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!--------------------------------------------------------------------------------------------------
! $Id$
!--------------------------------------------------------------------------------------------------
!> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
!> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
!> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH
!> @brief Basic scheme solver
!> @details this solver follows closely the original large strain formulation presented by
!> Suquet. The iterative procedure is solved using a fix-point iteration
!--------------------------------------------------------------------------------------------------
module DAMASK_spectral_SolverBasic
use prec, only: &
pInt, &
pReal
use math, only: &
math_I3
use DAMASK_spectral_Utilities, only: &
tSolutionState
implicit none
character (len=*), parameter, public :: &
DAMASK_spectral_SolverBasic_label = 'basic'
!--------------------------------------------------------------------------------------------------
! pointwise data
real(pReal), private, dimension(:,:,:,:,:), allocatable :: F, F_lastInc, Fdot, P
real(pReal), private, dimension(:,:,:,:), allocatable :: coordinates
real(pReal), private, dimension(:,:,:), allocatable :: temperature
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
real(pReal), private, dimension(3,3) :: &
F_aim = math_I3, &
F_aim_lastInc = math_I3
real(pReal), private,dimension(3,3,3,3) :: &
C = 0.0_pReal, C_lastInc = 0.0_pReal
contains
!--------------------------------------------------------------------------------------------------
!> @brief allocates all neccessary fields and fills them with data, potentially from restart info
!--------------------------------------------------------------------------------------------------
subroutine basic_init()
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_read_JobBinaryFile, &
IO_write_JobBinaryFile, &
IO_intOut
use FEsolving, only: &
restartInc
use DAMASK_interface, only: &
getSolverJobName
use DAMASK_spectral_Utilities, only: &
Utilities_init, &
Utilities_constitutiveResponse, &
Utilities_updateGamma, &
debugRestart
use mesh, only: &
res, &
geomdim
implicit none
integer(pInt) :: i,j,k
real(pReal), dimension(3,3) :: temp33_Real
call Utilities_Init()
write(6,'(/,a)') ' <<<+- DAMASK_spectral_solverBasic init -+>>>'
write(6,'(a)') ' $Id$'
#include "compilation_info.f90"
write(6,'(a)') ''
allocate (F ( 3,3,res(1), res(2),res(3)), source = 0.0_pReal)
allocate (F_lastInc ( 3,3,res(1), res(2),res(3)), source = 0.0_pReal)
allocate (Fdot ( 3,3,res(1), res(2),res(3)), source = 0.0_pReal)
allocate (P ( 3,3,res(1), 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 = 0.0_pReal)
!--------------------------------------------------------------------------------------------------
! init fields
if (restartInc == 1_pInt) then ! no deformation (no restart)
F = spread(spread(spread(math_I3,3,res(1)),4,res(2)),5,res(3)) ! initialize to identity
F_lastInc = F
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) &
- geomdim/real(2_pInt*res,pReal)
enddo; enddo; enddo
elseif (restartInc > 1_pInt) then ! using old values from file
if (debugRestart) write(6,'(a,'//IO_intOut(restartInc-1_pInt)//',a)') &
'Reading values of increment', restartInc - 1_pInt, 'from file'
call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
trim(getSolverJobName()),size(F))
read (777,rec=1) F
close (777)
call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad_lastInc',&
trim(getSolverJobName()),size(F_lastInc))
read (777,rec=1) F_lastInc
close (777)
call IO_read_jobBinaryFile(777,'F_aim',trim(getSolverJobName()),size(F_aim))
read (777,rec=1) F_aim
close (777)
call IO_read_jobBinaryFile(777,'F_aim_lastInc',trim(getSolverJobName()),size(F_aim_lastInc))
read (777,rec=1) F_aim_lastInc
close (777)
coordinates = 0.0 ! change it later!!!
endif
!no rotation bc call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,rotation_BC),1.0_pReal,F_lastInc,coordinates)
call Utilities_constitutiveResponse(coordinates,F,F_lastInc,temperature,0.0_pReal,&
P,C,temp33_Real,.false.,math_I3)
!--------------------------------------------------------------------------------------------------
! reference stiffness
if (restartInc == 1_pInt) then
call IO_write_jobBinaryFile(777,'C_ref',size(C))
write (777,rec=1) C
close(777)
elseif (restartInc > 1_pInt) then
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C))
read (777,rec=1) C
close (777)
endif
call Utilities_updateGamma(C)
end subroutine basic_init
!--------------------------------------------------------------------------------------------------
!> @brief solution for the basic scheme with internal iterations
!--------------------------------------------------------------------------------------------------
type(tSolutionState) function &
basic_solution(incInfo,guessmode,timeinc,timeinc_old,P_BC,F_BC,temperature_bc,rotation_BC)
use numerics, only: &
itmax, &
itmin, &
update_gamma
use math, only: &
math_mul33x33 ,&
math_rotate_backward33, &
math_transpose33, &
math_mul3333xx33
use mesh, only: &
res,&
geomdim, &
deformed_fft, &
wgt
use IO, only: &
IO_write_JobBinaryFile, &
IO_intOut
use DAMASK_spectral_Utilities, only: &
tBoundaryCondition, &
field_real, &
Utilities_forwardField, &
Utilities_maskedCompliance, &
Utilities_FFTforward, &
Utilities_divergenceRMS, &
Utilities_fourierConvolution, &
Utilities_FFTbackward, &
Utilities_updateGamma, &
Utilities_constitutiveResponse, &
Utilities_calculateRate
use FEsolving, only: &
restartWrite, &
terminallyIll
use DAMASK_spectral_Utilities, only: cutBack
implicit none
!--------------------------------------------------------------------------------------------------
! input data for solution
real(pReal), intent(in) :: timeinc, timeinc_old, temperature_bc, guessmode
type(tBoundaryCondition), intent(in) :: P_BC,F_BC
character(len=*), intent(in) :: incInfo
real(pReal), dimension(3,3), intent(in) :: rotation_BC
real(pReal), dimension(3,3,3,3) :: S
real(pReal), dimension(3,3), save :: f_aimDot = 0.0_pReal
real(pReal), dimension(3,3) :: F_aim_lab, &
F_aim_lab_lastIter, &
P_av
!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
real(pReal) :: err_div, err_stress
integer(pInt) :: iter, row, column, i, j, k
logical :: ForwardData
real(pReal) :: defgradDet, defgradDetMax, defgradDetMin
real(pReal), dimension(3,3) :: temp33_Real
!--------------------------------------------------------------------------------------------------
! restart information for spectral solver
if (restartWrite) then
write(6,'(a)') 'writing converged results for restart'
call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F_lastInc))
write (777,rec=1) F_LastInc
close (777)
call IO_write_jobBinaryFile(777,'C',size(C))
write (777,rec=1) C
close(777)
endif
if ( cutBack) then
F_aim = F_aim_lastInc
F = F_lastInc
C = C_lastInc
else
C_lastInc = C
!--------------------------------------------------------------------------------------------------
! calculate rate for aim
if (F_BC%myType=='l') then ! calculate f_aimDot from given L and current F
f_aimDot = F_BC%maskFloat * math_mul33x33(F_BC%values, F_aim)
elseif(F_BC%myType=='fdot') then ! f_aimDot is prescribed
f_aimDot = F_BC%maskFloat * F_BC%values
endif
f_aimDot = f_aimDot &
+ guessmode * P_BC%maskFloat * (F_aim - F_aim_lastInc)/timeinc_old
F_aim_lastInc = F_aim
!--------------------------------------------------------------------------------------------------
! update coordinates and rate and forward last inc
call deformed_fft(res,geomdim,math_rotate_backward33(F_aim_lastInc,rotation_BC), &
1.0_pReal,F_lastInc,coordinates)
Fdot = Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
timeinc,timeinc_old,guessmode,F_lastInc,F)
F_lastInc = F
endif
F_aim = F_aim + f_aimDot * timeinc
F = Utilities_forwardField(timeinc,F_aim,F_lastInc,Fdot) !I thin F aim should be rotated here
print*, 'F', sum(sum(sum(F,dim=5),dim=4),dim=3)*wgt
!--------------------------------------------------------------------------------------------------
! update stiffness (and gamma operator)
S = Utilities_maskedCompliance(rotation_BC,P_BC%maskLogical,C)
if (update_gamma) call Utilities_updateGamma(C)
iter = 0_pInt
convergenceLoop: do while(iter < itmax)
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
! report begin of new iteration
write(6,'(/,a,3(a,'//IO_intOut(itmax)//'))') trim(incInfo), &
' @ Iter. ', itmin, '<',iter, '≤', itmax
write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =', &
math_transpose33(F_aim)
F_aim_lab_lastIter = math_rotate_backward33(F_aim,rotation_BC)
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
basic_solution%termIll = .false.
call Utilities_constitutiveResponse(coordinates,F_lastInc,F,temperature,timeinc,&
P,C,P_av,ForwardData,rotation_BC)
basic_solution%termIll = terminallyIll
terminallyIll = .False.
ForwardData = .False.
!--------------------------------------------------------------------------------------------------
! stress BC handling
F_aim = F_aim - math_mul3333xx33(S, ((P_av - P_BC%values))) ! S = 0.0 for no bc
err_stress = maxval(abs(P_BC%maskFloat * (P_av - P_BC%values))) ! mask = 0.0 for no bc
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame
!--------------------------------------------------------------------------------------------------
! updated deformation gradient using fix point algorithm of basic scheme
field_real = 0.0_pReal
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = reshape(P,[res(1),res(2),res(3),3,3],&
order=[4,5,1,2,3]) ! field real has a different order
call Utilities_FFTforward()
err_div = Utilities_divergenceRMS()
call Utilities_fourierConvolution(F_aim_lab_lastIter - F_aim_lab)
call Utilities_FFTbackward()
F = F - reshape(field_real(1:res(1),1:res(2),1:res(3),1:3,1:3),shape(F),order=[3,4,5,1,2]) ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
basic_solution%converged = basic_Converged(err_div,P_av,err_stress,P_av)
write(6,'(/,a)') '=========================================================================='
if ((basic_solution%converged .and. iter > itmin) .or. basic_solution%termIll) exit
enddo convergenceLoop
end function basic_solution
!--------------------------------------------------------------------------------------------------
!> @brief convergence check for basic scheme based on div of P and deviation from stress aim
!--------------------------------------------------------------------------------------------------
logical function basic_Converged(err_div,pAvgDiv,err_stress,pAvgStress)
use numerics, only: &
itmin, &
err_div_tol, &
err_stress_tolrel, &
err_stress_tolabs
use math, only: &
math_mul33x33, &
math_eigenvalues33, &
math_transpose33
implicit none
real(pReal), dimension(3,3), intent(in) :: &
pAvgDiv,&
pAvgStress
real(pReal), intent(in) :: &
err_div, &
err_stress
real(pReal) :: &
err_stress_tol, &
pAvgDivL2
pAvgDivL2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(pAvgDiv,math_transpose33(pAvgDiv))))) ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
err_stress_tol = min(maxval(abs(pAvgStress))*err_stress_tolrel,err_stress_tolabs)
basic_Converged = all([ err_div/pAvgDivL2/err_div_tol,&
err_stress/err_stress_tol ] < 1.0_pReal)
write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/pAvgDivL2/err_div_tol,&
' (',err_div,' N/m³)'
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
' (',err_stress,' Pa)'
end function basic_Converged
subroutine basic_destroy()
use DAMASK_spectral_Utilities, only: &
Utilities_destroy
implicit none
call Utilities_destroy()
end subroutine basic_destroy
end module DAMASK_spectral_SolverBasic
!--------------------------------------------------------------------------------------------------
! 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
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
! if(debugGeneral) then
! defgradDetMax = -huge(1.0_pReal)
! defgradDetMin = +huge(1.0_pReal)
! do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
! defgradDet = math_det33(F(i,j,k,1:3,1:3))
! defgradDetMax = max(defgradDetMax,defgradDet)
! defgradDetMin = min(defgradDetMin,defgradDet)
! enddo; enddo; enddo
! write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
! write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
! endif
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