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! Copyright 2011 Max-Planck-Institut für Eisenforschung GmbH
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!
! This file is part of DAMASK,
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! the Düsseldorf Advanced MAterial Simulation Kit.
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!
! 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/>.
!
!##############################################################
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!* $Id$
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!##############################################################
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module numerics
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!##############################################################
use prec , only : pInt , pReal
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implicit none
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character ( len = 64 ) , parameter , private :: &
numerics_configFile = 'numerics.config' ! name of configuration file
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integer ( pInt ) :: iJacoStiffness = 1_pInt , & ! frequency of stiffness update
iJacoLpresiduum = 1_pInt , & ! frequency of Jacobian update of residuum in Lp
nHomog = 20_pInt , & ! homogenization loop limit (only for debugging info, loop limit is determined by "subStepMinHomog")
nMPstate = 10_pInt , & ! materialpoint state loop limit
nCryst = 20_pInt , & ! crystallite loop limit (only for debugging info, loop limit is determined by "subStepMinCryst")
nState = 10_pInt , & ! state loop limit
nStress = 40_pInt , & ! stress loop limit
pert_method = 1_pInt , & ! method used in perturbation technique for tangent
numerics_integrationMode = 0_pInt ! integrationMode 1 = central solution ; integrationMode 2 = perturbation, Default 0: undefined, is not read from file
integer ( pInt ) , dimension ( 2 ) :: numerics_integrator = 1_pInt ! method used for state integration (central & perturbed state), Default 1: fix-point iteration for both states
real ( pReal ) :: relevantStrain = 1.0e-7_pReal , & ! strain increment considered significant (used by crystallite to determine whether strain inc is considered significant)
defgradTolerance = 1.0e-7_pReal , & ! deviation of deformation gradient that is still allowed (used by CPFEM to determine outdated ffn1)
pert_Fg = 1.0e-7_pReal , & ! strain perturbation for FEM Jacobi
subStepMinCryst = 1.0e-3_pReal , & ! minimum (relative) size of sub-step allowed during cutback in crystallite
subStepMinHomog = 1.0e-3_pReal , & ! minimum (relative) size of sub-step allowed during cutback in homogenization
subStepSizeCryst = 0.25_pReal , & ! size of first substep when cutback in crystallite
subStepSizeHomog = 0.25_pReal , & ! size of first substep when cutback in homogenization
stepIncreaseCryst = 1.5_pReal , & ! increase of next substep size when previous substep converged in crystallite
stepIncreaseHomog = 1.5_pReal , & ! increase of next substep size when previous substep converged in homogenization
rTol_crystalliteState = 1.0e-6_pReal , & ! relative tolerance in crystallite state loop
rTol_crystalliteTemperature = 1.0e-6_pReal , & ! relative tolerance in crystallite temperature loop
rTol_crystalliteStress = 1.0e-6_pReal , & ! relative tolerance in crystallite stress loop
aTol_crystalliteStress = 1.0e-8_pReal , & ! absolute tolerance in crystallite stress loop, Default 1.0e-8: residuum is in Lp and hence strain is on this order
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absTol_RGC = 1.0e+4_pReal , & ! absolute tolerance of RGC residuum
relTol_RGC = 1.0e-3_pReal , & ! relative tolerance of RGC residuum
absMax_RGC = 1.0e+10_pReal , & ! absolute maximum of RGC residuum
relMax_RGC = 1.0e+2_pReal , & ! relative maximum of RGC residuum
pPert_RGC = 1.0e-7_pReal , & ! perturbation for computing RGC penalty tangent
xSmoo_RGC = 1.0e-5_pReal , & ! RGC penalty smoothing parameter (hyperbolic tangent)
viscPower_RGC = 1.0e+0_pReal , & ! power (sensitivity rate) of numerical viscosity in RGC scheme, Default 1.0e0: Newton viscosity (linear model)
viscModus_RGC = 0.0e+0_pReal , & ! stress modulus of RGC numerical viscosity, Default 0.0e0: No viscosity is applied
refRelaxRate_RGC = 1.0e-3_pReal , & ! reference relaxation rate in RGC viscosity
maxdRelax_RGC = 1.0e+0_pReal , & ! threshold of maximum relaxation vector increment (if exceed this then cutback)
maxVolDiscr_RGC = 1.0e-5_pReal , & ! threshold of maximum volume discrepancy allowed
volDiscrMod_RGC = 1.0e+12_pReal , & ! stiffness of RGC volume discrepancy (zero = without volume discrepancy constraint)
volDiscrPow_RGC = 5.0_pReal , & ! powerlaw penalty for volume discrepancy
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!* spectral parameters:
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err_div_tol = 1.0e-4_pReal , & ! error of divergence in fourier space, Default 1.0e-4: proposed by Suquet
err_stress_tolrel = 0.01_pReal , & ! relative tolerance for fullfillment of stress BC, Default: 0.01 allowing deviation of 1% of maximum stress
fftw_timelimit = - 1.0_pReal , & ! sets the timelimit of plan creation for FFTW, see manual on www.fftw.org, Default -1.0: disable timelimit
rotation_tol = 1.0e-12_pReal ! tolerance of rotation specified in loadcase, Default 1.0e-12: first guess
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character ( len = 64 ) :: fftw_plan_mode = 'FFTW_PATIENT' ! reads the planing-rigor flag, see manual on www.fftw.org, Default FFTW_PATIENT: use patiant planner flag
integer ( pInt ) :: fftw_planner_flag = - 1_pInt , & ! conversion of fftw_plan_mode to integer, basically what is usually done in the include file of fftw
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itmax = 20_pInt , & ! maximum number of iterations
itmin = 2_pInt ! minimum number of iterations
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logical :: memory_efficient = . true . , & ! for fast execution (pre calculation of gamma_hat), Default .true.: do not precalculate
divergence_correction = . false . , & ! correct divergence calculation in fourier space, Default .false.: no correction
update_gamma = . false . , & ! update gamma operator with current stiffness, Default .false.: use initial stiffness
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!* end of spectral parameters:
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analyticJaco = . false . ! use analytic Jacobian or perturbation, Default .false.: calculate Jacobian using perturbations
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!* Random seeding parameters
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integer ( pInt ) :: fixedSeed = 0_pInt ! fixed seeding for pseudo-random number generator, Default 0: use random seed
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!* OpenMP variable
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integer ( pInt ) :: DAMASK_NumThreadsInt = 0_pInt ! value stored in environment variable DAMASK_NUM_THREADS, set to zero if no OpenMP directive
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CONTAINS
!*******************************************
! initialization subroutine
!*******************************************
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subroutine numerics_init
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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)
use IO , only : IO_error , &
IO_open_file_stat , &
IO_isBlank , &
IO_stringPos , &
IO_stringValue , &
IO_lc , &
IO_floatValue , &
IO_intValue , &
IO_warning
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!$ use OMP_LIB ! the openMP function library
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implicit none
integer ( pInt ) , parameter :: fileunit = 300_pInt , &
maxNchunks = 2_pInt
!$ integer :: gotDAMASK_NUM_THREADS = 1
integer ( pInt ) , dimension ( 1 + 2 * maxNchunks ) :: positions
character ( len = 64 ) :: tag
character ( len = 1024 ) :: line
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!$ character(len=6) DAMASK_NumThreadsString !environment variable DAMASK_NUM_THREADS
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!$OMP CRITICAL (write2out)
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write ( 6 , * )
write ( 6 , * ) '<<<+- numerics init -+>>>'
write ( 6 , * ) '$Id$'
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#include "compilation_info.f90"
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!$OMP END CRITICAL (write2out)
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!$ call GET_ENVIRONMENT_VARIABLE(NAME='DAMASK_NUM_THREADS',VALUE=DAMASK_NumThreadsString,STATUS=gotDAMASK_NUM_THREADS) ! get environment variable DAMASK_NUM_THREADS...
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!$ if(gotDAMASK_NUM_THREADS /= 0) call IO_warning(47_pInt,ext_msg=DAMASK_NumThreadsString)
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!$ read(DAMASK_NumThreadsString,'(i6)') DAMASK_NumThreadsInt ! ...convert it to integer...
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!$ if (DAMASK_NumThreadsInt < 1_pInt) DAMASK_NumThreadsInt = 1_pInt ! ...ensure that its at least one...
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!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! ...and use it as number of threads for parallel execution
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! try to open the config file
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if ( IO_open_file_stat ( fileunit , numerics_configFile ) ) then
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!$OMP CRITICAL (write2out)
write ( 6 , * ) ' ... using values from config file'
write ( 6 , * )
!$OMP END CRITICAL (write2out)
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!* read variables from config file and overwrite parameters
line = ''
do
read ( fileunit , '(a1024)' , END = 100 ) line
if ( IO_isBlank ( line ) ) cycle ! skip empty lines
positions = IO_stringPos ( line , maxNchunks )
tag = IO_lc ( IO_stringValue ( line , positions , 1_pInt ) ) ! extract key
select case ( tag )
case ( 'relevantstrain' )
relevantStrain = IO_floatValue ( line , positions , 2_pInt )
case ( 'defgradtolerance' )
defgradTolerance = IO_floatValue ( line , positions , 2_pInt )
case ( 'ijacostiffness' )
iJacoStiffness = IO_intValue ( line , positions , 2_pInt )
case ( 'ijacolpresiduum' )
iJacoLpresiduum = IO_intValue ( line , positions , 2_pInt )
case ( 'pert_fg' )
pert_Fg = IO_floatValue ( line , positions , 2_pInt )
case ( 'pert_method' )
pert_method = IO_intValue ( line , positions , 2_pInt )
case ( 'nhomog' )
nHomog = IO_intValue ( line , positions , 2_pInt )
case ( 'nmpstate' )
nMPstate = IO_intValue ( line , positions , 2_pInt )
case ( 'ncryst' )
nCryst = IO_intValue ( line , positions , 2_pInt )
case ( 'nstate' )
nState = IO_intValue ( line , positions , 2_pInt )
case ( 'nstress' )
nStress = IO_intValue ( line , positions , 2_pInt )
case ( 'substepmincryst' )
subStepMinCryst = IO_floatValue ( line , positions , 2_pInt )
case ( 'substepsizecryst' )
subStepSizeCryst = IO_floatValue ( line , positions , 2_pInt )
case ( 'stepincreasecryst' )
stepIncreaseCryst = IO_floatValue ( line , positions , 2_pInt )
case ( 'substepminhomog' )
subStepMinHomog = IO_floatValue ( line , positions , 2_pInt )
case ( 'substepsizehomog' )
subStepSizeHomog = IO_floatValue ( line , positions , 2_pInt )
case ( 'stepincreasehomog' )
stepIncreaseHomog = IO_floatValue ( line , positions , 2_pInt )
case ( 'rtol_crystallitestate' )
rTol_crystalliteState = IO_floatValue ( line , positions , 2_pInt )
case ( 'rtol_crystallitetemperature' )
rTol_crystalliteTemperature = IO_floatValue ( line , positions , 2_pInt )
case ( 'rtol_crystallitestress' )
rTol_crystalliteStress = IO_floatValue ( line , positions , 2_pInt )
case ( 'atol_crystallitestress' )
aTol_crystalliteStress = IO_floatValue ( line , positions , 2_pInt )
case ( 'integrator' )
numerics_integrator ( 1 ) = IO_intValue ( line , positions , 2_pInt )
case ( 'integratorstiffness' )
numerics_integrator ( 2 ) = IO_intValue ( line , positions , 2_pInt )
case ( 'analyticjaco' )
analyticJaco = IO_intValue ( line , positions , 2_pInt ) > 0_pInt
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!* RGC parameters:
case ( 'atol_rgc' )
absTol_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'rtol_rgc' )
relTol_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'amax_rgc' )
absMax_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'rmax_rgc' )
relMax_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'perturbpenalty_rgc' )
pPert_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'relevantmismatch_rgc' )
xSmoo_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'viscositypower_rgc' )
viscPower_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'viscositymodulus_rgc' )
viscModus_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'refrelaxationrate_rgc' )
refRelaxRate_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'maxrelaxation_rgc' )
maxdRelax_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'maxvoldiscrepancy_rgc' )
maxVolDiscr_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'voldiscrepancymod_rgc' )
volDiscrMod_RGC = IO_floatValue ( line , positions , 2_pInt )
case ( 'discrepancypower_rgc' )
volDiscrPow_RGC = IO_floatValue ( line , positions , 2_pInt )
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!* spectral parameters
case ( 'err_div_tol' )
err_div_tol = IO_floatValue ( line , positions , 2_pInt )
case ( 'err_stress_tolrel' )
err_stress_tolrel = IO_floatValue ( line , positions , 2_pInt )
case ( 'itmax' )
itmax = IO_intValue ( line , positions , 2_pInt )
case ( 'itmin' )
itmin = IO_intValue ( line , positions , 2_pInt )
case ( 'memory_efficient' )
memory_efficient = IO_intValue ( line , positions , 2_pInt ) > 0_pInt
case ( 'fftw_timelimit' )
fftw_timelimit = IO_floatValue ( line , positions , 2_pInt )
case ( 'fftw_plan_mode' )
fftw_plan_mode = IO_stringValue ( line , positions , 2_pInt )
case ( 'rotation_tol' )
rotation_tol = IO_floatValue ( line , positions , 2_pInt )
case ( 'divergence_correction' )
divergence_correction = IO_intValue ( line , positions , 2_pInt ) > 0_pInt
case ( 'update_gamma' )
update_gamma = IO_intValue ( line , positions , 2_pInt ) > 0_pInt
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!* Random seeding parameters
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case ( 'fixed_seed' )
fixedSeed = IO_intValue ( line , positions , 2_pInt )
case default
call IO_error ( 300_pInt , ext_msg = tag )
endselect
enddo
100 close ( fileunit )
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! no config file, so we use standard values
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else
!$OMP CRITICAL (write2out)
write ( 6 , * ) ' ... using standard values'
write ( 6 , * )
!$OMP END CRITICAL (write2out)
endif
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select case ( IO_lc ( fftw_plan_mode ) ) ! setting parameters for the plan creation of FFTW. Basically a translation from fftw3.f
case ( 'estimate' , 'fftw_estimate' ) ! ordered from slow execution (but fast plan creation) to fast execution
fftw_planner_flag = 64_pInt
case ( 'measure' , 'fftw_measure' )
fftw_planner_flag = 0_pInt
case ( 'patient' , 'fftw_patient' )
fftw_planner_flag = 32_pInt
case ( 'exhaustive' , 'fftw_exhaustive' )
fftw_planner_flag = 8_pInt
case default
call IO_warning ( warning_ID = 47_pInt , ext_msg = trim ( IO_lc ( fftw_plan_mode ) ) )
fftw_planner_flag = 32_pInt
end select
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!* writing parameters to output file
!$OMP CRITICAL (write2out)
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write ( 6 , '(a24,1x,es8.1)' ) ' relevantStrain: ' , relevantStrain
write ( 6 , '(a24,1x,es8.1)' ) ' defgradTolerance: ' , defgradTolerance
write ( 6 , '(a24,1x,i8)' ) ' iJacoStiffness: ' , iJacoStiffness
write ( 6 , '(a24,1x,i8)' ) ' iJacoLpresiduum: ' , iJacoLpresiduum
write ( 6 , '(a24,1x,es8.1)' ) ' pert_Fg: ' , pert_Fg
write ( 6 , '(a24,1x,i8)' ) ' pert_method: ' , pert_method
write ( 6 , '(a24,1x,i8)' ) ' nCryst: ' , nCryst
write ( 6 , '(a24,1x,es8.1)' ) ' subStepMinCryst: ' , subStepMinCryst
write ( 6 , '(a24,1x,es8.1)' ) ' subStepSizeCryst: ' , subStepSizeCryst
write ( 6 , '(a24,1x,es8.1)' ) ' stepIncreaseCryst: ' , stepIncreaseCryst
write ( 6 , '(a24,1x,i8)' ) ' nState: ' , nState
write ( 6 , '(a24,1x,i8)' ) ' nStress: ' , nStress
write ( 6 , '(a24,1x,es8.1)' ) ' rTol_crystalliteState: ' , rTol_crystalliteState
write ( 6 , '(a24,1x,es8.1)' ) ' rTol_crystalliteTemp: ' , rTol_crystalliteTemperature
write ( 6 , '(a24,1x,es8.1)' ) ' rTol_crystalliteStress: ' , rTol_crystalliteStress
write ( 6 , '(a24,1x,es8.1)' ) ' aTol_crystalliteStress: ' , aTol_crystalliteStress
write ( 6 , '(a24,2(1x,i8))' ) ' integrator: ' , numerics_integrator
write ( 6 , '(a24,1x,L8,/)' ) ' analytic Jacobian: ' , analyticJaco
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write ( 6 , '(a24,1x,i8)' ) ' nHomog: ' , nHomog
write ( 6 , '(a24,1x,es8.1)' ) ' subStepMinHomog: ' , subStepMinHomog
write ( 6 , '(a24,1x,es8.1)' ) ' subStepSizeHomog: ' , subStepSizeHomog
write ( 6 , '(a24,1x,es8.1)' ) ' stepIncreaseHomog: ' , stepIncreaseHomog
write ( 6 , '(a24,1x,i8,/)' ) ' nMPstate: ' , nMPstate
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!* RGC parameters
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write ( 6 , '(a24,1x,es8.1)' ) ' aTol_RGC: ' , absTol_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' rTol_RGC: ' , relTol_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' aMax_RGC: ' , absMax_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' rMax_RGC: ' , relMax_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' perturbPenalty_RGC: ' , pPert_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' relevantMismatch_RGC: ' , xSmoo_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' viscosityrate_RGC: ' , viscPower_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' viscositymodulus_RGC: ' , viscModus_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' maxrelaxation_RGC: ' , maxdRelax_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' maxVolDiscrepancy_RGC: ' , maxVolDiscr_RGC
write ( 6 , '(a24,1x,es8.1)' ) ' volDiscrepancyMod_RGC: ' , volDiscrMod_RGC
write ( 6 , '(a24,1x,es8.1,/)' ) ' discrepancyPower_RGC: ' , volDiscrPow_RGC
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!* spectral parameters
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write ( 6 , '(a24,1x,es8.1)' ) ' err_div_tol: ' , err_div_tol
write ( 6 , '(a24,1x,es8.1)' ) ' err_stress_tolrel: ' , err_stress_tolrel
write ( 6 , '(a24,1x,i8)' ) ' itmax: ' , itmax
write ( 6 , '(a24,1x,i8)' ) ' itmin: ' , itmin
write ( 6 , '(a24,1x,L8)' ) ' memory_efficient: ' , memory_efficient
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if ( fftw_timelimit < 0.0_pReal ) then
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write ( 6 , '(a24,1x,L8)' ) ' fftw_timelimit: ' , . false .
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else
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write ( 6 , '(a24,1x,es8.1)' ) ' fftw_timelimit: ' , fftw_timelimit
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endif
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write ( 6 , '(a24,1x,a)' ) ' fftw_plan_mode: ' , trim ( fftw_plan_mode )
write ( 6 , '(a24,1x,i8)' ) ' fftw_planner_flag: ' , fftw_planner_flag
write ( 6 , '(a24,1x,es8.1)' ) ' rotation_tol: ' , rotation_tol
write ( 6 , '(a24,1x,L8,/)' ) ' divergence_correction: ' , divergence_correction
write ( 6 , '(a24,1x,L8,/)' ) ' update_gamma: ' , update_gamma
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!* Random seeding parameters
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write ( 6 , '(a24,1x,i16,/)' ) ' fixed_seed: ' , fixedSeed
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!$OMP END CRITICAL (write2out)
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!* openMP parameter
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!$ write(6,'(a24,1x,i8,/)') ' number of threads: ',DAMASK_NumThreadsInt
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!* sanity check
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if ( relevantStrain < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'relevantStrain' )
if ( defgradTolerance < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'defgradTolerance' )
if ( iJacoStiffness < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'iJacoStiffness' )
if ( iJacoLpresiduum < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'iJacoLpresiduum' )
if ( pert_Fg < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'pert_Fg' )
if ( pert_method < = 0_pInt . or . pert_method > = 4_pInt ) &
call IO_error ( 301_pInt , ext_msg = 'pert_method' )
if ( nHomog < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'nHomog' )
if ( nMPstate < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'nMPstate' )
if ( nCryst < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'nCryst' )
if ( nState < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'nState' )
if ( nStress < 1_pInt ) call IO_error ( 301_pInt , ext_msg = 'nStress' )
if ( subStepMinCryst < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'subStepMinCryst' )
if ( subStepSizeCryst < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'subStepSizeCryst' )
if ( stepIncreaseCryst < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'stepIncreaseCryst' )
if ( subStepMinHomog < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'subStepMinHomog' )
if ( subStepSizeHomog < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'subStepSizeHomog' )
if ( stepIncreaseHomog < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'stepIncreaseHomog' )
if ( rTol_crystalliteState < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'rTol_crystalliteState' )
if ( rTol_crystalliteTemperature < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'rTol_crystalliteTemperature' )
if ( rTol_crystalliteStress < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'rTol_crystalliteStress' )
if ( aTol_crystalliteStress < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'aTol_crystalliteStress' )
if ( any ( numerics_integrator < = 0_pInt ) . or . any ( numerics_integrator > = 6_pInt ) ) &
call IO_error ( 301_pInt , ext_msg = 'integrator' )
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!* RGC parameters
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if ( absTol_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'absTol_RGC' )
if ( relTol_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'relTol_RGC' )
if ( absMax_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'absMax_RGC' )
if ( relMax_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'relMax_RGC' )
if ( pPert_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'pPert_RGC' )
if ( xSmoo_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'xSmoo_RGC' )
if ( viscPower_RGC < 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'viscPower_RGC' )
if ( viscModus_RGC < 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'viscModus_RGC' )
if ( refRelaxRate_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'refRelaxRate_RGC' )
if ( maxdRelax_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'maxdRelax_RGC' )
if ( maxVolDiscr_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'maxVolDiscr_RGC' )
if ( volDiscrMod_RGC < 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'volDiscrMod_RGC' )
if ( volDiscrPow_RGC < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'volDiscrPw_RGC' )
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!* spectral parameters
if ( err_div_tol < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'err_div_tol' )
if ( err_stress_tolrel < = 0.0_pReal ) call IO_error ( 301_pInt , ext_msg = 'err_stress_tolrel' )
if ( itmax < = 1.0_pInt ) call IO_error ( 301_pInt , ext_msg = 'itmax' )
if ( itmin > itmax ) call IO_error ( 301_pInt , ext_msg = 'itmin' )
if ( fixedSeed < = 0_pInt ) then
!$OMP CRITICAL (write2out)
write ( 6 , '(a)' ) ' Random is random!'
!$OMP END CRITICAL (write2out)
endif
end subroutine numerics_init
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end module numerics