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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 global data
real(pReal), private, dimension(:,:,:,:,:), allocatable :: &
F, & !< deformation gradient field
F_lastInc, & !< deformation gradient field last increment
Fdot !< assumed rate for F n to F n+1
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
real(pReal), private, dimension(3,3) :: &
F_aim = math_I3, & !< deformation gradient aim
F_aim_lastInc = math_I3, & !< deformation gradient aim last increment
F_aimDot = 0.0_pReal !< assumed rate
real(pReal), private,dimension(3,3,3,3) :: &
C = 0.0_pReal, & !< average stiffness
C_lastInc = 0.0_pReal !< average stiffness last increment
contains
!--------------------------------------------------------------------------------------------------
!> @brief allocates all neccessary fields and fills them with data, potentially from restart info
!--------------------------------------------------------------------------------------------------
subroutine basic_init(temperature)
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, &
wgt, &
geomdim, &
scaledDim, &
mesh_ipCoordinates, &
mesh_NcpElems, &
mesh_deformedCoordsFFT
implicit none
real(pReal), intent(inout) :: &
temperature
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: P
integer(pInt) :: &
i, j, k
real(pReal), dimension(3,3) :: &
temp33_Real = 0.0_pReal
real(pReal), dimension(3,3,3,3) :: &
temp3333_Real
call Utilities_Init()
write(6,'(/,a)') ' <<<+- DAMASK_spectral_solverBasic init -+>>>'
write(6,'(a)') ' $Id$'
#include "compilation_info.f90"
write(6,'(a,3(f12.5)/)') ' scaledDim x y z:', scaledDim
!--------------------------------------------------------------------------------------------------
! allocate global fields
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)
!--------------------------------------------------------------------------------------------------
! init fields and average quantities
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
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'
flush(6)
call IO_read_jobBinaryFile(777,'F',&
trim(getSolverJobName()),size(F))
read (777,rec=1) F
close (777)
call IO_read_jobBinaryFile(777,'F_lastInc',&
trim(getSolverJobName()),size(F_lastInc))
read (777,rec=1) F_lastInc
close (777)
F_aim = sum(sum(sum(F,dim=5),dim=4),dim=3) * wgt ! average of F
F_aim_lastInc = sum(sum(sum(F_lastInc,dim=5),dim=4),dim=3) * wgt ! average of F_lastInc
call IO_read_jobBinaryFile(777,'F_aimDot',trim(getSolverJobName()),size(f_aimDot))
read (777,rec=1) f_aimDot
close (777)
call IO_read_jobBinaryFile(777,'C',trim(getSolverJobName()),size(C))
read (777,rec=1) C
close (777)
call IO_read_jobBinaryFile(777,'C_lastInc',trim(getSolverJobName()),size(C_lastInc))
read (777,rec=1) C_lastInc
close (777)
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(temp3333_Real))
read (777,rec=1) temp3333_Real
close (777)
endif
mesh_ipCoordinates = reshape(mesh_deformedCoordsFFT(geomdim,F),[3,1,mesh_NcpElems])
call Utilities_constitutiveResponse(F,F,temperature,0.0_pReal,P,C,temp33_Real,.false.,math_I3) ! constitutive response with no deformation in no time to get reference stiffness
if (restartInc == 1_pInt) then ! use initial stiffness as reference stiffness
temp3333_Real = C
endif
call Utilities_updateGamma(temp3333_Real,.True.)
end subroutine basic_init
!--------------------------------------------------------------------------------------------------
!> @brief solution for the basic scheme with internal iterations
!--------------------------------------------------------------------------------------------------
type(tSolutionState) function &
basic_solution(incInfo,guess,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, &
wgt, &
mesh_ipCoordinates,&
mesh_NcpElems, &
mesh_deformedCoordsFFT
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, &
debugRotation
use FEsolving, only: &
restartWrite, &
restartRead, &
terminallyIll
use DAMASK_spectral_Utilities, only: &
cutBack
implicit none
!--------------------------------------------------------------------------------------------------
! input data for solution
real(pReal), intent(in) :: &
timeinc, & !< increment in time for current solution
timeinc_old !< increment in time of last increment
logical, intent(in) :: &
guess !< if .false., assume homogeneous addon
type(tBoundaryCondition), intent(in) :: &
P_BC,& !< stress boundary conditions
F_BC !< deformation boundary conditions
character(len=*), intent(in) :: &
incInfo !< string with information of current increment for output to screen
real(pReal), dimension(3,3), intent(in) :: &
rotation_BC !< rotation load to lab
real(pReal), intent(inout) :: &
temperature_bc
real(pReal), dimension(3,3,3,3) :: &
S !< current average compliance
real(pReal), dimension(3,3) :: &
F_aim_lastIter, & !< aim of last iteration
P_av
real(pReal), dimension(3,3,res(1),res(2),res(3)) :: P
!--------------------------------------------------------------------------------------------------
! 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
!--------------------------------------------------------------------------------------------------
! write restart information for spectral solver
if (restartWrite) then
write(6,'(/,a)') ' writing converged results for restart'
flush(6)
call IO_write_jobBinaryFile(777,'F',size(F)) ! writing deformation gradient field to file
write (777,rec=1) F
close (777)
call IO_write_jobBinaryFile(777,'F_lastInc',size(F_lastInc)) ! writing F_lastInc field to file
write (777,rec=1) F_lastInc
close (777)
call IO_write_jobBinaryFile(777,'F_aimDot',size(f_aimDot))
write (777,rec=1) f_aimDot
close(777)
call IO_write_jobBinaryFile(777,'C',size(C))
write (777,rec=1) C
close(777)
call IO_write_jobBinaryFile(777,'C_lastInc',size(C_lastInc))
write (777,rec=1) C_lastInc
close(777)
endif
!--------------------------------------------------------------------------------------------------
! forward data
if (cutBack) then
F_aim = F_aim_lastInc
F = F_lastInc
C = C_lastInc
else
C_lastInc = C
mesh_ipCoordinates = reshape(mesh_deformedCoordsFFT(geomdim,F),[3,1,mesh_NcpElems])
!--------------------------------------------------------------------------------------------------
! 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
if (guess) f_aimDot = f_aimDot + P_BC%maskFloat * (F_aim - F_aim_lastInc)/timeinc_old
F_aim_lastInc = F_aim
!--------------------------------------------------------------------------------------------------
! update rate and forward last inc
Fdot = utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
timeinc_old,guess,F_lastInc,F)
F_lastInc = F
endif
F_aim = F_aim + f_aimDot * timeinc
F = Utilities_forwardField(timeinc,F_lastInc,Fdot,math_rotate_backward33(F_aim,rotation_BC))
!--------------------------------------------------------------------------------------------------
! update stiffness (and gamma operator)
S = Utilities_maskedCompliance(rotation_BC,P_BC%maskLogical,C)
if (update_gamma) call Utilities_updateGamma(C,restartWrite)
!--------------------------------------------------------------------------------------------------
! iteration till converged
if (.not. restartRead) ForwardData = .True.
iter = 0_pInt
basic_solution%iterationsNeeded = itmax
convergenceLoop: do while(iter < itmax)
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
! report begin of new iteration
write(6,'(1x,a,3(a,'//IO_intOut(itmax)//'))') trim(incInfo), &
' @ Iteration ', itmin, '≤',iter, '≤', itmax
if (debugRotation) &
write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') ' deformation gradient aim (lab)=', &
math_transpose33(math_rotate_backward33(F_aim,rotation_BC))
write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') ' deformation gradient aim =', &
math_transpose33(F_aim)
flush(6)
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
F_aim_lastIter = F_aim
basic_solution%termIll = .false.
call Utilities_constitutiveResponse(F_lastInc,F,temperature_bc,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
!--------------------------------------------------------------------------------------------------
! 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(math_rotate_backward33(F_aim_lastIter-F_aim,rotation_BC))
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)') ' =========================================================================='
flush(6)
if ((basic_solution%converged .and. iter >= itmin) .or. basic_solution%termIll) then
basic_solution%iterationsNeeded = iter
exit
endif
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,f8.2,a,es11.5,a,es11.4,a)') ' error divergence = ', &
err_div/pAvgDivL2/err_div_tol, ' (',err_div/pAvgDivL2,' / m, tol =',err_div_tol,')'
write(6,'(a,f8.2,a,es11.5,a,es11.4,a)') ' error stress BC = ', &
err_stress/err_stress_tol, ' (',err_stress, ' Pa , tol =',err_stress_tol,')'
flush(6)
end function basic_Converged
!--------------------------------------------------------------------------------------------------
!> @brief does the cleaning up after the simulation has finished
!--------------------------------------------------------------------------------------------------
subroutine basic_destroy()
use DAMASK_spectral_Utilities, only: &
Utilities_destroy
implicit none
call Utilities_destroy()
end subroutine basic_destroy
end module DAMASK_spectral_SolverBasic
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