2012-03-07 23:07:40 +05:30
! Copyright 2011 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/>.
!
!##################################################################################################
2012-03-30 01:24:31 +05:30
!* $Id$
2012-03-07 23:07:40 +05:30
!##################################################################################################
! 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
!##################################################################################################
! used modules
!##################################################################################################
2012-03-20 23:31:31 +05:30
program DAMASK_spectral_AL
2012-03-07 23:07:40 +05:30
use , intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
use DAMASK_interface
use prec , only : pInt , pReal , DAMASK_NaN
use IO
use debug , only : debug_spectral , &
debug_levelBasic , &
debug_spectralRestart , &
debug_spectralFFTW
use math
use CPFEM , only : CPFEM_general , CPFEM_initAll
use FEsolving , only : restartWrite , restartInc
use numerics , only : err_div_tol , err_stress_tolrel , rotation_tol , itmax , itmin , &
memory_efficient , update_gamma , DAMASK_NumThreadsInt , &
fftw_planner_flag , fftw_timelimit
use homogenization , only : materialpoint_sizeResults , materialpoint_results
!$ use OMP_LIB ! the openMP function library
!##################################################################################################
! variable declaration
!##################################################################################################
implicit none
!--------------------------------------------------------------------------------------------------
! variables to read from load case and geom file
real ( pReal ) , dimension ( 9 ) :: temp_valueVector ! stores information temporarily from loadcase file
logical , dimension ( 9 ) :: temp_maskVector
integer ( pInt ) , parameter :: maxNchunksLoadcase = ( 1_pInt + 9_pInt ) * 3_pInt + & ! deformation, rotation, and stress
( 1_pInt + 1_pInt ) * 5_pInt + & ! time, (log)incs, temp, restartfrequency, and outputfrequency
1_pInt , & ! dropguessing
maxNchunksGeom = 7_pInt , & ! 4 identifiers, 3 values
myUnit = 234_pInt
integer ( pInt ) , dimension ( 1_pInt + maxNchunksLoadcase * 2_pInt ) :: positions ! this is longer than needed for geometry parsing
integer ( pInt ) :: headerLength , &
N_l = 0_pInt , &
N_t = 0_pInt , &
N_n = 0_pInt , &
N_Fdot = 0_pInt
character ( len = 1024 ) :: path , line , keyword
logical :: gotResolution = . false . , &
gotDimension = . false . , &
gotHomogenization = . false .
!--------------------------------------------------------------------------------------------------
! variable storing information from load case file
type bc_type
real ( pReal ) , dimension ( 3 , 3 ) :: deformation = 0.0_pReal , & ! applied velocity gradient or time derivative of deformation gradient
2012-03-20 23:31:31 +05:30
P = 0.0_pReal , & ! stress BC (if applicable)
2012-03-07 23:07:40 +05:30
rotation = math_I3 ! rotation of BC (if applicable)
real ( pReal ) :: time = 0.0_pReal , & ! length of increment
temperature = 30 0.0_pReal ! isothermal starting conditions
integer ( pInt ) :: incs = 0_pInt , & ! number of increments
outputfrequency = 1_pInt , & ! frequency of result writes
restartfrequency = 0_pInt , & ! frequency of restart writes
logscale = 0_pInt ! linear/logaritmic time inc flag
logical :: followFormerTrajectory = . true . , & ! follow trajectory of former loadcase
velGradApplied = . false . ! decide wether velocity gradient or fdot is given
logical , dimension ( 3 , 3 ) :: maskDeformation = . false . , & ! mask of deformation boundary conditions
maskStress = . false . ! mask of stress boundary conditions
logical , dimension ( 9 ) :: maskStressVector = . false . ! linear mask of boundary conditions
end type
type ( bc_type ) , allocatable , dimension ( : ) :: bc
!--------------------------------------------------------------------------------------------------
! variables storing information from geom file
real ( pReal ) :: wgt
real ( pReal ) , dimension ( 3 ) :: geomdim = 0.0_pReal ! physical dimension of volume element per direction
integer ( pInt ) :: Npoints , & ! number of Fourier points
homog ! homogenization scheme used
integer ( pInt ) , dimension ( 3 ) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
integer ( pInt ) :: res1_red ! to store res(1)/2 +1
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
2012-03-30 01:24:31 +05:30
real ( pReal ) , dimension ( 3 , 3 ) :: P_av = 0.0_pReal , P_star_av = 0.0_pReal , P , &
F_aim = math_I3 , F_aim_lastInc = math_I3 , lambda_av , &
2012-03-07 23:07:40 +05:30
mask_stress , mask_defgrad , deltaF , F_star_av , &
F_aim_lab ! quantities rotated to other coordinate system
real ( pReal ) , dimension ( 3 , 3 , 3 , 3 ) :: dPdF , C_inc0 , C = 0.0_pReal , S_lastInc , C_lastInc ! stiffness and compliance
real ( pReal ) , dimension ( 6 ) :: sigma ! cauchy stress
real ( pReal ) , dimension ( 6 , 6 ) :: dsde ! small strain stiffness
real ( pReal ) , dimension ( 9 , 9 ) :: s_prev99 , c_prev99 ! compliance and stiffness in matrix notation
real ( pReal ) , dimension ( : , : ) , allocatable :: s_reduced , c_reduced ! reduced compliance and stiffness (only for stress BC)
integer ( pInt ) :: size_reduced = 0_pInt ! number of stress BCs
!--------------------------------------------------------------------------------------------------
! pointwise data
type ( C_PTR ) :: tensorField ! fields in real an fourier space
real ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: lambda_real , F_real ! fields in real space (pointer)
complex ( pReal ) , dimension ( : , : , : , : , : ) , pointer :: lambda_fourier , F_fourier ! fields in fourier space (pointer)
real ( pReal ) , dimension ( : , : , : , : , : ) , allocatable :: F_lastInc , F_star , lambda
real ( pReal ) , dimension ( : , : , : , : ) , allocatable :: coordinates
real ( pReal ) , dimension ( : , : , : ) , allocatable :: temperature
!--------------------------------------------------------------------------------------------------
! variables storing information for spectral method and FFTW
type ( C_PTR ) :: plan_correction , plan_lambda ! plans for fftw
real ( pReal ) , dimension ( 3 , 3 ) :: xiDyad ! product of wave vectors
real ( pReal ) , dimension ( : , : , : , : , : , : , : ) , allocatable :: gamma_hat ! gamma operator (field) for spectral method
real ( pReal ) , dimension ( : , : , : , : ) , allocatable :: xi ! wave vector field for divergence and for gamma operator
integer ( pInt ) , dimension ( 3 ) :: k_s
!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
real ( pReal ) :: time = 0.0_pReal , time0 = 0.0_pReal , timeinc = 1.0_pReal , timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
2012-03-30 01:24:31 +05:30
real ( pReal ) :: guessmode , err_stress , err_stress_tol , err_f , err_p , err_crit , err_f_point , pstress_av_L2 , err_div_rms , err_div
2012-03-07 23:07:40 +05:30
real ( pReal ) , dimension ( 3 , 3 ) , parameter :: ones = 1.0_pReal , zeroes = 0.0_pReal
complex ( pReal ) , dimension ( 3 , 3 ) :: temp33_Complex
real ( pReal ) , dimension ( 3 , 3 ) :: temp33_Real
integer ( pInt ) :: i , j , k , l , u , v , w , errorID = 0_pInt , ierr
integer ( pInt ) :: N_Loadcases , loadcase , inc , iter , ielem , CPFEM_mode , &
totalIncsCounter = 0_pInt , notConvergedCounter = 0_pInt , convergedCounter = 0_pInt
logical :: errmatinv
character ( len = 6 ) :: loadcase_string
!--------------------------------------------------------------------------------------------------
!variables controlling debugging
logical :: debugGeneral , debugDivergence , debugRestart , debugFFTW
!##################################################################################################
! reading of information from load case file and geometry file
!##################################################################################################
!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
open ( 6 , encoding = 'UTF-8' )
call DAMASK_interface_init
print '(a)' , ''
2012-03-30 01:24:31 +05:30
print '(a)' , ' <<<+- DAMASK_spectral_AL init -+>>>'
print '(a)' , ' $Id$'
2012-03-07 23:07:40 +05:30
#include "compilation_info.f90"
print '(a,a)' , ' Working Directory: ' , trim ( getSolverWorkingDirectoryName ( ) )
print '(a,a)' , ' Solver Job Name: ' , trim ( getSolverJobName ( ) )
print '(a)' , ''
!--------------------------------------------------------------------------------------------------
! reading the load case file and allocate data structure containing load cases
path = getLoadcaseName ( )
call IO_open_file ( myUnit , path )
rewind ( myUnit )
do
read ( myUnit , '(a1024)' , END = 100 ) line
if ( IO_isBlank ( line ) ) cycle ! skip empty lines
positions = IO_stringPos ( line , maxNchunksLoadcase )
do i = 1_pInt , maxNchunksLoadcase , 1_pInt ! reading compulsory parameters for loadcase
select case ( IO_lc ( IO_stringValue ( line , positions , i ) ) )
case ( 'l' , 'velocitygrad' , 'velgrad' , 'velocitygradient' )
N_l = N_l + 1_pInt
case ( 'fdot' , 'dotf' )
N_Fdot = N_Fdot + 1_pInt
case ( 't' , 'time' , 'delta' )
N_t = N_t + 1_pInt
case ( 'n' , 'incs' , 'increments' , 'steps' , 'logincs' , 'logsteps' )
N_n = N_n + 1_pInt
end select
enddo ! count all identifiers to allocate memory and do sanity check
enddo
100 N_Loadcases = N_n
if ( ( N_l + N_Fdot / = N_n ) . or . ( N_n / = N_t ) ) & ! sanity check
call IO_error ( error_ID = 837_pInt , ext_msg = trim ( path ) ) ! error message for incomplete loadcase
!if (N_Loadcases>9000_pInt) stop !discuss with Philip, stop code trouble. suggesting warning
allocate ( bc ( N_Loadcases ) )
!--------------------------------------------------------------------------------------------------
! reading the load case and assign values to the allocated data structure
rewind ( myUnit )
loadcase = 0_pInt
do
read ( myUnit , '(a1024)' , END = 101 ) line
if ( IO_isBlank ( line ) ) cycle ! skip empty lines
loadcase = loadcase + 1_pInt
positions = IO_stringPos ( line , maxNchunksLoadcase )
do j = 1_pInt , maxNchunksLoadcase
select case ( IO_lc ( IO_stringValue ( line , positions , j ) ) )
case ( 'fdot' , 'dotf' , 'l' , 'velocitygrad' , 'velgrad' , 'velocitygradient' ) ! assign values for the deformation BC matrix
bc ( loadcase ) % velGradApplied = &
( IO_lc ( IO_stringValue ( line , positions , j ) ) == 'l' . or . & ! in case of given L, set flag to true
IO_lc ( IO_stringValue ( line , positions , j ) ) == 'velocitygrad' . or . &
IO_lc ( IO_stringValue ( line , positions , j ) ) == 'velgrad' . or . &
IO_lc ( IO_stringValue ( line , positions , j ) ) == 'velocitygradient' )
temp_valueVector = 0.0_pReal
temp_maskVector = . false .
forall ( k = 1_pInt : 9_pInt ) temp_maskVector ( k ) = IO_stringValue ( line , positions , j + k ) / = '*'
do k = 1_pInt , 9_pInt
if ( temp_maskVector ( k ) ) temp_valueVector ( k ) = IO_floatValue ( line , positions , j + k )
enddo
bc ( loadcase ) % maskDeformation = transpose ( reshape ( temp_maskVector , [ 3 , 3 ] ) )
bc ( loadcase ) % deformation = math_plain9to33 ( temp_valueVector )
case ( 'p' , 'pk1' , 'piolakirchhoff' , 'stress' )
temp_valueVector = 0.0_pReal
forall ( k = 1_pInt : 9_pInt ) bc ( loadcase ) % maskStressVector ( k ) = &
IO_stringValue ( line , positions , j + k ) / = '*'
do k = 1_pInt , 9_pInt
if ( bc ( loadcase ) % maskStressVector ( k ) ) temp_valueVector ( k ) = &
2012-03-20 23:31:31 +05:30
IO_floatValue ( line , positions , j + k ) ! assign values for the bc(loadcase)%P matrix
2012-03-07 23:07:40 +05:30
enddo
bc ( loadcase ) % maskStress = transpose ( reshape ( bc ( loadcase ) % maskStressVector , [ 3 , 3 ] ) )
2012-03-20 23:31:31 +05:30
bc ( loadcase ) % P = math_plain9to33 ( temp_valueVector )
2012-03-07 23:07:40 +05:30
case ( 't' , 'time' , 'delta' ) ! increment time
bc ( loadcase ) % time = IO_floatValue ( line , positions , j + 1_pInt )
case ( 'temp' , 'temperature' ) ! starting temperature
bc ( loadcase ) % temperature = IO_floatValue ( line , positions , j + 1_pInt )
case ( 'n' , 'incs' , 'increments' , 'steps' ) ! number of increments
bc ( loadcase ) % incs = IO_intValue ( line , positions , j + 1_pInt )
case ( 'logincs' , 'logincrements' , 'logsteps' ) ! number of increments (switch to log time scaling)
bc ( loadcase ) % incs = IO_intValue ( line , positions , j + 1_pInt )
bc ( loadcase ) % logscale = 1_pInt
case ( 'f' , 'freq' , 'frequency' , 'outputfreq' ) ! frequency of result writings
bc ( loadcase ) % outputfrequency = IO_intValue ( line , positions , j + 1_pInt )
case ( 'r' , 'restart' , 'restartwrite' ) ! frequency of writing restart information
bc ( loadcase ) % restartfrequency = max ( 0_pInt , IO_intValue ( line , positions , j + 1_pInt ) )
case ( 'guessreset' , 'dropguessing' )
bc ( loadcase ) % followFormerTrajectory = . false . ! do not continue to predict deformation along former trajectory
case ( 'euler' ) ! rotation of loadcase given in euler angles
u = 0_pInt ! assuming values given in radians
v = 1_pInt ! assuming keyword indicating degree/radians
select case ( IO_lc ( IO_stringValue ( line , positions , j + 1_pInt ) ) )
case ( 'deg' , 'degree' )
u = 1_pInt ! for conversion from degree to radian
case ( 'rad' , 'radian' )
case default
v = 0_pInt ! immediately reading in angles, assuming radians
end select
forall ( k = 1_pInt : 3_pInt ) temp33_Real ( k , 1 ) = &
IO_floatValue ( line , positions , j + v + k ) * real ( u , pReal ) * inRad
bc ( loadcase ) % rotation = math_EulerToR ( temp33_Real ( : , 1 ) )
case ( 'rotation' , 'rot' ) ! assign values for the rotation of loadcase matrix
temp_valueVector = 0.0_pReal
forall ( k = 1_pInt : 9_pInt ) temp_valueVector ( k ) = IO_floatValue ( line , positions , j + k )
bc ( loadcase ) % rotation = math_plain9to33 ( temp_valueVector )
end select
enddo ; enddo
101 close ( myUnit )
!-------------------------------------------------------------------------------------------------- ToDo: if temperature at CPFEM is treated properly, move this up immediately after interface init
! initialization of all related DAMASK modules (e.g. mesh.f90 reads in geometry)
call CPFEM_initAll ( bc ( 1 ) % temperature , 1_pInt , 1_pInt )
if ( update_gamma . and . . not . memory_efficient ) call IO_error ( error_ID = 847_pInt )
!--------------------------------------------------------------------------------------------------
! read header of geom file to get size information. complete geom file is intepretated by mesh.f90
path = getModelName ( )
call IO_open_file ( myUnit , trim ( path ) / / InputFileExtension )
rewind ( myUnit )
read ( myUnit , '(a1024)' ) line
positions = IO_stringPos ( line , 2_pInt )
keyword = IO_lc ( IO_StringValue ( line , positions , 2_pInt ) )
if ( keyword ( 1 : 4 ) == 'head' ) then
headerLength = IO_intValue ( line , positions , 1_pInt ) + 1_pInt
else
call IO_error ( error_ID = 842_pInt )
endif
rewind ( myUnit )
do i = 1_pInt , headerLength
read ( myUnit , '(a1024)' ) line
positions = IO_stringPos ( line , maxNchunksGeom )
select case ( IO_lc ( IO_StringValue ( line , positions , 1 ) ) )
case ( 'dimension' )
gotDimension = . true .
do j = 2_pInt , 6_pInt , 2_pInt
select case ( IO_lc ( IO_stringValue ( line , positions , j ) ) )
case ( 'x' )
geomdim ( 1 ) = IO_floatValue ( line , positions , j + 1_pInt )
case ( 'y' )
geomdim ( 2 ) = IO_floatValue ( line , positions , j + 1_pInt )
case ( 'z' )
geomdim ( 3 ) = IO_floatValue ( line , positions , j + 1_pInt )
end select
enddo
case ( 'homogenization' )
gotHomogenization = . true .
homog = IO_intValue ( line , positions , 2_pInt )
case ( 'resolution' )
gotResolution = . true .
do j = 2_pInt , 6_pInt , 2_pInt
select case ( IO_lc ( IO_stringValue ( line , positions , j ) ) )
case ( 'a' )
res ( 1 ) = IO_intValue ( line , positions , j + 1_pInt )
case ( 'b' )
res ( 2 ) = IO_intValue ( line , positions , j + 1_pInt )
case ( 'c' )
res ( 3 ) = IO_intValue ( line , positions , j + 1_pInt )
end select
enddo
end select
enddo
close ( myUnit )
!--------------------------------------------------------------------------------------------------
! sanity checks of geometry parameters
if ( . not . ( gotDimension . and . gotHomogenization . and . gotResolution ) ) &
call IO_error ( error_ID = 845_pInt )
if ( any ( geomdim < = 0.0_pReal ) ) call IO_error ( error_ID = 802_pInt )
if ( mod ( res ( 1 ) , 2_pInt ) / = 0_pInt . or . &
mod ( res ( 2 ) , 2_pInt ) / = 0_pInt . or . &
( mod ( res ( 3 ) , 2_pInt ) / = 0_pInt . and . res ( 3 ) / = 1_pInt ) ) call IO_error ( error_ID = 803_pInt )
!--------------------------------------------------------------------------------------------------
! variables derived from resolution
res1_red = res ( 1 ) / 2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
Npoints = res ( 1 ) * res ( 2 ) * res ( 3 )
wgt = 1.0_pReal / real ( Npoints , pReal )
!--------------------------------------------------------------------------------------------------
! output of geometry
print '(a)' , ''
print '(a)' , '#############################################################'
2012-03-30 01:24:31 +05:30
print '(a)' , 'DAMASK spectral_AL:'
print '(a)' , 'The AL spectral method boundary value problem solver for'
2012-03-07 23:07:40 +05:30
print '(a)' , 'the Duesseldorf Advanced Material Simulation Kit'
print '(a)' , '#############################################################'
print '(a,a)' , 'geometry file: ' , trim ( path ) / / '.geom'
print '(a)' , '============================================================='
print '(a,3(i12 ))' , 'resolution a b c:' , res
print '(a,3(f12.5))' , 'dimension x y z:' , geomdim
print '(a,i5)' , 'homogenization: ' , homog
print '(a)' , '#############################################################'
print '(a,a)' , 'loadcase file: ' , trim ( getLoadcaseName ( ) )
!--------------------------------------------------------------------------------------------------
! consistency checks and output of load case
bc ( 1 ) % followFormerTrajectory = . false . ! cannot guess along trajectory for first inc of first loadcase
do loadcase = 1_pInt , N_Loadcases
write ( loadcase_string , '(i6)' ) loadcase
print '(a)' , '============================================================='
print '(a,i6)' , 'loadcase: ' , loadcase
if ( . not . bc ( loadcase ) % followFormerTrajectory ) print '(a)' , 'drop guessing along trajectory'
if ( bc ( loadcase ) % velGradApplied ) then
do j = 1_pInt , 3_pInt
if ( any ( bc ( loadcase ) % maskDeformation ( j , 1 : 3 ) . eqv . . true . ) . and . &
any ( bc ( loadcase ) % maskDeformation ( j , 1 : 3 ) . eqv . . false . ) ) errorID = 832_pInt ! each row should be either fully or not at all defined
enddo
print '(a)' , 'velocity gradient:'
else
print '(a)' , 'deformation gradient rate:'
endif
write ( * , '(3(3(f12.7,1x)/))' , advance = 'no' ) merge ( math_transpose33 ( bc ( loadcase ) % deformation ) , &
reshape ( spread ( DAMASK_NaN , 1 , 9 ) , [ 3 , 3 ] ) , transpose ( bc ( loadcase ) % maskDeformation ) )
write ( * , '(a,/,3(3(f12.7,1x)/))' , advance = 'no' ) 'stress / GPa:' , &
2012-03-20 23:31:31 +05:30
1e-9_pReal * merge ( math_transpose33 ( bc ( loadcase ) % P ) , &
2012-03-07 23:07:40 +05:30
reshape ( spread ( DAMASK_NaN , 1 , 9 ) , [ 3 , 3 ] ) , transpose ( bc ( loadcase ) % maskStress ) )
if ( any ( bc ( loadcase ) % rotation / = math_I3 ) ) &
write ( * , '(a,/,3(3(f12.7,1x)/))' , advance = 'no' ) ' rotation of loadframe:' , &
math_transpose33 ( bc ( loadcase ) % rotation )
print '(a,f12.6)' , 'temperature:' , bc ( loadcase ) % temperature
print '(a,f12.6)' , 'time: ' , bc ( loadcase ) % time
print '(a,i5)' , 'increments: ' , bc ( loadcase ) % incs
print '(a,i5)' , 'output frequency: ' , bc ( loadcase ) % outputfrequency
print '(a,i5)' , 'restart frequency: ' , bc ( loadcase ) % restartfrequency
if ( any ( bc ( loadcase ) % maskStress . eqv . bc ( loadcase ) % maskDeformation ) ) errorID = 831_pInt ! exclusive or masking only
if ( any ( bc ( loadcase ) % maskStress . and . transpose ( bc ( loadcase ) % maskStress ) . and . &
reshape ( [ . false . , . true . , . true . , . true . , . false . , . true . , . true . , . true . , . false . ] , [ 3 , 3 ] ) ) ) &
errorID = 838_pInt ! no rotation is allowed by stress BC
if ( any ( abs ( math_mul33x33 ( bc ( loadcase ) % rotation , math_transpose33 ( bc ( loadcase ) % rotation ) ) &
- math_I3 ) > reshape ( spread ( rotation_tol , 1 , 9 ) , [ 3 , 3 ] ) ) &
. or . abs ( math_det33 ( bc ( loadcase ) % rotation ) ) > 1.0_pReal + rotation_tol ) &
errorID = 846_pInt ! given rotation matrix contains strain
if ( bc ( loadcase ) % time < 0.0_pReal ) errorID = 834_pInt ! negative time increment
if ( bc ( loadcase ) % incs < 1_pInt ) errorID = 835_pInt ! non-positive incs count
if ( bc ( loadcase ) % outputfrequency < 1_pInt ) errorID = 836_pInt ! non-positive result frequency
if ( errorID > 0_pInt ) call IO_error ( error_ID = errorID , ext_msg = loadcase_string )
enddo
!--------------------------------------------------------------------------------------------------
! debugging parameters
debugRestart = iand ( debug_spectral , debug_spectralRestart ) > 0_pInt
debugFFTW = iand ( debug_spectral , debug_spectralFFTW ) > 0_pInt
debugGeneral = . true .
!##################################################################################################
! initialization
!##################################################################################################
!--------------------------------------------------------------------------------------------------
! allocate more memory
allocate ( F_star ( 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 ( lambda ( 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 )
allocate ( temperature ( res ( 1 ) , res ( 2 ) , res ( 3 ) ) , source = bc ( 1 ) % temperature ) ! 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 , lambda_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3 , 3 ] ) ! place a pointer for the real representation
call c_f_pointer ( tensorField , F_real , [ res ( 1 ) + 2_pInt , res ( 2 ) , res ( 3 ) , 3 , 3 ] ) ! place a pointer for the real representation
call c_f_pointer ( tensorField , lambda_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3 , 3 ] ) ! place a pointer for the complex representation
call c_f_pointer ( tensorField , F_fourier , [ res1_red , res ( 2 ) , res ( 3 ) , 3 , 3 ] ) ! place a pointer for the complex representation
!--------------------------------------------------------------------------------------------------
! 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
#ifdef _OPENMP
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
#endif
call fftw_set_timelimit ( fftw_timelimit ) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! creating plans
plan_lambda = fftw_plan_many_dft_r2c ( 3 , [ res ( 3 ) , res ( 2 ) , res ( 1 ) ] , 9 , & ! dimensions , length in each dimension in reversed order
lambda_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
lambda_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 , &
F_fourier , [ res ( 3 ) , res ( 2 ) , res1_red ] , &
1 , res ( 3 ) * res ( 2 ) * res1_red , &
F_real , [ res ( 3 ) , res ( 2 ) , res ( 1 ) + 2_pInt ] , &
1 , res ( 3 ) * res ( 2 ) * ( res ( 1 ) + 2_pInt ) , fftw_planner_flag )
if ( debugGeneral ) print '(a)' , 'FFTW initialized'
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) and remove the given highest frequencies
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 ) / geomdim
enddo ; enddo ; enddo
!--------------------------------------------------------------------------------------------------
! 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 , u = 1_pInt : 3_pInt ) &
xiDyad ( l , u ) = xi ( l , i , j , k ) * xi ( u , i , j , k )
forall ( l = 1_pInt : 3_pInt , u = 1_pInt : 3_pInt ) &
temp33_Real ( l , u ) = sum ( C_inc0 ( l , 1 : 3 , u , 1 : 3 ) * xiDyad )
temp33_Real = math_inv33 ( temp33_Real )
forall ( l = 1_pInt : 3_pInt , u = 1_pInt : 3_pInt , v = 1_pInt : 3_pInt , w = 1_pInt : 3_pInt ) &
gamma_hat ( i , j , k , l , u , v , w ) = temp33_Real ( l , v ) * xiDyad ( u , w )
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
!--------------------------------------------------------------------------------------------------
! init fields to no deformation
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_real ( 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 * [ i , j , k ] , pReal ) - geomdim / real ( 2_pInt * res , pReal )
call CPFEM_general ( 3_pInt , coordinates ( i , j , k , 1 : 3 ) , math_I3 , math_I3 , temperature ( i , j , k ) , &
0.0_pReal , ielem , 1_pInt , sigma , dsde , temp33_Real , dPdF )
enddo ; enddo ; enddo
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 ( 2_pInt , coordinates ( i , j , k , 1 : 3 ) , math_I3 , math_I3 , temperature ( i , j , k ) , &
0.0_pReal , ielem , 1_pInt , sigma , dsde , temp33_Real , dPdF )
C = C + dPdF
enddo ; enddo ; enddo
C_inc0 = C * wgt ! linear reference material stiffness
2012-03-30 01:24:31 +05:30
!--------------------------------------------------------------------------------------------------
2012-03-07 23:07:40 +05:30
! possible restore deformation gradient from saved state
if ( restartInc > 1_pInt ) then ! using old values from file
if ( debugRestart ) print '(a,i6,a)' , 'Reading values of increment ' , &
restartInc - 1_pInt , ' from file'
call IO_read_jobBinaryFile ( 777 , 'convergedSpectralDefgrad' , &
trim ( getSolverJobName ( ) ) , size ( F_star ) )
read ( 777 , rec = 1 ) F_star
close ( 777 )
F_real ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) = F_star
F_lastInc = F_star
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_real ( i , j , k , 1 : 3 , 1 : 3 ) ! calculating old average deformation
enddo ; enddo ; enddo
F_aim = F_aim * wgt
F_aim_lastInc = F_aim
endif
!--------------------------------------------------------------------------------------------------
! write header of output file
open ( 538 , file = trim ( getSolverWorkingDirectoryName ( ) ) / / trim ( getSolverJobName ( ) ) &
/ / '.spectralOut' , form = 'UNFORMATTED' , status = 'REPLACE' )
write ( 538 ) 'load' , trim ( getLoadcaseName ( ) )
write ( 538 ) 'workingdir' , trim ( getSolverWorkingDirectoryName ( ) )
write ( 538 ) 'geometry' , trim ( getSolverJobName ( ) ) / / InputFileExtension
write ( 538 ) 'resolution' , res
write ( 538 ) 'dimension' , geomdim
write ( 538 ) 'materialpoint_sizeResults' , materialpoint_sizeResults
write ( 538 ) 'loadcases' , N_Loadcases
write ( 538 ) 'frequencies' , bc ( 1 : N_Loadcases ) % outputfrequency ! one entry per loadcase
write ( 538 ) 'times' , bc ( 1 : N_Loadcases ) % time ! one entry per loadcase
write ( 538 ) 'logscales' , bc ( 1 : N_Loadcases ) % logscale
write ( 538 ) 'increments' , bc ( 1 : N_Loadcases ) % incs ! one entry per loadcase
write ( 538 ) 'startingIncrement' , restartInc - 1_pInt ! start with writing out the previous inc
write ( 538 ) 'eoh' ! end of header
write ( 538 ) materialpoint_results ( 1_pInt : materialpoint_sizeResults , 1 , 1_pInt : Npoints ) ! initial (non-deformed or read-in) results
if ( debugGeneral ) print '(a)' , 'Header of result file written out'
!##################################################################################################
! Loop over loadcases defined in the loadcase file
!##################################################################################################
do loadcase = 1_pInt , N_Loadcases
time0 = time ! loadcase start time
if ( bc ( loadcase ) % followFormerTrajectory . and . &
( restartInc < totalIncsCounter . or . &
restartInc > totalIncsCounter + bc ( loadcase ) % incs ) ) then ! continue to guess along former trajectory where applicable
guessmode = 1.0_pReal
else
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
endif
!--------------------------------------------------------------------------------------------------
! arrays for mixed boundary conditions
mask_defgrad = merge ( ones , zeroes , bc ( loadcase ) % maskDeformation )
mask_stress = merge ( ones , zeroes , bc ( loadcase ) % maskStress )
size_reduced = int ( count ( bc ( loadcase ) % maskStressVector ) , pInt )
allocate ( c_reduced ( size_reduced , size_reduced ) , source = 0.0_pReal )
allocate ( s_reduced ( size_reduced , size_reduced ) , source = 0.0_pReal )
!##################################################################################################
! loop oper incs defined in input file for current loadcase
!##################################################################################################
do inc = 1_pInt , bc ( loadcase ) % incs
totalIncsCounter = totalIncsCounter + 1_pInt
if ( totalIncsCounter > = restartInc ) then ! do calculations (otherwise just forwarding)
!--------------------------------------------------------------------------------------------------
! forwarding time
timeinc_old = timeinc
if ( bc ( loadcase ) % logscale == 0_pInt ) then ! linear scale
timeinc = bc ( loadcase ) % time / bc ( loadcase ) % incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
else
if ( loadcase == 1_pInt ) then ! 1st loadcase of logarithmic scale
if ( inc == 1_pInt ) then ! 1st inc of 1st loadcase of logarithmic scale
timeinc = bc ( 1 ) % time * ( 2.0_pReal ** real ( 1_pInt - bc ( 1 ) % incs , pReal ) ) ! assume 1st inc is equal to 2nd
else ! not-1st inc of 1st loadcase of logarithmic scale
timeinc = bc ( 1 ) % time * ( 2.0_pReal ** real ( inc - 1_pInt - bc ( 1 ) % incs , pReal ) )
endif
else ! not-1st loadcase of logarithmic scale
timeinc = time0 * ( ( 1.0_pReal + bc ( loadcase ) % time / time0 ) ** ( real ( inc , pReal ) / &
real ( bc ( loadcase ) % incs , pReal ) ) &
- ( 1.0_pReal + bc ( loadcase ) % time / time0 ) ** ( real ( ( inc - 1_pInt ) , pReal ) / &
real ( bc ( loadcase ) % incs , pReal ) ) )
endif
endif
time = time + timeinc
if ( bc ( loadcase ) % velGradApplied ) then ! calculate deltaF from given L and current F
deltaF = timeinc * mask_defgrad * math_mul33x33 ( bc ( loadcase ) % deformation , F_aim )
else ! deltaF = fDot *timeinc where applicable
deltaF = timeinc * mask_defgrad * bc ( loadcase ) % deformation
endif
!--------------------------------------------------------------------------------------------------
! coordinates at beginning of inc
2012-03-30 01:24:31 +05:30
!call deformed_fft(res,geomdim,1.0_pReal,F_real(1:res(1),1:res(2),1:res(3),1:3,1:3),coordinates)! calculate current coordinates
2012-03-07 23:07:40 +05:30
!--------------------------------------------------------------------------------------------------
! 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
F_aim_lastInc = temp33_Real
F_star_av = F_aim
2012-03-30 01:24:31 +05:30
!--------------------------------------------------------------------------------------------------
! Initialize / Update lambda to useful value
temp33_real = math_mul3333xx33 ( C * wgt , F_aim - F_aim_lastInc )
P_av = P_av + temp33_real
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
lambda ( i , j , k , 1 : 3 , 1 : 3 ) = lambda ( i , j , k , 1 : 3 , 1 : 3 ) + temp33_real
enddo ; enddo ; enddo
2012-03-07 23:07:40 +05:30
!--------------------------------------------------------------------------------------------------
! update local deformation gradient
deltaF = math_rotate_backward33 ( deltaF , bc ( loadcase ) % rotation )
do k = 1_pInt , res ( 3 ) ; do j = 1_pInt , res ( 2 ) ; do i = 1_pInt , res ( 1 )
temp33_Real = F_real ( i , j , k , 1 : 3 , 1 : 3 )
F_real ( i , j , k , 1 : 3 , 1 : 3 ) = F_real ( i , j , k , 1 : 3 , 1 : 3 ) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * ( F_real ( 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 ! if not guessing, use prescribed average deformation where applicable
F_lastInc ( i , j , k , 1 : 3 , 1 : 3 ) = temp33_Real
enddo ; enddo ; enddo
!--------------------------------------------------------------------------------------------------
!Initialize pointwise data for AL scheme: ToDo: good choice?
F_star ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) = F_real ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 )
!--------------------------------------------------------------------------------------------------
! calculate reduced compliance
if ( size_reduced > 0_pInt ) then ! calculate compliance in case stress BC is applied
C_lastInc = math_rotate_forward3333 ( C * wgt , bc ( loadcase ) % rotation ) ! calculate stiffness from former inc
c_prev99 = math_Plain3333to99 ( C_lastInc )
k = 0_pInt ! build reduced stiffness
do v = 1_pInt , 9_pInt
if ( bc ( loadcase ) % maskStressVector ( v ) ) then
k = k + 1_pInt
j = 0_pInt
do u = 1_pInt , 9_pInt
if ( bc ( loadcase ) % maskStressVector ( u ) ) then
j = j + 1_pInt
c_reduced ( k , j ) = c_prev99 ( v , u )
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 )
s_prev99 = 0.0_pReal ! build full compliance
k = 0_pInt
do v = 1_pInt , 9_pInt
if ( bc ( loadcase ) % maskStressVector ( v ) ) then
k = k + 1_pInt
j = 0_pInt
do u = 1_pInt , 9_pInt
if ( bc ( loadcase ) % maskStressVector ( u ) ) then
j = j + 1_pInt
s_prev99 ( v , u ) = s_reduced ( k , j )
endif ; enddo ; endif ; enddo
S_lastInc = ( math_Plain99to3333 ( s_prev99 ) )
endif
!--------------------------------------------------------------------------------------------------
! report begin of new increment
print '(a)' , '##################################################################'
print '(A,I5.5,A,es12.5)' , 'Increment ' , totalIncsCounter , ' Time ' , time
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
CPFEM_mode = 1_pInt ! winding forward
iter = 0_pInt
2012-03-20 23:31:31 +05:30
err_crit = huge ( err_div_tol ) ! go into loop
2012-03-07 23:07:40 +05:30
!##################################################################################################
! convergence loop (looping over iterations)
!##################################################################################################
2012-03-30 01:24:31 +05:30
do while ( ( iter < itmax . and . ( err_div > err_div_tol . or . err_stress > err_stress_tol . or . err_crit > 5.0e-4 ) ) &
2012-03-07 23:07:40 +05:30
. or . iter < itmin )
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
! report begin of new iteration
print '(a)' , ''
print '(a)' , '=================================================================='
print '(5(a,i6.6))' , 'Loadcase ' , loadcase , ' Increment ' , inc , '/' , bc ( loadcase ) % incs , &
' @ Iteration ' , iter , '/' , itmax
!--------------------------------------------------------------------------------------------------
! stress BC handling
if ( size_reduced > 0_pInt ) then ! calculate stress BC if applied
2012-03-20 23:31:31 +05:30
err_stress = maxval ( abs ( mask_stress * ( P_av - bc ( loadcase ) % P ) ) ) ! maximum deviaton (tensor norm not applicable)
2012-03-07 23:07:40 +05:30
write ( * , '(a,/,3(3(es14.7,1x)/))' , advance = 'no' ) 'stress deviation =' , &
2012-03-20 23:31:31 +05:30
math_transpose33 ( mask_stress * ( P_av - bc ( loadcase ) % P ) ) / 1.0e6_pReal
F_aim = F_aim + math_mul3333xx33 ( S_lastInc , bc ( loadcase ) % P - P_av )
2012-03-07 23:07:40 +05:30
err_stress_tol = maxval ( abs ( P_av ) ) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
else
err_stress_tol = + huge ( 1.0_pReal )
endif
F_aim_lab = math_rotate_backward33 ( F_aim , bc ( loadcase ) % rotation )
2012-03-30 01:24:31 +05:30
write ( * , '(a,/,3(3(f12.7,1x)/))' , advance = 'no' ) 'F aim =' , &
2012-03-07 23:07:40 +05:30
math_transpose33 ( F_aim )
!--------------------------------------------------------------------------------------------------
! doing Fourier transform
print '(a)' , '... spectral method ...............................................'
lambda_real ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) = lambda ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 )
call fftw_execute_dft_r2c ( plan_lambda , lambda_real , lambda_fourier )
lambda_fourier ( res1_red , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) &
= cmplx ( 0.0_pReal , 0.0_pReal , pReal )
lambda_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 ) &
lambda_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 )
2012-03-30 01:24:31 +05:30
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
pstress_av_L2 = sqrt ( maxval ( math_eigenvalues33 ( math_mul33x33 ( lambda_av , & ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
math_transpose33 ( lambda_av ) ) ) ) )
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 ( lambda_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 ( lambda_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 ( lambda_fourier ( 1 , j , k , 1 : 3 , 1 : 3 ) , &
xi ( 1 : 3 , 1 , j , k ) ) * TWOPIIMG ) ** 2.0_pReal ) &
+ sum ( aimag ( math_mul33x3_complex ( lambda_fourier ( 1 , j , k , 1 : 3 , 1 : 3 ) , &
xi ( 1 : 3 , 1 , j , k ) ) * TWOPIIMG ) ** 2.0_pReal ) &
+ sum ( real ( math_mul33x3_complex ( lambda_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 ( lambda_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
err_div = err_div_RMS / pstress_av_L2
2012-03-07 23:07:40 +05:30
!--------------------------------------------------------------------------------------------------
! using gamma operator to update F
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 , u = 1_pInt : 3_pInt ) &
xiDyad ( l , u ) = xi ( l , i , j , k ) * xi ( u , i , j , k )
forall ( l = 1_pInt : 3_pInt , u = 1_pInt : 3_pInt ) &
temp33_Real ( l , u ) = sum ( C_inc0 ( l , 1 : 3 , u , 1 : 3 ) * xiDyad )
temp33_Real = math_inv33 ( temp33_Real )
forall ( l = 1_pInt : 3_pInt , u = 1_pInt : 3_pInt , v = 1_pInt : 3_pInt , w = 1_pInt : 3_pInt ) &
gamma_hat ( 1 , 1 , 1 , l , u , v , w ) = temp33_Real ( l , v ) * xiDyad ( u , w )
forall ( l = 1_pInt : 3_pInt , u = 1_pInt : 3_pInt ) &
temp33_Complex ( l , u ) = sum ( gamma_hat ( 1 , 1 , 1 , l , u , 1 : 3 , 1 : 3 ) * &
lambda_fourier ( i , j , k , 1 : 3 , 1 : 3 ) )
F_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 ( u = 1_pInt : 3_pInt , v = 1_pInt : 3_pInt ) &
temp33_Complex ( u , v ) = sum ( gamma_hat ( i , j , k , u , v , 1 : 3 , 1 : 3 ) * &
lambda_fourier ( i , j , k , 1 : 3 , 1 : 3 ) )
F_fourier ( i , j , k , 1 : 3 , 1 : 3 ) = - temp33_Complex
enddo ; enddo ; enddo
endif
F_fourier ( 1 , 1 , 1 , 1 : 3 , 1 : 3 ) = cmplx ( ( F_aim_lab - F_star_av ) * real ( Npoints , pReal ) , 0.0_pReal , pReal )
2012-03-30 01:24:31 +05:30
2012-03-07 23:07:40 +05:30
!--------------------------------------------------------------------------------------------------
! doing inverse Fourier transform
call fftw_execute_dft_c2r ( plan_correction , F_fourier , F_real ) ! back transform of fluct deformation gradient
F_real ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) = F_real ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 ) * wgt + &
F_star ( 1 : res ( 1 ) , 1 : res ( 2 ) , 1 : res ( 3 ) , 1 : 3 , 1 : 3 )
!--------------------------------------------------------------------------------------------------
!
2012-03-30 01:24:31 +05:30
print '(a)' , '... update stress field P(F*) and update F* and λ..........................'
2012-03-07 23:07:40 +05:30
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_star ( i , j , k , 1 : 3 , 1 : 3 ) , temperature ( i , j , k ) , timeinc , ielem , 1_pInt , &
sigma , dsde , P , dPdF )
enddo ; enddo ; enddo
2012-03-30 01:24:31 +05:30
2012-03-07 23:07:40 +05:30
ielem = 0_pInt
err_f = 0.0_pReal
2012-03-30 01:24:31 +05:30
err_f_point = 0.0_pReal
2012-03-07 23:07:40 +05:30
F_star_av = 0.0_pReal
2012-03-30 01:24:31 +05:30
P_star_av = 0.0_pReal
lambda_av = 0.0_pReal
2012-03-07 23:07:40 +05:30
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 , &
coordinates ( i , j , k , 1 : 3 ) , F_lastInc ( i , j , k , 1 : 3 , 1 : 3 ) , &
F_star ( i , j , k , 1 : 3 , 1 : 3 ) , temperature ( i , j , k ) , timeinc , ielem , 1_pInt , &
sigma , dsde , P , dPdF )
CPFEM_mode = 2_pInt ! winding forward
temp33_Real = lambda ( i , j , k , 1 : 3 , 1 : 3 ) - P &
+ math_mul3333xx33 ( C_inc0 , F_real ( i , j , k , 1 : 3 , 1 : 3 ) - F_star ( i , j , k , 1 : 3 , 1 : 3 ) )
2012-03-30 01:24:31 +05:30
2012-03-07 23:07:40 +05:30
F_star ( i , j , k , 1 : 3 , 1 : 3 ) = F_star ( i , j , k , 1 : 3 , 1 : 3 ) + &
math_mul3333xx33 ( math_invSym3333 ( C_inc0 + dPdF ) , temp33_Real )
lambda ( i , j , k , 1 : 3 , 1 : 3 ) = lambda ( i , j , k , 1 : 3 , 1 : 3 ) + math_mul3333xx33 ( C_inc0 , F_real ( i , j , k , 1 : 3 , 1 : 3 ) &
- F_star ( i , j , k , 1 : 3 , 1 : 3 ) )
F_star_av = F_star_av + F_star ( i , j , k , 1 : 3 , 1 : 3 )
2012-03-30 01:24:31 +05:30
lambda_av = lambda_av + lambda ( i , j , k , 1 : 3 , 1 : 3 )
P_star_av = P_star_av + P
2012-03-07 23:07:40 +05:30
temp33_real = F_star ( i , j , k , 1 : 3 , 1 : 3 ) - F_real ( i , j , k , 1 : 3 , 1 : 3 )
2012-03-30 01:24:31 +05:30
err_f_point = max ( err_f_point , maxval ( temp33_real ) )
2012-03-07 23:07:40 +05:30
err_f = max ( err_f , sqrt ( math_mul33xx33 ( temp33_real , temp33_real ) ) )
2012-03-30 01:24:31 +05:30
temp33_real = lambda ( i , j , k , 1 : 3 , 1 : 3 ) - P
err_p = max ( err_p , sqrt ( math_mul33xx33 ( temp33_real , temp33_real ) ) )
2012-03-07 23:07:40 +05:30
enddo ; enddo ; enddo
2012-03-20 23:31:31 +05:30
2012-03-07 23:07:40 +05:30
F_star_av = F_star_av * wgt
2012-03-30 01:24:31 +05:30
write ( * , '(a,/,3(3(f12.7,1x)/))' , advance = 'no' ) 'F* =' , &
2012-03-07 23:07:40 +05:30
math_transpose33 ( F_star_av )
2012-03-30 01:24:31 +05:30
P_star_av = P_star_av * wgt
write ( * , '(a,/,3(3(es14.7,1x)/))' , advance = 'no' ) 'P(F*) / GPa =' , &
math_transpose33 ( P_star_av ) / 1.e6_pReal
lambda_av = lambda_av * wgt
write ( * , '(a,/,3(3(es14.7,1x)/))' , advance = 'no' ) 'λ / GPa =' , &
math_transpose33 ( lambda_av ) / 1.e6_pReal
! print '(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_real(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
! sigma,dsde,P,dPdF)
! enddo; enddo; enddo
2012-03-07 23:07:40 +05:30
2012-03-30 01:24:31 +05:30
! ielem = 0_pInt
! err_p = 0.0_pReal
! P_av =0.0_pReal
! 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(2_pInt,&
! coordinates(i,j,k,1:3),F_lastInc(i,j,k,1:3,1:3), &
! F_real(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
! sigma,dsde,P,dPdF)
! P_av = P_av + P
! temp33_real = lambda(i,j,k,1:3,1:3) - P
! err_p = max(err_p, sqrt(math_mul33xx33(temp33_real,temp33_real)))
! enddo; enddo; enddo
2012-03-07 23:07:40 +05:30
2012-03-30 01:24:31 +05:30
! P_av = math_rotate_forward33(P_av * wgt,bc(loadcase)%rotation)
! write (*,'(a,/,3(3(es14.7,1x)/))',advance='no') 'P(F) / GPa =',&
! math_transpose33(P_av)/1.e6_pReal
! write (*,'(a,/,3(3(es14.7,1x)/))',advance='no') 'P(F*) - P(F) =',&
! math_transpose33(P_star_av - P_av)
P_av = lambda_av
2012-03-07 23:07:40 +05:30
err_f = err_f / sqrt ( math_mul33xx33 ( F_star_av , F_star_av ) )
err_p = err_p / sqrt ( math_mul33xx33 ( P_av , P_av ) )
2012-03-30 01:24:31 +05:30
write ( 6 , '(a,es14.7,1x)' ) 'error F' , err_f
write ( 6 , '(a,es14.7,1x)' ) 'max abs err F' , err_f_point
write ( 6 , '(a,es14.7,1x)' ) 'error P' , err_p
write ( 6 , '(a,es11.4)' ) 'error divergence FT RMS = ' , err_div_RMS
write ( 6 , '(a,es11.4)' ) 'error div = ' , err_div
write ( 6 , '(a,es11.4)' ) 'error stress = ' , err_stress / err_stress_tol
2012-03-07 23:07:40 +05:30
err_crit = max ( err_p , err_f )
enddo ! end looping when convergency is achieved
print '(a)' , ''
print '(a)' , '=================================================================='
2012-03-20 23:31:31 +05:30
if ( err_crit > err_div_tol . or . err_stress > err_stress_tol ) then
2012-03-07 23:07:40 +05:30
print '(A,I5.5,A)' , 'increment ' , totalIncsCounter , ' NOT converged'
notConvergedCounter = notConvergedCounter + 1_pInt
else
convergedCounter = convergedCounter + 1_pInt
print '(A,I5.5,A)' , 'increment ' , totalIncsCounter , ' converged'
endif
if ( mod ( totalIncsCounter - 1_pInt , bc ( loadcase ) % outputfrequency ) == 0_pInt ) then ! at output frequency
print '(a)' , ''
print '(a)' , '... writing results to file ......................................'
write ( 538 ) materialpoint_results ( 1_pInt : materialpoint_sizeResults , 1 , 1_pInt : Npoints ) ! write result to file
endif
if ( bc ( loadcase ) % restartFrequency > 0_pInt . and . &
mod ( inc - 1_pInt , bc ( loadcase ) % restartFrequency ) == 0_pInt ) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
restartWrite = . true .
print '(A)' , 'writing converged results for restart'
call IO_write_jobBinaryFile ( 777 , 'convergedSpectralDefgrad' , size ( F_star ) ) ! writing deformation gradient field to file
write ( 777 , rec = 1 ) F_star
close ( 777 )
restartInc = totalIncsCounter
endif
endif ! end calculation/forwarding
enddo ! end looping over incs in current loadcase
deallocate ( c_reduced )
deallocate ( s_reduced )
enddo ! end looping over loadcases
print '(a)' , ''
print '(a)' , '##################################################################'
print '(i6.6,a,i6.6,a)' , notConvergedCounter , ' out of ' , &
notConvergedCounter + convergedCounter , ' increments did not converge!'
close ( 538 )
call fftw_destroy_plan ( plan_lambda ) ; call fftw_destroy_plan ( plan_correction )
call quit ( 0_pInt )
2012-03-20 23:31:31 +05:30
end program DAMASK_spectral_AL
2012-03-07 23:07:40 +05:30
!********************************************************************
! quit subroutine to satisfy IO_error
!
!********************************************************************
subroutine quit ( stop_id )
2012-03-30 01:24:31 +05:30
use prec , only : &
pInt
2012-03-07 23:07:40 +05:30
implicit none
integer ( pInt ) , intent ( in ) :: stop_id
2012-03-30 01:24:31 +05:30
if ( stop_id == 0_pInt ) stop 0 ! normal termination
if ( stop_id < = 9000_pInt ) then ! trigger regridding
write ( 6 , '(i4)' ) stop_id
stop 1
endif
stop 'abnormal termination of DAMASK_spectral'
2012-03-07 23:07:40 +05:30
end subroutine
