634 lines
32 KiB
Fortran
634 lines
32 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
|
|
|
|
module DAMASK_spectral_Utilities
|
|
|
|
use prec, only: &
|
|
pReal, &
|
|
pInt
|
|
|
|
use math
|
|
|
|
use IO, only: &
|
|
IO_error
|
|
|
|
implicit none
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! variables storing information for spectral method and FFTW
|
|
type(C_PTR) :: plan_forward, plan_backward ! plans for fftw
|
|
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
|
|
complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! debug divergence
|
|
type(C_PTR) :: plan_divergence
|
|
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
|
|
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
|
|
real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!variables controlling debugging
|
|
logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
|
|
|
|
|
|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! solution state
|
|
type solutionState
|
|
logical :: converged = .false.
|
|
logical :: regrid = .false.
|
|
logical :: term_ill = .false.
|
|
end type solutionState
|
|
contains
|
|
|
|
subroutine Utilities_init(C_ref)
|
|
|
|
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, &
|
|
debug_spectralFFTW
|
|
|
|
use numerics, only: &
|
|
memory_efficient
|
|
|
|
implicit none
|
|
|
|
real(pReal), dimension(3,3) :: temp33_Real, xiDyad
|
|
integer(pInt) :: i, j, k, l, m, n, q, ierr
|
|
integer(pInt), dimension(3) :: k_s
|
|
real(pReal), dimension(3,3,3,3) :: &
|
|
C_ref
|
|
|
|
type(C_PTR) :: tensorField ! field in real and fourier space
|
|
type(C_PTR) :: scalarField_realC, scalarField_fourierC
|
|
type(C_PTR) :: divergence
|
|
|
|
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') ' <<<+- DAMASK_spectralSolver Utilities init -+>>>'
|
|
write(6,'(a)') ' $Id$'
|
|
#include "compilation_info.f90"
|
|
write(6,'(a)') ''
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! set 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
|
|
!##################################################################################################
|
|
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)
|
|
|
|
allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal) ! start out isothermally
|
|
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)
|
|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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_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
|
|
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
|
|
field_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,fftw_planner_flag)
|
|
|
|
plan_backward =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
|
|
field_fourier,[ res(3),res(2) ,res1_red],&
|
|
1, res(3)*res(2)* res1_red,&
|
|
field_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
|
|
|
|
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, q=1_pInt:3_pInt)&
|
|
gamma_hat(i,j,k, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
|
|
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
|
|
end subroutine Utilities_init
|
|
|
|
real(pReal) function convolution(calcDivergence,field_aim,C_ref)
|
|
|
|
use numerics, only: &
|
|
memory_efficient, &
|
|
err_div_tol
|
|
|
|
real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
|
|
real(pReal) :: err_div = 0.0_pReal
|
|
real(pReal), dimension(3,3) :: temp33_Real
|
|
integer(pInt) :: i, j, k, l, m, n, q
|
|
real(pReal), dimension(3,3,3,3) :: C_ref
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
!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 .................'
|
|
!--------------------------------------------------------------------------------------------------
|
|
! copy one component of the stress field to to a single FT and check for mismatch
|
|
if (debugFFTW) then
|
|
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
|
|
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
|
|
cmplx(field_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,&
|
|
field_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_forward,field_real,field_fourier)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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))-&
|
|
field_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))-&
|
|
field_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
|
|
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
|
|
= cmplx(0.0_pReal,0.0_pReal,pReal)
|
|
field_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) &
|
|
field_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)
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculating RMS divergence criterion in Fourier space
|
|
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)))))
|
|
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(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
|
|
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
|
|
+sum(aimag(math_mul33x3_complex(field_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(field_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
|
|
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
|
|
+ sum( real(math_mul33x3_complex(field_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(field_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
|
|
err_div = err_div_RMS/field_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(field_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)'
|
|
end if
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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, q=1_pInt:3_pInt)&
|
|
gamma_hat(1,1,1, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
|
|
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) *&
|
|
field_fourier(i,j,k,1:3,1:3))
|
|
field_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) *&
|
|
field_fourier(i,j,k,1:3,1:3))
|
|
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
|
|
enddo; enddo; enddo
|
|
endif
|
|
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
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! 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) = field_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_backward,field_fourier,field_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)))-&
|
|
field_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(field_real(i,j,k,1:3,1:3))))
|
|
maxCorrectionSkew = max(maxCorrectionSkew,&
|
|
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)
|
|
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
|
|
field_real = field_real * wgt
|
|
convolution = err_div/err_div_tol
|
|
|
|
end function convolution
|
|
|
|
|
|
function S_lastInc(rot_BC,mask_stressVector1,C)
|
|
|
|
real(pReal), dimension(3,3,3,3) :: S_lastInc
|
|
real(pReal), dimension(3,3,3,3), intent(in) :: C
|
|
integer(pInt) :: i, j, k, m, n
|
|
real(pReal), dimension(3,3), intent(in) :: rot_BC
|
|
logical, dimension(9), intent(in) :: mask_stressVector1
|
|
real(pReal), dimension(3,3,3,3) :: C_lastInc
|
|
real(pReal), dimension(9,9) :: temp99_Real
|
|
integer(pInt) :: size_reduced = 0_pInt
|
|
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
|
|
logical :: errmatinv
|
|
size_reduced = count(mask_stressVector1)
|
|
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
|
|
|
|
C_lastInc = math_rotate_forward3333(C,rot_BC) ! calculate stiffness from former inc
|
|
temp99_Real = math_Plain3333to99(C_lastInc)
|
|
k = 0_pInt ! build reduced stiffness
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector1(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector1(m)) then
|
|
j = j + 1_pInt
|
|
c_reduced(k,j) = temp99_Real(n,m)
|
|
endif; enddo; endif; enddo
|
|
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
|
|
if(errmatinv) call IO_error(error_ID=400_pInt)
|
|
temp99_Real = 0.0_pReal ! build full compliance
|
|
k = 0_pInt
|
|
do n = 1_pInt,9_pInt
|
|
if(mask_stressVector1(n)) then
|
|
k = k + 1_pInt
|
|
j = 0_pInt
|
|
do m = 1_pInt,9_pInt
|
|
if(mask_stressVector1(m)) then
|
|
j = j + 1_pInt
|
|
temp99_Real(n,m) = s_reduced(k,j)
|
|
endif; enddo; endif; enddo
|
|
S_lastInc = math_Plain99to3333(temp99_Real)
|
|
|
|
end function S_lastInc
|
|
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! calculate reduced compliance
|
|
|
|
real(pReal) function BCcorrection(mask_stressVector,P_BC,P_av,F_aim,S_lastInc)
|
|
|
|
use numerics, only: err_stress_tolrel, err_stress_tolabs
|
|
|
|
logical, dimension(9) :: mask_stressVector
|
|
real(pReal) :: err_stress, err_stress_tol
|
|
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
|
|
real(pReal), dimension(3,3,3,3) :: S_lastInc
|
|
real(pReal), dimension(3,3) :: &
|
|
P_BC , &
|
|
P_av, &
|
|
F_aim, &
|
|
mask_stress, &
|
|
mask_defgrad
|
|
mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3]))
|
|
mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3]))
|
|
|
|
!--------------------------------------------------------------------------------------------------
|
|
! stress BC handling
|
|
! 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)
|
|
BCcorrection = err_stress/err_stress_tol
|
|
|
|
end function BCcorrection
|
|
|
|
subroutine constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
|
|
P,C,P_av,ForwardData,rotation_BC)
|
|
use debug, only: &
|
|
debug_reset, &
|
|
debug_info
|
|
use CPFEM, only: &
|
|
CPFEM_general
|
|
use FEsolving, only: restartWrite
|
|
|
|
implicit none
|
|
|
|
real(pReal), dimension(res(1),res(2),res(3)) :: temperature
|
|
real(pReal), dimension(res(1),res(2),res(3),3) :: coordinates
|
|
|
|
real(pReal), dimension(res(1),res(2),res(3),3,3) :: F,F_lastInc, P
|
|
real(pReal) :: timeinc
|
|
logical :: ForwardData
|
|
integer(pInt) :: i, j, k, ielem
|
|
integer(pInt) :: CPFEM_mode
|
|
real(pReal), dimension(3,3,3,3) :: dPdF, C
|
|
real(pReal), dimension(6) :: sigma ! cauchy stress
|
|
real(pReal), dimension(6,6) :: dsde
|
|
real(pReal), dimension(3,3) :: P_av_lab, P_av, rotation_BC
|
|
|
|
if (ForwardData) then
|
|
CPFEM_mode = 1_pInt
|
|
else
|
|
CPFEM_mode = 2_pInt
|
|
endif
|
|
write(6,'(a)') ''
|
|
write(6,'(a)') '... update stress field P(F) .....................................'
|
|
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(i,j,k,1:3,1:3),dPdF)
|
|
enddo; enddo; enddo
|
|
|
|
P = 0.0_pReal ! needed because of the padding for FFTW
|
|
C = 0.0_pReal
|
|
P_av_lab = 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(i,j,k,1:3,1:3),dPdF)
|
|
CPFEM_mode = 2_pInt
|
|
C = C + dPdF
|
|
P_av_lab = P_av_lab + P(i,j,k,1:3,1:3)
|
|
enddo; enddo; enddo
|
|
call debug_info()
|
|
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
|
|
C = C * wgt
|
|
end subroutine constitutiveResponse
|
|
|
|
subroutine Utilities_destroy
|
|
|
|
implicit none
|
|
|
|
if (debugDivergence) then
|
|
call fftw_destroy_plan(plan_divergence)
|
|
endif
|
|
|
|
if (debugFFTW) then
|
|
call fftw_destroy_plan(plan_scalarField_forth)
|
|
call fftw_destroy_plan(plan_scalarField_back)
|
|
endif
|
|
|
|
call fftw_destroy_plan(plan_forward)
|
|
call fftw_destroy_plan(plan_backward)
|
|
|
|
end subroutine Utilities_destroy
|
|
|
|
end module DAMASK_spectral_Utilities
|