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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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use CPFEM, only: &
CPFEM_general
use numerics, only: &
memory_efficient
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implicit none
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type solution_t ! mask of stress boundary conditions
logical :: converged = .false.
logical :: regrid = .false.
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logical :: term_ill = .false.
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end type solution_t
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character(len=5) :: solverType, parameter = 'basic'
real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc,P
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real(pReal), dimension(:,:,:,:), allocatable :: coordinates
real(pReal), dimension(:,:,:), allocatable :: temperature
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!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
type(C_PTR) :: plan_forward, plan_backward ! 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
real(pReal), dimension(:,:,:,:,:), pointer :: field_real
complex(pReal), dimension(:,:,:,:,:), pointer :: field_fourier
!--------------------------------------------------------------------------------------------------
! debug fftw
type(C_PTR) :: plan_scalarField_forth, plan_scalarField_back
complex(pReal), dimension(:,:,:), pointer :: scalarField_real
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complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
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!--------------------------------------------------------------------------------------------------
! debug divergence
type(C_PTR) :: plan_divergence
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real(pReal), dimension(:,:,:,:), pointer :: divergence_real
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
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!--------------------------------------------------------------------------------------------------
!variables controlling debugging
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
real(pReal), dimension(3,3) :: &
F_aim = math_I3, &
F_aim_lastInc = math_I3
real(pReal), dimension(3,3,3,3) :: &
C_ref = 0.0_pReal, &
C = 0.0_pReal
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
real(pReal) :: wgt
integer(pInt) :: res1_red, Npoints
contains
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subroutine Solver_Init()
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use mesh, only : &
mesh_spectral_getResolution, &
mesh_spectral_getDimension
use numerics, only: &
divergence_correction, &
DAMASK_NumThreadsInt, &
fftw_planner_flag, &
fftw_timelimit
use debug, only: &
debug_level, &
debug_spectral, &
debug_levelBasic, &
debug_spectralDivergence, &
debug_spectralRestart, &
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debug_spectralFFTW
use FEsolving, only: &
restartInc
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implicit none
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!--------------------------------------------------------------------------------------------------
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! loop variables, convergence etc.
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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real(pReal), dimension(3,3) :: temp33_Real
integer(pInt) :: i, j, k, l, m, n, q, ielem
real(pReal), dimension(3,3,3,3) :: dPdF
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type(C_PTR) :: tensorField ! field in real and fourier space
type(C_PTR) :: scalarField_realC, scalarField_fourierC
type(C_PTR) :: divergence
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integer(pInt), dimension(3) :: k_s
real(pReal), dimension(6) :: sigma ! cauchy stress
real(pReal), dimension(6,6) :: dsde
integer(pInt) :: ierr
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write(6,'(a)') ''
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write(6,'(a)') ' <<<+- DAMASK_spectralSolver init -+>>>'
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write(6,'(a)') ' $Id$'
#include "compilation_info.f90"
write(6,'(a)') ''
!--------------------------------------------------------------------------------------------------
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! set debugging parameters
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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
!##################################################################################################
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res = mesh_spectral_getResolution()
geomdim = mesh_spectral_getDimension()
res1_red = res(1)/2_pInt + 1_pInt
Npoints = res(1)*res(2)*res(3)
wgt = 1.0/real(Npoints,pReal)
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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)
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allocate (P ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
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allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
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allocate (temperature( res(1), res(2),res(3)), source = 0.0_pReal) ! start out isothermally
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tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
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call c_f_pointer(tensorField, field_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
call c_f_pointer(tensorField, field_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
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!--------------------------------------------------------------------------------------------------
! 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
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plan_forward = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
field_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
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1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
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field_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,fftw_planner_flag)
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plan_backward =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
field_fourier,[ res(3),res(2) ,res1_red],&
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1, res(3)*res(2)* res1_red,&
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field_real,[ res(3),res(2) ,res(1)+2_pInt],&
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1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
!--------------------------------------------------------------------------------------------------
! 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'
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!--------------------------------------------------------------------------------------------------
! 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),&
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0.0_pReal,ielem,1_pInt,sigma,dsde,P(i,j,k,1:3,1:3),dPdF)
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C = C + dPdF
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)
endif
!--------------------------------------------------------------------------------------------------
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! 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
!--------------------------------------------------------------------------------------------------
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! 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)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(i,j,k, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
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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 subroutine Solver_Init
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type(solution_t) function solution(guessmode,timeinc,timeinc_old,P_BC,F_BC,mask_stressVector,velgrad,rotation_BC)
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use numerics, only: &
err_div_tol, &
err_stress_tolrel, &
err_stress_tolabs, &
rotation_tol, &
itmax,&
itmin, &
divergence_correction, &
DAMASK_NumThreadsInt, &
fftw_planner_flag, &
fftw_timelimit
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use debug, only: &
debug_reset, &
debug_info
!--------------------------------------------------------------------------------------------------
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! arrays for mixed boundary conditions
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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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integer(pInt) :: size_reduced = 0_pInt
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
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real(pReal), dimension(3,3,3,3) :: &
C_lastInc
integer(pInt) :: iter, ielem
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!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
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real(pReal) :: timeinc, timeinc_old ! elapsed time, begin of interval, time interval
real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
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real(pReal), dimension(3,3) :: temp33_Real
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integer(pInt) :: i, j, k, m, n
integer(pInt) :: CPFEM_mode=1_pInt
logical :: errmatinv, restartWrite
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real(pReal) :: defgradDet
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!--------------------------------------------------------------------------------------------------
intermediate, not working state of new solver structure
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! variables for additional output of divergence calculations
further modularisation of spectral solver (only for basic scheme so far)
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intermediate, not working state of new solver structure
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real(pReal), dimension(3,3) :: &
P_av, &
mask_stress, &
mask_defgrad, &
deltaF_aim, &
F_aim_lab, &
F_aim_lab_lastIter, &
P_av_lab
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real(pReal), dimension(3,3,3,3) :: &
intermediate, not working state of new solver structure
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dPdF, &
C = 0.0_pReal, &
further modularisation of spectral solver (only for basic scheme so far)
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S_lastInc
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further modularisation of spectral solver (only for basic scheme so far)
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logical :: velgrad
real(pReal), dimension(3,3) :: P_BC,F_BC,rotation_BC
logical, dimension(9) :: mask_stressVector
real(pReal) :: defgradDetMax, defgradDetMin
mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3]))
mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3]))
size_reduced = int(count(mask_stressVector), pInt)
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allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
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if (velgrad) then ! calculate deltaF_aim from given L and current F
deltaF_aim = timeinc * mask_defgrad * math_mul33x33(F_BC, F_aim)
else ! deltaF_aim = fDot *timeinc where applicable
deltaF_aim = timeinc * mask_defgrad * F_BC
endif
!--------------------------------------------------------------------------------------------------
! winding forward of deformation aim in loadcase system
temp33_Real = F_aim
F_aim = F_aim &
+ guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
+ deltaF_aim
F_aim_lastInc = temp33_Real
!--------------------------------------------------------------------------------------------------
! winding forward of deformation aim in loadcase system
temp33_Real = F_aim
F_aim = F_aim &
+ guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
+ deltaF_aim
F_aim_lastInc = temp33_Real
!--------------------------------------------------------------------------------------------------
! update local deformation gradient and coordinates
deltaF_aim = math_rotate_backward33(deltaF_aim,rotation_BC)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = F(i,j,k,1:3,1:3)
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
*timeinc/timeinc_old &
+ (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
F_lastInc(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,rotation_BC),& ! calculate current coordinates
1.0_pReal,F_lastInc,coordinates)
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further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
intermediate, not working state of new solver structure
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!--------------------------------------------------------------------------------------------------
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
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C_lastInc = math_rotate_forward3333(C,rotation_BC) ! calculate stiffness from former inc
removed old standalone AL solver and introduced new structure for solver zoo
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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(mask_stressVector(n)) then
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k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
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if(mask_stressVector(m)) then
removed old standalone AL solver and introduced new structure for solver zoo
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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
further modularisation of spectral solver (only for basic scheme so far)
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if(mask_stressVector(n)) then
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k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
further modularisation of spectral solver (only for basic scheme so far)
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if(mask_stressVector(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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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
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
P_av = math_rotate_forward33(P_av_lab,rotation_BC)
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
math_transpose33(P_av)/1.e6_pReal
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (P_av - P_BC))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
write(6,'(a)') ''
write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
' (',err_stress,' Pa)'
F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - P_BC))) ! residual on given stress components
write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
else
err_stress_tol = +huge(1.0_pReal)
endif
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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!--------------------------------------------------------------------------------------------------
! report begin of new iteration
write(6,'(a)') ''
write(6,'(a)') '=================================================================='
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write(6,'(3(a,i6.6))') ' @ Iter. ',itmin,' < ',iter,' < ',itmax
removed old standalone AL solver and introduced new structure for solver zoo
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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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if(restartWrite) then
write(6,'(a)') 'writing converged results for restart'
call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F_lastInc)) ! writing deformation gradient field to file
write (777,rec=1) F_LastInc
close (777)
call IO_write_jobBinaryFile(777,'C',size(C))
write (777,rec=1) C
close(777)
endif
F_aim_lab_lastIter = math_rotate_backward33(F_aim,rotation_BC)
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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,&
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P(i,j,k,1:3,1:3),dPdF)
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enddo; enddo; enddo
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P = 0.0_pReal ! needed because of the padding for FFTW
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C = 0.0_pReal
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P_av_lab = 0.0_pReal
removed old standalone AL solver and introduced new structure for solver zoo
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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, &
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P(i,j,k,1:3,1:3),dPdF)
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CPFEM_mode = 2_pInt
C = C + dPdF
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P_av_lab = P_av_lab + P(i,j,k,1:3,1:3)
removed old standalone AL solver and introduced new structure for solver zoo
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enddo; enddo; enddo
call debug_info()
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restartWrite = .false.
P_av_lab = P_av_lab * wgt
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
P_av = math_rotate_forward33(P_av_lab,rotation_BC)
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
math_transpose33(P_av)/1.e6_pReal
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (P_av - P_BC))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
write(6,'(a)') ''
write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
' (',err_stress,' Pa)'
F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - P_BC))) ! residual on given stress components
write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
else
err_stress_tol = +huge(1.0_pReal)
endif
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC)
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = P
call convolution(.True.,F_aim_lab_lastIter - F_aim_lab)
!--------------------------------------------------------------------------------------------------
! updated deformation gradient
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - field_real(i,j,k,1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
enddo; enddo; enddo
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
if(debugGeneral) then
defgradDetMax = -huge(1.0_pReal)
defgradDetMin = +huge(1.0_pReal)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
defgradDet = math_det33(F(i,j,k,1:3,1:3))
defgradDetMax = max(defgradDetMax,defgradDet)
defgradDetMin = min(defgradDetMin,defgradDet)
enddo; enddo; enddo
write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
endif
enddo ! end looping when convergency is achieved
CPFEM_mode = 1_pInt ! winding forward
C = C * wgt
deallocate(c_reduced)
deallocate(s_reduced)
end function solution
subroutine convolution(calcDivergence, field_aim)
real(pReal) :: err_div
real(pReal), dimension(3,3) :: temp33_Real
integer(pInt) :: i, j, k, l, m, n, q
removed old standalone AL solver and introduced new structure for solver zoo
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!--------------------------------------------------------------------------------------------------
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
!variables for additional output due to general debugging
real(pReal) :: maxCorrectionSym, maxCorrectionSkew
logical :: calcDivergence
real(pReal), dimension(3,3) :: field_avg, field_aim
integer(pInt) :: row, column
real(pReal) :: field_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
err_div_max, err_real_div_max
complex(pReal), dimension(3) :: temp3_complex
complex(pReal), dimension(3,3) :: temp33_complex
!--------------------------------------------------------------------------------------------------
! actual spectral method
write(6,'(a)') ''
write(6,'(a)') '... doing convolution .................'
!--------------------------------------------------------------------------------------------------
removed old standalone AL solver and introduced new structure for solver zoo
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! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
row = 3 ! (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
column = 3 !(mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
cmplx(field_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
removed old standalone AL solver and introduced new structure for solver zoo
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endif
!--------------------------------------------------------------------------------------------------
! call function to calculate divergence from math (for post processing) to check results
if (debugDivergence) &
call divergence_fft(res,virt_dim,3_pInt,&
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
!--------------------------------------------------------------------------------------------------
! doing the FT because it simplifies calculation of average stress in real space also
further modularisation of spectral solver (only for basic scheme so far)
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call fftw_execute_dft_r2c(plan_forward,field_real,field_fourier)
removed old standalone AL solver and introduced new structure for solver zoo
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!--------------------------------------------------------------------------------------------------
! 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))-&
further modularisation of spectral solver (only for basic scheme so far)
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field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
removed old standalone AL solver and introduced new structure for solver zoo
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scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
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2012-07-23 15:42:31 +05:30
field_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
! removing highest frequencies
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
= cmplx(0.0_pReal,0.0_pReal,pReal)
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2012-07-23 15:42:31 +05:30
field_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
= cmplx(0.0_pReal,0.0_pReal,pReal)
if(res(3)>1_pInt) &
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
field_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
= cmplx(0.0_pReal,0.0_pReal,pReal)
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
if( calcDivergence) then
field_avg = real(field_fourier(1,1,1,1:3,1:3),pReal)*wgt
field_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(field_avg,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
math_transpose33(field_avg)))))
removed old standalone AL solver and introduced new structure for solver zoo
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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 &
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+ 2.0_pReal*(sum (real(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+sum(aimag(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
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
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+ sum( real(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+ sum( real(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
further modularisation of spectral solver (only for basic scheme so far)
2012-07-23 15:42:31 +05:30
+ sum(aimag(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
removed old standalone AL solver and introduced new structure for solver zoo
2012-07-19 22:54:56 +05:30
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
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err_div = err_div_RMS/field_av_L2 ! criterion to stop iterations
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!--------------------------------------------------------------------------------------------------
! 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
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temp3_Complex = math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
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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
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! write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
! ' (',err_div,' N/m³)'
end if
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!--------------------------------------------------------------------------------------------------
! 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)
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forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(1,1,1, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
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forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
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field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k,1:3,1:3) = temp33_Complex
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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) *&
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field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
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enddo; enddo; enddo
endif
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field_fourier(1,1,1,1:3,1:3) = cmplx(field_aim,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
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!--------------------------------------------------------------------------------------------------
! 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
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scalarField_fourier(i,j,k) = field_fourier(i,j,k,row,column)
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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
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call fftw_execute_dft_c2r(plan_backward,field_fourier,field_real) ! back transform of fluct deformation gradient
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!--------------------------------------------------------------------------------------------------
! 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)))-&
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field_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))))
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,&
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maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
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maxCorrectionSkew = max(maxCorrectionSkew,&
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maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
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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
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end subroutine convolution
intermediate, not working state of new solver structure
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end module DAMASK_spectralSolver