
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real(pReal), dimension(6) :: sigma ! cauchy stress
real(pReal), dimension(6,6) :: dsde
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
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!--------------------------------------------------------------------------------------------------
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! pointwise data ! 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)
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!--------------------------------------------------------------------------------------------------
!variables controlling debugging
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
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!--------------------------------------------------------------------------------------------------
! 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
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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)') ' $Id$'
#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
!##################################################################################################
allocate (F ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
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)
!--------------------------------------------------------------------------------------------------
! general initialization of fftw (see manual on fftw.org for more details)
if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=808_pInt) ! check for correct precision in C
!$ if(DAMASK_NumThreadsInt > 0_pInt) then
!$ ierr = fftw_init_threads()
!$ if (ierr == 0_pInt) call IO_error(error_ID = 809_pInt)
!$ call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
!$ endif
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! 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)
!--------------------------------------------------------------------------------------------------
! depending on (debug) options, allocate more memory and create additional plans
if (debugDivergence) then
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
allocate (divergence_post(res(1),res(2),res(3),3)); divergence_post = 0.0_pReal
plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
divergence_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,&
divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
endif
if (debugFFTW) then
scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T))
call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)])
call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)])
plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
scalarField_real,scalarField_fourier,-1,fftw_planner_flag)
plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
scalarField_fourier,scalarField_real,+1,fftw_planner_flag)
endif
if (debugGeneral) write(6,'(a)') 'FFTW initialized'
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
if (divergence_correction) then
do i = 1_pInt, 3_pInt
if (i /= minloc(geomdim,1) .and. i /= maxloc(geomdim,1)) virt_dim = geomdim/geomdim(i)
enddo
else
virt_dim = geomdim
endif
do k = 1_pInt, res(3)
k_s(3) = k - 1_pInt
if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
do j = 1_pInt, res(2)
k_s(2) = j - 1_pInt
if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
do i = 1_pInt, res1_red
k_s(1) = i - 1_pInt
xi(1:3,i,j,k) = real(k_s, pReal)/virt_dim
enddo; enddo; enddo
!--------------------------------------------------------------------------------------------------
! 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
!--------------------------------------------------------------------------------------------------
! calculate the gamma operator
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
else ! precalculation of gamma_hat field
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source = 0.0_pReal)
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(i,j,k, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
endif
enddo; enddo; enddo
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
endif
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end function solverInit
type(solution_t) function solution(solver,load,restartWrite)
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
!--------------------------------------------------------------------------------------------------
! arrays for mixed boundary conditions
logical restartWrite
character(len=*) :: solver
type(bc_type) :: load
real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
err_div_max, err_real_div_max
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
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
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!--------------------------------------------------------------------------------------------------
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! 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)
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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 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
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!--------------------------------------------------------------------------------------------------
! 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
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!--------------------------------------------------------------------------------------------------
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!variables controlling debugging
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
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!--------------------------------------------------------------------------------------------------
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!variables for additional output due to general debugging
real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
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!--------------------------------------------------------------------------------------------------
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! 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)
!--------------------------------------------------------------------------------------------------
removed old standalone AL solver and introduced new structure for solver zoo
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! calculate reduced compliance
if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
intermediate, not working state of new solver structure
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C_lastInc = math_rotate_forward3333(C,load%rotation) ! calculate stiffness from former inc
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temp99_Real = math_Plain3333to99(C_lastInc)
k = 0_pInt ! build reduced stiffness
do n = 1_pInt,9_pInt
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if(load%maskStressVector(n)) then
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k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
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if(load%maskStressVector(m)) then
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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
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if(load%maskStressVector(n)) then
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k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
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if(load%maskStressVector(m)) then
removed old standalone AL solver and introduced new structure for solver zoo
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j = j + 1_pInt
temp99_Real(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
S_lastInc = (math_Plain99to3333(temp99_Real))
endif
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guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
removed old standalone AL solver and introduced new structure for solver zoo
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iter = 0_pInt
err_div = huge(err_div_tol) ! go into loop
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!##################################################################################################
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! convergence loop (looping over iterations)
!##################################################################################################
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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)') '=================================================================='
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write(6,'(6(a,i6.6))') 'Loadcase ',loadcase,' Inc. ',inc,'/',load%incs,&
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' @ 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'
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F_aim_lab_lastIter = math_rotate_backward33(F_aim,load%rotation)
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!--------------------------------------------------------------------------------------------------
! 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
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P_av = math_rotate_forward33(P_av_lab,load%rotation)
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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
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err_stress = maxval(abs(mask_stress * (P_av - load%stress))) ! maximum deviaton (tensor norm not applicable)
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err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
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)'
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F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - load%stress))) ! residual on given stress components
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write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
else
err_stress_tol = +huge(1.0_pReal)
endif
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F_aim_lab = math_rotate_backward33(F_aim,load%rotation) ! boundary conditions from load frame into lab (Fourier) frame
removed old standalone AL solver and introduced new structure for solver zoo
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!--------------------------------------------------------------------------------------------------
! 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
intermediate, not working state of new solver structure
2012-07-20 21:03:13 +05:30
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
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
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
intermediate, not working state of new solver structure
2012-07-20 21:03:13 +05:30
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
deallocate(c_reduced)
deallocate(s_reduced)
intermediate, not working state of new solver structure
2012-07-20 21:03:13 +05:30
end function solution
end module DAMASK_spectralSolver