grid_mech_spectral_basic.f90

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# 1 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/grid/grid_mech_spectral_basic.f90"
# 1 "<built-in>"
# 1 "<command-line>"
# 1 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/grid/grid_mech_spectral_basic.f90"
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
module grid_mech_spectral_basic
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscsnes.h" 1
!
!  Include file for Fortran use of the SNES package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscksp.h" 1
!
!
!  Include file for Fortran use of the KSP package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscpc.h" 1
!
!
!  Include file for Fortran use of the PC (preconditioner) package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h" 1
!
!
!  Include file for Fortran use of the Mat package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscvec.h" 1
!
!
!  Include file for Fortran use of the Vec package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscao.h" 1
!
!
!  Include file for Fortran use of the AO (application ordering) package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscis.h" 1
!
!
!  Include file for Fortran use of the IS (index set) package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 1
!
!
!  Part of the base include file for Fortran use of 1.
!  Note: This file should contain only define statements and
!  not the declaration of variables.
 
! No spaces for #defines as some compilers (PGI) also adds
! those additional spaces during preprocessing - bad for fixed format
!
 
 
 
# 1 "/opt/petsc-3.10.3/Intel-18.4-IntelMPI-2018/include/petscconf.h" 1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
# 13 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petscversion.h" 1
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
# 17 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscviewer.h" 1
!
!  Include file for Fortran use of the PetscViewer package in 1
!
 
 
 
 
 
 
 
 
 
 
 
 
 
# 31 "/opt/petsc-3.10.3/include/petsc/finclude/petscviewer.h"
 
# 18 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscerror.h" 1
 
!
!  Include file for Fortran error codes
!    These are also in include/petscerror.h
!
 
 
 
# 24 "/opt/petsc-3.10.3/include/petsc/finclude/petscerror.h"
 
# 38 "/opt/petsc-3.10.3/include/petsc/finclude/petscerror.h"
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
# 19 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petsclog.h" 1
!
!  No includes needed for logging
# 20 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscbag.h" 1
!
!
!  Include file for Fortran use of the Bag package in 1
!
 
 
 
 
 
!
!  End of Fortran include file for the IS package in 1
 
# 21 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h" 2
 
!
! The real*8,complex*16 notatiton is used so that the
! 1 double/complex variables are not affected by
! compiler options like -r4,-r8, sometimes invoked
! by the user. NAG compiler does not like integer*4,real*8
 
# 41 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
 
 
 
 
 
 
 
 
 
# 63 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
 
 
 
 
 
 
!
 
 
 
 
 
!
# 85 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
!
 
 
 
 
 
 
!
 
 
 
 
!
 
!
 
 
!
# 128 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
 
# 150 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
!
!     Macro for templating between real and complex
!
# 174 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
 
 
 
 
 
 
 
 
 
!
!    Allows the matrix Fortran Kernels to work with single precision
!    matrix data structures
!
 
!
!     PetscLogDouble variables are used to contain double precision numbers
!     that are not used in the numerical computations, but rather in logging,
!     timing etc.
!
 
 
!
!     Macros for error checking
!
 
 
 
 
 
 
 
 
# 215 "/opt/petsc-3.10.3/include/petsc/finclude/petscsys.h"
 
 
 
 
 
 
 
 
 
 
 
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscis.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscviewer.h" 1
!
!  Include file for Fortran use of the type(tPetscViewer) package in 1
!
# 10 "/opt/petsc-3.10.3/include/petsc/finclude/petscis.h" 2
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscao.h" 2
 
 
 
 
 
 
 
 
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscvec.h" 2
 
 
 
 
 
 
 
 
 
 
 
 
 
# 30 "/opt/petsc-3.10.3/include/petsc/finclude/petscvec.h"
 
 
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h" 2
 
 
 
 
 
# 49 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h"
 
 
 
 
 
 
 
 
 
 
 
 
 
# 71 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h"
!
!  Matrix types
!
# 115 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h"
 
# 140 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h"
 
!
! MatMFFDType values
!
 
 
 
!
! MatSolverTypes
!
# 168 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h"
 
!
! GPU Storage Formats for CUSPARSE
!
 
 
 
!
! sparsity reducing ordering for STRUMPACK
!
 
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscpc.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h" 1
 
!
!  Include file for Fortran use of the DM package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscis.h" 1
!
!
!  Include file for Fortran use of the type(tIS) (index set) package in 1
!
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscvec.h" 1
!
!
!  Include file for Fortran use of the type(tVec) package in 1
!
# 10 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h" 1
!
!
!  Include file for Fortran use of the type(tMat) package in 1
!
# 11 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h" 2
 
 
 
 
 
 
 
 
 
 
 
# 32 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h"
 
 
# 47 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h"
 
# 10 "/opt/petsc-3.10.3/include/petsc/finclude/petscpc.h" 2
 
 
 
# 26 "/opt/petsc-3.10.3/include/petsc/finclude/petscpc.h"
!
! GAMG types
!
 
 
!
!  Various preconditioners
!
# 74 "/opt/petsc-3.10.3/include/petsc/finclude/petscpc.h"
 
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscksp.h" 2
 
 
 
 
# 21 "/opt/petsc-3.10.3/include/petsc/finclude/petscksp.h"
!
!  Various Krylov subspace methods
!
# 57 "/opt/petsc-3.10.3/include/petsc/finclude/petscksp.h"
!
!  Various Initial guesses for Krylov subspace methods
!
# 8 "/opt/petsc-3.10.3/include/petsc/finclude/petscsnes.h" 2
 
 
 
 
 
# 30 "/opt/petsc-3.10.3/include/petsc/finclude/petscsnes.h"
 
!
!  character*(80)
!
# 47 "/opt/petsc-3.10.3/include/petsc/finclude/petscsnes.h"
 
!
! character*(80)
!
 
 
 
 
 
 
 
!
! integer(kind=selected_int_kind(5))
!
 
 
 
 
 
 
!
!  character*(80)
!
# 78 "/opt/petsc-3.10.3/include/petsc/finclude/petscsnes.h"
 
 
 
# 9 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/grid/grid_mech_spectral_basic.f90" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h" 1
 
!
!  Include file for Fortran use of the 'da' (distributed array) package in 1
!
 
 
 
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscis.h" 1
!
!
!  Include file for Fortran use of the type(tIS) (index set) package in 1
!
# 9 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscvec.h" 1
!
!
!  Include file for Fortran use of the type(tVec) package in 1
!
# 10 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscmat.h" 1
!
!
!  Include file for Fortran use of the type(tMat) package in 1
!
# 11 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h" 2
 
# 1 "/opt/petsc-3.10.3/include/petsc/finclude/petscdm.h" 1
 
!
!  Include file for Fortran use of the type(tDM) package in 1
!
# 12 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h" 2
 
 
 
 
 
!
!   DMDA_LOCAL_INFO_SIZE is one large than the size incase the DA is larger than an integer (on 64 bit systems).
!   non-int fields are not accessiable from fortran.
!
# 39 "/opt/petsc-3.10.3/include/petsc/finclude/petscdmda.h"
 
 
 
 
 
 
 
 
 
 
 
 
 
# 10 "/home/damask_user/GitLabCI_Pipeline_4301/DAMASK/src/grid/grid_mech_spectral_basic.f90" 2
  use petscdmda
  use petscsnes
 
  use prec
  use damask_interface
  use hdf5_utilities
  use math
  use spectral_utilities
  use fesolving
  use config
  use numerics
  use homogenization
  use discretization_grid
  use debug
 
  implicit none
  private
 
!--------------------------------------------------------------------------------------------------
! derived types
  type(tsolutionparams), private :: params
 
  type, private :: tnumerics
    logical :: update_gamma
  end type tnumerics
 
  type(tnumerics) :: num                                                                            ! numerics parameters. Better name?
 
!--------------------------------------------------------------------------------------------------
! 1 data
  type(tdm),   private :: da
  type(tsnes), private :: snes
  type(tvec),  private :: solution_vec
 
!--------------------------------------------------------------------------------------------------
! common pointwise data
  real(preal), private, dimension(:,:,:,:,:), allocatable ::  &
    f_lastinc, &                                                                                    !< field of previous compatible deformation gradients
    fdot
 
!--------------------------------------------------------------------------------------------------
! stress, stiffness and compliance average etc.
  real(preal), private, dimension(3,3) :: &
    f_aimdot = 0.0_preal, &                                                                         
    f_aim = math_i3, &                                                                              
    f_aim_lastinc = math_i3, &                                                                      
    p_av = 0.0_preal                                                                                
 
  character(len=pStringLen), private :: incinfo
  real(preal), private, dimension(3,3,3,3) :: &
    c_volavg = 0.0_preal, &                                                                         
    c_volavglastinc = 0.0_preal, &                                                                  
    c_minmaxavg = 0.0_preal, &                                                                      
    c_minmaxavglastinc = 0.0_preal, &                                                               
    s = 0.0_preal                                                                                   
 
  real(preal), private :: &
    err_bc, &                                                                                       !< deviation from stress BC
    err_div
 
  integer, private :: &
    totaliter = 0
 
  public :: &
    grid_mech_spectral_basic_init, &
    grid_mech_spectral_basic_solution, &
    grid_mech_spectral_basic_forward, &
    grid_mech_spectral_basic_updatecoords, &
    grid_mech_spectral_basic_restartwrite
 
contains
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine grid_mech_spectral_basic_init
 
  real(preal), dimension(3,3,grid(1),grid(2),grid3) :: p
  real(preal), dimension(3,3) :: &
    temp33_real = 0.0_preal
 
  integer(kind=selected_int_kind(5)) :: ierr
  real(kind=selected_real_kind(10)), pointer, dimension(:,:,:,:) :: &
    f                                                                                               ! pointer to solution data
  integer(kind=selected_int_kind(5)), dimension(worldsize) :: localk
  integer(HID_T) :: filehandle, grouphandle
  integer        :: fileunit
  character(len=pStringLen) :: filename
 
  write(6,'(/,a)') ' <<<+-  grid_mech_spectral_basic init  -+>>>'; flush(6)
 
  write(6,'(/,a)') ' Eisenlohr et al., International Journal of Plasticity 46:37–53, 2013'
  write(6,'(a)')   ' https://doi.org/10.1016/j.ijplas.2012.09.012'
 
  write(6,'(/,a)') ' Shanthraj et al., International Journal of Plasticity 66:31–45, 2015'
  write(6,'(a)')   ' https://doi.org/10.1016/j.ijplas.2014.02.006'
 
  num%update_gamma = config_numerics%getInt('update_gamma',defaultval=0) > 0
 
!--------------------------------------------------------------------------------------------------
! set default and user defined options for 1
  call petscoptionsinsertstring(petsc_null_options,'-mech_snes_type ngmres',ierr)
  if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call petscoptionsinsertstring(petsc_null_options,trim(petsc_options),ierr)
  if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
!--------------------------------------------------------------------------------------------------
! 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 1
  call snescreate(petsc_comm_world,snes,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call snessetoptionsprefix(snes,'mech_',ierr);if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  localk              = 0
  localk(worldrank+1) = 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
  if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call snessetdm(snes,da,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif                                                       ! connect snes to da
  call dmsetfromoptions(da,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call dmsetup(da,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call dmcreateglobalvector(da,solution_vec,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif                                    ! 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
  if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call snessetconvergencetest(snes,converged,petsc_null_snes,petsc_null_function,ierr)              ! specify custom convergence check function "converged"
  if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call snessetfromoptions(snes,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif                                                 ! pull it all together with additional CLI arguments
 
!--------------------------------------------------------------------------------------------------
! init fields
  call dmdavecgetarrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif                                   ! places pointer on 1 data
 
  restartread: if (interface_restartinc > 0) then
    write(6,'(/,a,i0,a)') ' reading restart data of increment ', interface_restartinc, ' from file'
 
    write(filename,'(a,a,i0,a)') trim(getsolverjobname()),'_',worldrank,'.hdf5'
    filehandle  = hdf5_openfile(filename)
    grouphandle = hdf5_opengroup(filehandle,'solver')
 
    call hdf5_read(grouphandle,f_aim,        'F_aim')
    call hdf5_read(grouphandle,f_aim_lastinc,'F_aim_lastInc')
    call hdf5_read(grouphandle,f_aimdot,     'F_aimDot')
    call hdf5_read(grouphandle,f,            'F')
    call hdf5_read(grouphandle,f_lastinc,    '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
 
  materialpoint_f0 = reshape(f_lastinc, [3,3,1,product(grid(1:2))*grid3])                           ! set starting condition for materialpoint_stressAndItsTangent
  call utilities_updatecoords(reshape(f,shape(f_lastinc)))
  call utilities_constitutiveresponse(p,temp33_real,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); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif                                ! deassociate pointer
 
  restartread2: if (interface_restartinc > 0) then
    write(6,'(/,a,i0,a)') ' reading more restart data of increment ', interface_restartinc, ' from file'
    call hdf5_read(grouphandle,c_volavg,       'C_volAvg')
    call hdf5_read(grouphandle,c_volavglastinc,'C_volAvgLastInc')
 
    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_mech_spectral_basic_init
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
function grid_mech_spectral_basic_solution(incInfoIn,timeinc,timeinc_old,stress_BC,rotation_BC) result(solution)
 
!--------------------------------------------------------------------------------------------------
! input data for solution
  character(len=*),            intent(in) :: &
    incinfoin
  real(preal),                 intent(in) :: &
    timeinc, &                                                                                      !< time increment of current solution
    timeinc_old
  type(tboundarycondition),    intent(in) :: &
    stress_bc
  type(rotation),              intent(in) :: &
    rotation_bc
  type(tsolutionstate)                    :: &
    solution
!--------------------------------------------------------------------------------------------------
! 1 Data
  integer(kind=selected_int_kind(5)) :: ierr
  integer(kind=selected_int_kind(5)) :: reason
 
  incinfo = incinfoin
 
!--------------------------------------------------------------------------------------------------
! update stiffness (and gamma operator)
  s = utilities_maskedcompliance(rotation_bc,stress_bc%maskLogical,c_volavg)
  if(num%update_gamma) call utilities_updategamma(c_minmaxavg)
 
!--------------------------------------------------------------------------------------------------
! set module wide available data
  params%stress_mask = stress_bc%maskFloat
  params%stress_BC   = stress_bc%values
  params%rotation_BC = rotation_bc
  params%timeinc     = timeinc
  params%timeincOld  = timeinc_old
 
!--------------------------------------------------------------------------------------------------
! solve BVP
  call snessolve(snes,petsc_null_vec,solution_vec,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
!--------------------------------------------------------------------------------------------------
! check convergence
  call snesgetconvergedreason(snes,reason,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
  solution%converged = reason > 0
  solution%iterationsNeeded = totaliter
  solution%termIll = terminallyill
  terminallyill = .false.
 
end function grid_mech_spectral_basic_solution
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine grid_mech_spectral_basic_forward(cutBack,guess,timeinc,timeinc_old,loadCaseTime,&
                                            deformation_BC,stress_BC,rotation_BC)
 
  logical,                     intent(in) :: &
    cutback, &
    guess
  real(preal),                 intent(in) :: &
    timeinc_old, &
    timeinc, &
    loadcasetime
  type(tboundarycondition),    intent(in) :: &
    stress_bc, &
    deformation_bc
  type(rotation),              intent(in) :: &
    rotation_bc
  integer(kind=selected_int_kind(5)) :: ierr
  real(kind=selected_real_kind(10)), dimension(:,:,:,:), pointer :: f
 
  call dmdavecgetarrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
  if (cutback) then
    c_volavg    = c_volavglastinc
    c_minmaxavg = c_minmaxavglastinc
  else
    c_volavglastinc    = c_volavg
    c_minmaxavglastinc = c_minmaxavg
 
    f_aimdot = merge(stress_bc%maskFloat*(f_aim-f_aim_lastinc)/timeinc_old, 0.0_preal, guess)
    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 + deformation_bc%maskFloat * matmul(deformation_bc%values, f_aim_lastinc)
    elseif(deformation_bc%myType=='fdot') then                                                       ! F_aimDot is prescribed
      f_aimdot = &
      f_aimdot + deformation_bc%maskFloat * deformation_bc%values
    elseif (deformation_bc%myType=='f') then                                                         ! aim at end of load case is prescribed
      f_aimdot = &
      f_aimdot + deformation_bc%maskFloat * (deformation_bc%values - f_aim_lastinc)/loadcasetime
    endif
 
    fdot = utilities_calculaterate(guess, &
                                   f_lastinc,reshape(f,[3,3,grid(1),grid(2),grid3]),timeinc_old, &
                                   rotation_bc%rotate(f_aimdot,active=.true.))
    f_lastinc = reshape(f,[3,3,grid(1),grid(2),grid3])
 
    materialpoint_f0 = reshape(f, [3,3,1,product(grid(1:2))*grid3])
  endif
 
!--------------------------------------------------------------------------------------------------
! update average and local deformation gradients
  f_aim = f_aim_lastinc + f_aimdot * timeinc
  f = reshape(utilities_forwardfield(timeinc,f_lastinc,fdot, &                                       ! estimate of F at end of time+timeinc 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); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
end subroutine grid_mech_spectral_basic_forward
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine grid_mech_spectral_basic_updatecoords
 
  integer(kind=selected_int_kind(5)) :: ierr
  real(kind=selected_real_kind(10)), dimension(:,:,:,:), pointer :: f
 
  call dmdavecgetarrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call utilities_updatecoords(f)
  call dmdavecrestorearrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
end subroutine grid_mech_spectral_basic_updatecoords
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine grid_mech_spectral_basic_restartwrite
 
  integer(kind=selected_int_kind(5)) :: ierr
  integer(HID_T) :: filehandle, grouphandle
  real(kind=selected_real_kind(10)), dimension(:,:,:,:), pointer :: f
  character(len=pStringLen) :: filename
 
  call dmdavecgetarrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
  write(6,'(a)') ' writing solver data required for restart to file'; flush(6)
 
  write(filename,'(a,a,i0,a)') trim(getsolverjobname()),'_',worldrank,'.hdf5'
  filehandle  = hdf5_openfile(filename,'w')
  grouphandle = hdf5_addgroup(filehandle,'solver')
 
  call hdf5_write(grouphandle,f_aim,        'F_aim')
  call hdf5_write(grouphandle,f_aim_lastinc,'F_aim_lastInc')
  call hdf5_write(grouphandle,f_aimdot,     'F_aimDot')
  call hdf5_write(grouphandle,f,            'F')
  call hdf5_write(grouphandle,f_lastinc,    'F_lastInc')
 
  call hdf5_write(grouphandle,c_volavg,       'C_volAvg')
  call hdf5_write(grouphandle,c_volavglastinc,'C_volAvgLastInc')
  call hdf5_write(grouphandle,c_minmaxavg,    'C_minMaxAvg')
 
  call hdf5_closegroup(grouphandle)
  call hdf5_closefile(filehandle)
 
  if (num%update_gamma) call utilities_savereferencestiffness
 
  call dmdavecrestorearrayf90(da,solution_vec,f,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
end subroutine grid_mech_spectral_basic_restartwrite
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine converged(snes_local,PETScIter,devNull1,devNull2,devNull3,reason,dummy,ierr)
 
  type(tsnes) :: snes_local
  integer(kind=selected_int_kind(5)),  intent(in) :: PETScIter
  real(kind=selected_real_kind(10)), intent(in) :: &
    devnull1, &
    devnull2, &
    devnull3
  integer(kind=selected_int_kind(5)) :: reason
  integer(kind=selected_int_kind(10)) :: dummy
  integer(kind=selected_int_kind(5)) :: ierr
  real(pReal) :: &
    divTol, &
    BCTol
 
  divtol = max(maxval(abs(p_av))*err_div_tolrel   ,err_div_tolabs)
  bctol  = max(maxval(abs(p_av))*err_stress_tolrel,err_stress_tolabs)
 
  if ((totaliter >= itmin .and. &
                            all([ err_div/divtol, &
                                  err_bc /bctol       ] < 1.0_preal)) &
              .or.    terminallyill) then
    reason = 1
  elseif (totaliter >= itmax) then
    reason = -1
  else
    reason = 0
  endif
 
!--------------------------------------------------------------------------------------------------
! report
  write(6,'(1/,a)') ' ... reporting .............................................................'
  write(6,'(1/,a,f12.2,a,es8.2,a,es9.2,a)') ' error divergence = ', &
          err_div/divtol,  ' (',err_div,' / m, tol = ',divtol,')'
  write(6,'(a,f12.2,a,es8.2,a,es9.2,a)')    ' error stress BC  = ', &
          err_bc/bctol,    ' (',err_bc, ' Pa,  tol = ',bctol,')'
  write(6,'(/,a)') ' ==========================================================================='
  flush(6)
 
end subroutine converged
 
 
!--------------------------------------------------------------------------------------------------
!--------------------------------------------------------------------------------------------------
subroutine formresidual(in, F, &
                        residuum, dummy, ierr)
 
  integer(kind=selected_int_kind(5)), dimension(25) :: in
  real(kind=selected_real_kind(10)), dimension(3,3,in(13)+1:in(13)+in(16),in(14)+1:in(14)+in(17),in(15)+1:in(15)+in(18)), &
    intent(in) :: f                                                                                 
  real(kind=selected_real_kind(10)), dimension(3,3,in(7)+1:in(7)+in(10),in(8)+1:in(8)+in(11),in(9)+1:in(9)+in(12)), &
    intent(out) :: residuum                                                                         
  real(pReal),  dimension(3,3) :: &
    deltaF_aim
  integer(kind=selected_int_kind(5)) :: &
    PETScIter, &
    nfuncs
  integer(kind=selected_int_kind(10)) :: dummy
  integer(kind=selected_int_kind(5)) :: ierr
 
  call snesgetnumberfunctionevals(snes,nfuncs,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
  call snesgetiterationnumber(snes,petsciter,ierr); if (ierr .ne. 0) then;call petscerrorf(ierr);return;endif
 
  if (nfuncs == 0 .and. petsciter == 0) totaliter = -1                                              ! new increment
!--------------------------------------------------------------------------------------------------
! begin of new iteration
  newiteration: if (totaliter <= petsciter) then
    totaliter = totaliter + 1
    write(6,'(1x,a,3(a,i0))') trim(incinfo), ' @ Iteration ', itmin, '≤',totaliter, '≤', itmax
    if (iand(debug_level(debug_spectral),debug_spectralrotation) /= 0) &
      write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') &
              ' deformation gradient aim (lab) =', transpose(params%rotation_BC%rotate(f_aim,active=.true.))
    write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') &
              ' deformation gradient aim       =', transpose(f_aim)
    flush(6)
  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 - params%stress_BC)
  f_aim = f_aim - deltaf_aim
  err_bc = maxval(abs(params%stress_mask * (p_av - params%stress_BC)))                              ! mask = 0.0 when no stress bc
 
!--------------------------------------------------------------------------------------------------
! 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_mech_spectral_basic