!--------------------------------------------------------------------------------------------------
!> @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 Grid solver for mechanics: Spectral basic
!--------------------------------------------------------------------------------------------------
module grid_mechanical_spectral_basic
#include <petsc/finclude/petscsnes.h>
#include <petsc/finclude/petscdmda.h>
use PETScdmda
use PETScsnes
use prec
use parallelization
use DAMASK_interface
use IO
use HDF5_utilities
use math
use rotations
use spectral_utilities
use config
use homogenization
use discretization_grid
implicit none
private
type(tSolutionParams) :: params
type :: tNumerics
logical :: update_gamma !< update gamma operator with current stiffness
integer :: &
itmin, & !< minimum number of iterations
itmax !< maximum number of iterations
real(pReal) :: &
eps_div_atol, & !< absolute tolerance for equilibrium
eps_div_rtol, & !< relative tolerance for equilibrium
eps_stress_atol, & !< absolute tolerance for fullfillment of stress BC
eps_stress_rtol !< relative tolerance for fullfillment of stress BC
end type tNumerics
type(tNumerics) :: num ! numerics parameters. Better name?
logical :: debugRotation
!--------------------------------------------------------------------------------------------------
! PETSc data
DM :: da
SNES :: snes
Vec :: solution_vec
!--------------------------------------------------------------------------------------------------
! common pointwise data
real(pReal), dimension(:,:,:,:,:), allocatable :: &
F_lastInc, & !< field of previous compatible deformation gradients
Fdot !< field of assumed rate of compatible deformation gradient
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
real(pReal), dimension(3,3) :: &
F_aimDot = 0.0_pReal, & !< assumed rate of average deformation gradient
F_aim = math_I3, & !< current prescribed deformation gradient
F_aim_lastInc = math_I3, & !< previous average deformation gradient
P_av = 0.0_pReal, & !< average 1st Piola--Kirchhoff stress
P_aim = 0.0_pReal
character(len=:), allocatable :: incInfo !< time and increment information
real(pReal), dimension(3,3,3,3) :: &
C_volAvg = 0.0_pReal, & !< current volume average stiffness
C_volAvgLastInc = 0.0_pReal, & !< previous volume average stiffness
C_minMaxAvg = 0.0_pReal, & !< current (min+max)/2 stiffness
C_minMaxAvgLastInc = 0.0_pReal, & !< previous (min+max)/2 stiffness
S = 0.0_pReal !< current compliance (filled up with zeros)
real(pReal) :: &
err_BC, & !< deviation from stress BC
err_div !< RMS of div of P
integer :: &
totalIter = 0 !< total iteration in current increment
public :: &
grid_mechanical_spectral_basic_init, &
grid_mechanical_spectral_basic_solution, &
grid_mechanical_spectral_basic_forward, &
grid_mechanical_spectral_basic_updateCoords, &
grid_mechanical_spectral_basic_restartWrite
contains
!--------------------------------------------------------------------------------------------------
!> @brief allocates all necessary fields and fills them with data, potentially from restart info
!--------------------------------------------------------------------------------------------------
subroutine grid_mechanical_spectral_basic_init
real(pReal), dimension(3,3,grid(1),grid(2),grid3) :: P
PetscErrorCode :: ierr
PetscScalar, pointer, dimension(:,:,:,:) :: &
F ! pointer to solution data
PetscInt, dimension(0:worldsize-1) :: localK
integer(HID_T) :: fileHandle, groupHandle
integer :: fileUnit
class (tNode), pointer :: &
num_grid, &
debug_grid
print'(/,a)', ' <<<+- grid_mechanical_spectral_basic init -+>>>'; flush(IO_STDOUT)
print*, 'P. Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013'
print*, 'https://doi.org/10.1016/j.ijplas.2012.09.012'//IO_EOL
print*, 'P. Shanthraj et al., International Journal of Plasticity 66:31–45, 2015'
print*, 'https://doi.org/10.1016/j.ijplas.2014.02.006'
!-------------------------------------------------------------------------------------------------
! debugging options
debug_grid => config_debug%get('grid',defaultVal=emptyList)
debugRotation = debug_grid%contains('rotation')
!-------------------------------------------------------------------------------------------------
! read numerical parameters and do sanity checks
num_grid => config_numerics%get('grid',defaultVal=emptyDict)
num%update_gamma = num_grid%get_asBool ('update_gamma', defaultVal=.false.)
num%eps_div_atol = num_grid%get_asFloat('eps_div_atol', defaultVal=1.0e-4_pReal)
num%eps_div_rtol = num_grid%get_asFloat('eps_div_rtol', defaultVal=5.0e-4_pReal)
num%eps_stress_atol = num_grid%get_asFloat('eps_stress_atol',defaultVal=1.0e3_pReal)
num%eps_stress_rtol = num_grid%get_asFloat('eps_stress_rtol',defaultVal=1.0e-3_pReal)
num%itmin = num_grid%get_asInt ('itmin',defaultVal=1)
num%itmax = num_grid%get_asInt ('itmax',defaultVal=250)
if (num%eps_div_atol <= 0.0_pReal) call IO_error(301,ext_msg='eps_div_atol')
if (num%eps_div_rtol < 0.0_pReal) call IO_error(301,ext_msg='eps_div_rtol')
if (num%eps_stress_atol <= 0.0_pReal) call IO_error(301,ext_msg='eps_stress_atol')
if (num%eps_stress_rtol < 0.0_pReal) call IO_error(301,ext_msg='eps_stress_rtol')
if (num%itmax <= 1) call IO_error(301,ext_msg='itmax')
if (num%itmin > num%itmax .or. num%itmin < 1) call IO_error(301,ext_msg='itmin')
!--------------------------------------------------------------------------------------------------
! set default and user defined options for PETSc
call PetscOptionsInsertString(PETSC_NULL_OPTIONS,'-mechanical_snes_type ngmres',ierr)
CHKERRQ(ierr)
call PetscOptionsInsertString(PETSC_NULL_OPTIONS,num_grid%get_asString('petsc_options',defaultVal=''),ierr)
CHKERRQ(ierr)
!--------------------------------------------------------------------------------------------------
! allocate global fields
allocate(F_lastInc(3,3,grid(1),grid(2),grid3),source = 0.0_pReal)
allocate(Fdot (3,3,grid(1),grid(2),grid3),source = 0.0_pReal)
!--------------------------------------------------------------------------------------------------
! initialize solver specific parts of PETSc
call SNESCreate(PETSC_COMM_WORLD,snes,ierr); CHKERRQ(ierr)
call SNESSetOptionsPrefix(snes,'mechanical_',ierr);CHKERRQ(ierr)
localK = 0
localK(worldrank) = grid3
call MPI_Allreduce(MPI_IN_PLACE,localK,worldsize,MPI_INTEGER,MPI_SUM,PETSC_COMM_WORLD,ierr)
call DMDACreate3d(PETSC_COMM_WORLD, &
DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE, & ! cut off stencil at boundary
DMDA_STENCIL_BOX, & ! Moore (26) neighborhood around central point
grid(1),grid(2),grid(3), & ! global grid
1 , 1, worldsize, &
9, 0, & ! #dof (F tensor), ghost boundary width (domain overlap)
[grid(1)],[grid(2)],localK, & ! local grid
da,ierr) ! handle, error
CHKERRQ(ierr)
call SNESSetDM(snes,da,ierr); CHKERRQ(ierr) ! connect snes to da
call DMsetFromOptions(da,ierr); CHKERRQ(ierr)
call DMsetUp(da,ierr); CHKERRQ(ierr)
call DMcreateGlobalVector(da,solution_vec,ierr); CHKERRQ(ierr) ! global solution vector (grid x 9, i.e. every def grad tensor)
call DMDASNESsetFunctionLocal(da,INSERT_VALUES,formResidual,PETSC_NULL_SNES,ierr) ! residual vector of same shape as solution vector
CHKERRQ(ierr)
call SNESsetConvergenceTest(snes,converged,PETSC_NULL_SNES,PETSC_NULL_FUNCTION,ierr) ! specify custom convergence check function "converged"
CHKERRQ(ierr)
call SNESsetFromOptions(snes,ierr); CHKERRQ(ierr) ! pull it all together with additional CLI arguments
!--------------------------------------------------------------------------------------------------
! init fields
call DMDAVecGetArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr) ! places pointer on PETSc data
restartRead: if (interface_restartInc > 0) then
print'(/,a,i0,a)', ' reading restart data of increment ', interface_restartInc, ' from file'
fileHandle = HDF5_openFile(getSolverJobName()//'_restart.hdf5','r')
groupHandle = HDF5_openGroup(fileHandle,'solver')
call HDF5_read(P_aim,groupHandle,'P_aim',.false.)
call MPI_Bcast(P_aim,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_read(F_aim,groupHandle,'F_aim',.false.)
call MPI_Bcast(F_aim,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_read(F_aim_lastInc,groupHandle,'F_aim_lastInc',.false.)
call MPI_Bcast(F_aim_lastInc,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_read(F_aimDot,groupHandle,'F_aimDot',.false.)
call MPI_Bcast(F_aimDot,9,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_read(F,groupHandle,'F')
call HDF5_read(F_lastInc,groupHandle,'F_lastInc')
elseif (interface_restartInc == 0) then restartRead
F_lastInc = spread(spread(spread(math_I3,3,grid(1)),4,grid(2)),5,grid3) ! initialize to identity
F = reshape(F_lastInc,[9,grid(1),grid(2),grid3])
endif restartRead
homogenization_F0 = reshape(F_lastInc, [3,3,product(grid(1:2))*grid3]) ! set starting condition for materialpoint_stressAndItsTangent
call utilities_updateCoords(reshape(F,shape(F_lastInc)))
call utilities_constitutiveResponse(P,P_av,C_volAvg,C_minMaxAvg, & ! stress field, stress avg, global average of stiffness and (min+max)/2
reshape(F,shape(F_lastInc)), & ! target F
0.0_pReal) ! time increment
call DMDAVecRestoreArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr) ! deassociate pointer
restartRead2: if (interface_restartInc > 0) then
print'(a,i0,a)', ' reading more restart data of increment ', interface_restartInc, ' from file'
call HDF5_read(C_volAvg,groupHandle,'C_volAvg',.false.)
call MPI_Bcast(C_volAvg,81,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_read(C_volAvgLastInc,groupHandle,'C_volAvgLastInc',.false.)
call MPI_Bcast(C_volAvgLastInc,81,MPI_DOUBLE,0,PETSC_COMM_WORLD,ierr)
if(ierr /=0) error stop 'MPI error'
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
call MPI_File_open(PETSC_COMM_WORLD, trim(getSolverJobName())//'.C_ref', &
MPI_MODE_RDONLY,MPI_INFO_NULL,fileUnit,ierr)
call MPI_File_read(fileUnit,C_minMaxAvg,81,MPI_DOUBLE,MPI_STATUS_IGNORE,ierr)
call MPI_File_close(fileUnit,ierr)
endif restartRead2
call utilities_updateGamma(C_minMaxAvg)
call utilities_saveReferenceStiffness
end subroutine grid_mechanical_spectral_basic_init
!--------------------------------------------------------------------------------------------------
!> @brief solution for the basic scheme with internal iterations
!--------------------------------------------------------------------------------------------------
function grid_mechanical_spectral_basic_solution(incInfoIn) result(solution)
!--------------------------------------------------------------------------------------------------
! input data for solution
character(len=*), intent(in) :: &
incInfoIn
type(tSolutionState) :: &
solution
!--------------------------------------------------------------------------------------------------
! PETSc Data
PetscErrorCode :: ierr
SNESConvergedReason :: reason
incInfo = incInfoIn
!--------------------------------------------------------------------------------------------------
! update stiffness (and gamma operator)
S = utilities_maskedCompliance(params%rotation_BC,params%stress_mask,C_volAvg)
if(num%update_gamma) call utilities_updateGamma(C_minMaxAvg)
!--------------------------------------------------------------------------------------------------
! solve BVP
call SNESsolve(snes,PETSC_NULL_VEC,solution_vec,ierr); CHKERRQ(ierr)
!--------------------------------------------------------------------------------------------------
! check convergence
call SNESGetConvergedReason(snes,reason,ierr); CHKERRQ(ierr)
solution%converged = reason > 0
solution%iterationsNeeded = totalIter
solution%termIll = terminallyIll
terminallyIll = .false.
P_aim = merge(P_aim,P_av,params%stress_mask)
end function grid_mechanical_spectral_basic_solution
!--------------------------------------------------------------------------------------------------
!> @brief forwarding routine
!> @details find new boundary conditions and best F estimate for end of current timestep
!--------------------------------------------------------------------------------------------------
subroutine grid_mechanical_spectral_basic_forward(cutBack,guess,Delta_t,Delta_t_old,t_remaining,&
deformation_BC,stress_BC,rotation_BC)
logical, intent(in) :: &
cutBack, &
guess
real(pReal), intent(in) :: &
Delta_t_old, &
Delta_t, &
t_remaining !< remaining time of current load case
type(tBoundaryCondition), intent(in) :: &
stress_BC, &
deformation_BC
type(rotation), intent(in) :: &
rotation_BC
PetscErrorCode :: ierr
PetscScalar, pointer, dimension(:,:,:,:) :: F
call DMDAVecGetArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
if (cutBack) then
C_volAvg = C_volAvgLastInc
C_minMaxAvg = C_minMaxAvgLastInc
else
C_volAvgLastInc = C_volAvg
C_minMaxAvgLastInc = C_minMaxAvg
F_aimDot = merge(merge((F_aim-F_aim_lastInc)/Delta_t_old,0.0_pReal,stress_BC%mask), 0.0_pReal, guess) ! estimate deformation rate for prescribed stress components
F_aim_lastInc = F_aim
!-----------------------------------------------------------------------------------------------
! calculate rate for aim
if (deformation_BC%myType=='L') then ! calculate F_aimDot from given L and current F
F_aimDot = F_aimDot &
+ merge(matmul(deformation_BC%values, F_aim_lastInc),.0_pReal,deformation_BC%mask)
elseif (deformation_BC%myType=='dot_F') then ! F_aimDot is prescribed
F_aimDot = F_aimDot &
+ merge(deformation_BC%values,.0_pReal,deformation_BC%mask)
elseif (deformation_BC%myType=='F') then ! aim at end of load case is prescribed
F_aimDot = F_aimDot &
+ merge((deformation_BC%values - F_aim_lastInc)/t_remaining,.0_pReal,deformation_BC%mask)
endif
Fdot = utilities_calculateRate(guess, &
F_lastInc,reshape(F,[3,3,grid(1),grid(2),grid3]),Delta_t_old, &
rotation_BC%rotate(F_aimDot,active=.true.))
F_lastInc = reshape(F,[3,3,grid(1),grid(2),grid3])
homogenization_F0 = reshape(F,[3,3,product(grid(1:2))*grid3])
endif
!--------------------------------------------------------------------------------------------------
! update average and local deformation gradients
F_aim = F_aim_lastInc + F_aimDot * Delta_t
if (stress_BC%myType=='P') P_aim = P_aim &
+ merge((stress_BC%values - P_aim)/t_remaining,0.0_pReal,stress_BC%mask)*Delta_t
if (stress_BC%myType=='dot_P') P_aim = P_aim &
+ merge(stress_BC%values,0.0_pReal,stress_BC%mask)*Delta_t
F = reshape(utilities_forwardField(Delta_t,F_lastInc,Fdot, & ! estimate of F at end of time+Delta_t that matches rotated F_aim on average
rotation_BC%rotate(F_aim,active=.true.)),[9,grid(1),grid(2),grid3])
call DMDAVecRestoreArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
!--------------------------------------------------------------------------------------------------
! set module wide available data
params%stress_mask = stress_BC%mask
params%rotation_BC = rotation_BC
params%timeinc = Delta_t
end subroutine grid_mechanical_spectral_basic_forward
!--------------------------------------------------------------------------------------------------
!> @brief Update coordinates
!--------------------------------------------------------------------------------------------------
subroutine grid_mechanical_spectral_basic_updateCoords
PetscErrorCode :: ierr
PetscScalar, dimension(:,:,:,:), pointer :: F
call DMDAVecGetArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
call utilities_updateCoords(F)
call DMDAVecRestoreArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
end subroutine grid_mechanical_spectral_basic_updateCoords
!--------------------------------------------------------------------------------------------------
!> @brief Write current solver and constitutive data for restart to file
!--------------------------------------------------------------------------------------------------
subroutine grid_mechanical_spectral_basic_restartWrite
PetscErrorCode :: ierr
integer(HID_T) :: fileHandle, groupHandle
PetscScalar, dimension(:,:,:,:), pointer :: F
call DMDAVecGetArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
print*, 'writing solver data required for restart to file'; flush(IO_STDOUT)
fileHandle = HDF5_openFile(getSolverJobName()//'_restart.hdf5','w')
groupHandle = HDF5_addGroup(fileHandle,'solver')
call HDF5_write(P_aim,groupHandle,'P_aim',.false.)
call HDF5_write(F_aim,groupHandle,'F_aim',.false.)
call HDF5_write(F_aim_lastInc,groupHandle,'F_aim_lastInc',.false.)
call HDF5_write(F_aimDot,groupHandle,'F_aimDot',.false.)
call HDF5_write(F,groupHandle,'F')
call HDF5_write(F_lastInc,groupHandle,'F_lastInc')
call HDF5_write(C_volAvg,groupHandle,'C_volAvg',.false.)
call HDF5_write(C_volAvgLastInc,groupHandle,'C_volAvgLastInc',.false.)
call HDF5_write(C_minMaxAvg,groupHandle,'C_minMaxAvg',.false.)
call HDF5_closeGroup(groupHandle)
call HDF5_closeFile(fileHandle)
if (num%update_gamma) call utilities_saveReferenceStiffness
call DMDAVecRestoreArrayF90(da,solution_vec,F,ierr); CHKERRQ(ierr)
end subroutine grid_mechanical_spectral_basic_restartWrite
!--------------------------------------------------------------------------------------------------
!> @brief convergence check
!--------------------------------------------------------------------------------------------------
subroutine converged(snes_local,PETScIter,devNull1,devNull2,devNull3,reason,dummy,ierr)
SNES :: snes_local
PetscInt, intent(in) :: PETScIter
PetscReal, intent(in) :: &
devNull1, &
devNull2, &
devNull3
SNESConvergedReason :: reason
PetscObject :: dummy
PetscErrorCode :: ierr
real(pReal) :: &
divTol, &
BCTol
divTol = max(maxval(abs(P_av))*num%eps_div_rtol ,num%eps_div_atol)
BCTol = max(maxval(abs(P_av))*num%eps_stress_rtol,num%eps_stress_atol)
if ((totalIter >= num%itmin .and. all([err_div/divTol, err_BC/BCTol] < 1.0_pReal)) &
.or. terminallyIll) then
reason = 1
elseif (totalIter >= num%itmax) then
reason = -1
else
reason = 0
endif
!--------------------------------------------------------------------------------------------------
! report
print'(1/,a)', ' ... reporting .............................................................'
print'(1/,a,f12.2,a,es8.2,a,es9.2,a)', ' error divergence = ', &
err_div/divTol, ' (',err_div,' / m, tol = ',divTol,')'
print'(a,f12.2,a,es8.2,a,es9.2,a)', ' error stress BC = ', &
err_BC/BCTol, ' (',err_BC, ' Pa, tol = ',BCTol,')'
print'(/,a)', ' ==========================================================================='
flush(IO_STDOUT)
end subroutine converged
!--------------------------------------------------------------------------------------------------
!> @brief forms the residual vector
!--------------------------------------------------------------------------------------------------
subroutine formResidual(in, F, &
residuum, dummy, ierr)
DMDALocalInfo, dimension(DMDA_LOCAL_INFO_SIZE) :: in !< DMDA info (needs to be named "in" for macros like XRANGE to work)
PetscScalar, dimension(3,3,XG_RANGE,YG_RANGE,ZG_RANGE), &
intent(in) :: F !< deformation gradient field
PetscScalar, dimension(3,3,X_RANGE,Y_RANGE,Z_RANGE), &
intent(out) :: residuum !< residuum field
real(pReal), dimension(3,3) :: &
deltaF_aim
PetscInt :: &
PETScIter, &
nfuncs
PetscObject :: dummy
PetscErrorCode :: ierr
call SNESGetNumberFunctionEvals(snes,nfuncs,ierr); CHKERRQ(ierr)
call SNESGetIterationNumber(snes,PETScIter,ierr); CHKERRQ(ierr)
if (nfuncs == 0 .and. PETScIter == 0) totalIter = -1 ! new increment
!--------------------------------------------------------------------------------------------------
! begin of new iteration
newIteration: if (totalIter <= PETScIter) then
totalIter = totalIter + 1
print'(1x,a,3(a,i0))', trim(incInfo), ' @ Iteration ', num%itmin, '≤',totalIter, '≤', num%itmax
if (debugRotation) print'(/,a,/,2(3(f12.7,1x)/),3(f12.7,1x))', &
' deformation gradient aim (lab) =', transpose(params%rotation_BC%rotate(F_aim,active=.true.))
print'(/,a,/,2(3(f12.7,1x)/),3(f12.7,1x))', &
' deformation gradient aim =', transpose(F_aim)
flush(IO_STDOUT)
endif newIteration
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
call utilities_constitutiveResponse(residuum, & ! "residuum" gets field of first PK stress (to save memory)
P_av,C_volAvg,C_minMaxAvg, &
F,params%timeinc,params%rotation_BC)
call MPI_Allreduce(MPI_IN_PLACE,terminallyIll,1,MPI_LOGICAL,MPI_LOR,PETSC_COMM_WORLD,ierr)
!--------------------------------------------------------------------------------------------------
! stress BC handling
deltaF_aim = math_mul3333xx33(S, P_av - P_aim) ! S = 0.0 for no bc
F_aim = F_aim - deltaF_aim
err_BC = maxval(abs(merge(P_av - P_aim,.0_pReal,params%stress_mask)))
!--------------------------------------------------------------------------------------------------
! updated deformation gradient using fix point algorithm of basic scheme
tensorField_real = 0.0_pReal
tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) = residuum ! store fPK field for subsequent FFT forward transform
call utilities_FFTtensorForward ! FFT forward of global "tensorField_real"
err_div = utilities_divergenceRMS() ! divRMS of tensorField_fourier for later use
call utilities_fourierGammaConvolution(params%rotation_BC%rotate(deltaF_aim,active=.true.)) ! convolution of Gamma and tensorField_fourier
call utilities_FFTtensorBackward ! FFT backward of global tensorField_fourier
!--------------------------------------------------------------------------------------------------
! constructing residual
residuum = tensorField_real(1:3,1:3,1:grid(1),1:grid(2),1:grid3) ! Gamma*P gives correction towards div(P) = 0, so needs to be zero, too
end subroutine formResidual
end module grid_mechanical_spectral_basic