added Polarisation scheme as solver

code/DAMASK_spectral_driver.f90

@@ -82,6 +82,7 @@ program DAMASK_spectral_Driver
 #ifdef PETSc
  use DAMASK_spectral_SolverBasicPETSC
  use DAMASK_spectral_SolverAL
+ use DAMASK_spectral_SolverPolarisation
 #endif
 
  implicit none
@@ -337,6 +338,10 @@ program DAMASK_spectral_Driver
      if(iand(debug_level(debug_spectral),debug_levelBasic)/= 0) &
        call IO_warning(42_pInt, ext_msg='debug Divergence')
      call AL_init(loadCases(1)%temperature)
+   case (DAMASK_spectral_SolverPolarisation_label)
+     if(iand(debug_level(debug_spectral),debug_levelBasic)/= 0) &
+       call IO_warning(42_pInt, ext_msg='debug Divergence')
+     call Polarisation_init(loadCases(1)%temperature)
 #endif
    case default
       call IO_error(error_ID = 891, ext_msg = trim(myspectralsolver))
@@ -459,7 +464,6 @@ program DAMASK_spectral_Driver
                  F_BC               = loadCases(currentLoadCase)%deformation, &
                  temperature_bc     = loadCases(currentLoadCase)%temperature, &
                  rotation_BC        = loadCases(currentLoadCase)%rotation)
-            
            case (DAMASK_spectral_SolverAL_label)
              solres = AL_solution (&
                  incInfo,guess,timeinc,timeIncOld,remainingLoadCaseTime, &
@@ -467,6 +471,13 @@ program DAMASK_spectral_Driver
                  F_BC               = loadCases(currentLoadCase)%deformation, &
                  temperature_bc     = loadCases(currentLoadCase)%temperature, &
                  rotation_BC        = loadCases(currentLoadCase)%rotation)
+           case (DAMASK_spectral_SolverPolarisation_label)
+             solres = Polarisation_solution (&
+                 incInfo,guess,timeinc,timeIncOld,remainingLoadCaseTime, &
+                 P_BC               = loadCases(currentLoadCase)%P, &
+                 F_BC               = loadCases(currentLoadCase)%deformation, &
+                 temperature_bc     = loadCases(currentLoadCase)%temperature, &
+                 rotation_BC        = loadCases(currentLoadCase)%rotation)
 #endif
          end select 
 
@@ -525,15 +536,15 @@ program DAMASK_spectral_Driver
  enddo loadCaseLooping
  
  select case (myspectralsolver)
- 
    case (DAMASK_spectral_SolverBasic_label)
      call basic_destroy()
 #ifdef PETSc
    case (DAMASK_spectral_SolverBasicPETSC_label)
      call BasicPETSC_destroy()
-     
    case (DAMASK_spectral_SolverAL_label)
      call AL_destroy()
+   case (DAMASK_spectral_SolverPolarisation_label)
+     call Polarisation_destroy()
 #endif 
  end select
  

code/DAMASK_spectral_solverAL.f90

@@ -17,7 +17,7 @@
 ! along with DAMASK. If not, see <http://www.gnu.org/licenses/>.
 !
 !--------------------------------------------------------------------------------------------------
-! $Id$
+! $Id: DAMASK_spectral_solverAL.f90 2487 2013-06-14 09:49:33Z MPIE\f.roters $
 !--------------------------------------------------------------------------------------------------
 !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH
 !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH
@@ -40,7 +40,7 @@ module DAMASK_spectral_solverAL
 #include <finclude/petscsnes.h>
 
  character (len=*), parameter, public :: &
-   DAMASK_spectral_SolverAL_label = 'al'
+   DAMASK_spectral_solverAL_label = 'al'
    
 !--------------------------------------------------------------------------------------------------
 ! derived types 
@@ -63,9 +63,9 @@ module DAMASK_spectral_solverAL
 ! common pointwise data
  real(pReal), private, dimension(:,:,:,:,:), allocatable :: &
    F_lastInc, &                                                                                     !< field of previous compatible deformation gradients
-   F_tau_lastInc, &                                                                                 !< field of previous incompatible deformation gradient 
+   F_lambda_lastInc, &                                                                                 !< field of previous incompatible deformation gradient 
    Fdot, &                                                                                          !< field of assumed rate of compatible deformation gradient
-   F_tauDot                                                                                         !< field of assumed rate of incopatible deformation gradient
+   F_lambdaDot                                                                                         !< field of assumed rate of incopatible deformation gradient
 
 !--------------------------------------------------------------------------------------------------
 ! stress, stiffness and compliance average etc.
@@ -162,11 +162,11 @@ subroutine AL_init(temperature)
 
  PetscErrorCode :: ierr
  PetscObject :: dummy
- PetscScalar, pointer, dimension(:,:,:,:) :: xx_psc, F, F_tau
+ PetscScalar, pointer, dimension(:,:,:,:) :: xx_psc, F, F_lambda
  
  call Utilities_init()
  write(6,'(/,a)') ' <<<+-  DAMASK_spectral_solverAL init  -+>>>'
- write(6,'(a)') ' $Id$'
+ write(6,'(a)') ' $Id: DAMASK_spectral_solverAL.f90 2487 2013-06-14 09:49:33Z MPIE\f.roters $'
  write(6,'(a16,a)')   ' Current time : ',IO_timeStamp()
 #include "compilation_info.f90"
 
@@ -175,8 +175,8 @@ subroutine AL_init(temperature)
 ! allocate global fields
  allocate (F_lastInc    (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
  allocate (Fdot         (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
- allocate (F_tau_lastInc(3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+ allocate (F_lambda_lastInc(3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
- allocate (F_tauDot     (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+ allocate (F_lambdaDot     (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
     
 !--------------------------------------------------------------------------------------------------
 ! PETSc Init
@@ -197,12 +197,12 @@ subroutine AL_init(temperature)
 ! init fields                 
  call DMDAVecGetArrayF90(da,solution_vec,xx_psc,ierr); CHKERRQ(ierr)                                ! places pointer xx_psc on PETSc data
  F => xx_psc(0:8,:,:,:)
- F_tau => xx_psc(9:17,:,:,:)
+ F_lambda => xx_psc(9:17,:,:,:)
  if (restartInc == 1_pInt) then                                                                     ! no deformation (no restart)
    F_lastInc     = spread(spread(spread(math_I3,3,grid(1)),4,grid(2)),5,grid(3))                    ! initialize to identity
-   F_tau_lastInc = F_lastInc
+   F_lambda_lastInc = F_lastInc
    F = reshape(F_lastInc,[9,grid(1),grid(2),grid(3)])
-   F_tau = F
+   F_lambda = F
  elseif (restartInc > 1_pInt) then 
    if (iand(debug_level(debug_spectral),debug_spectralRestart)/= 0) &
      write(6,'(/,a,'//IO_intOut(restartInc-1_pInt)//',a)') &
@@ -218,13 +218,13 @@ subroutine AL_init(temperature)
    close (777)
    F_aim         = reshape(sum(sum(sum(F,dim=4),dim=3),dim=2) * wgt, [3,3])                         ! 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_tau',&
+   call IO_read_jobBinaryFile(777,'F_lambda',&
-                                           trim(getSolverJobName()),size(F_tau))
+                                           trim(getSolverJobName()),size(F_lambda))
-   read (777,rec=1) F_tau
+   read (777,rec=1) F_lambda
    close (777)
-   call IO_read_jobBinaryFile(777,'F_tau_lastInc',&
+   call IO_read_jobBinaryFile(777,'F_lambda_lastInc',&
-                                        trim(getSolverJobName()),size(F_tau_lastInc))
+                                        trim(getSolverJobName()),size(F_lambda_lastInc))
-   read (777,rec=1) F_tau_lastInc
+   read (777,rec=1) F_lambda_lastInc
    close (777)
    call IO_read_jobBinaryFile(777,'F_aimDot',trim(getSolverJobName()),size(f_aimDot))
    read (777,rec=1) f_aimDot
@@ -274,7 +274,7 @@ type(tSolutionState) function &
    math_mul3333xx33, &
    math_rotate_backward33, &
    math_invSym3333
- use mesh, only: &
+use mesh, only: &
    mesh_ipCoordinates, &
    mesh_deformedCoordsFFT
  use IO, only: &
@@ -311,17 +311,18 @@ type(tSolutionState) function &
  character(len=*), intent(in) :: &
    incInfoIn
  real(pReal), dimension(3,3), intent(in) :: rotation_BC
+
  real(pReal) :: err_stress_tol
 !--------------------------------------------------------------------------------------------------
 ! PETSc Data
- PetscScalar, dimension(:,:,:,:), pointer :: xx_psc, F, F_tau
+ PetscScalar, dimension(:,:,:,:), pointer :: xx_psc, F, F_lambda
  PetscErrorCode :: ierr   
- SNESConvergedReason :: reason
+ SNESConvergedReason ::reason
 
- incInfo = incInfoIn                                                                                ! set global variable to incoming one
+ incInfo = incInfoIn
  call DMDAVecGetArrayF90(da,solution_vec,xx_psc,ierr)
  F => xx_psc(0:8,:,:,:)
- F_tau => xx_psc(9:17,:,:,:)
+ F_lambda => xx_psc(9:17,:,:,:)
  
 !--------------------------------------------------------------------------------------------------
 ! restart information for spectral solver
@@ -334,11 +335,11 @@ type(tSolutionState) function &
    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_tau',size(F_tau))                                             ! writing deformation gradient field to file
+   call IO_write_jobBinaryFile(777,'F_lambda',size(F_lambda))                                                     ! writing deformation gradient field to file
-   write (777,rec=1) F_tau
+   write (777,rec=1) F_lambda
    close (777)
-   call IO_write_jobBinaryFile(777,'F_tau_lastInc',size(F_tau_lastInc))                             ! writing F_lastInc field to file
+   call IO_write_jobBinaryFile(777,'F_lambda_lastInc',size(F_lambda_lastInc))                                     ! writing F_lastInc field to file
-   write (777,rec=1) F_tau_lastInc
+   write (777,rec=1) F_lambda_lastInc
    close (777)
    call IO_write_jobBinaryFile(777,'F_aimDot',size(F_aimDot))
    write (777,rec=1) F_aimDot
@@ -354,7 +355,7 @@ type(tSolutionState) function &
 
  if (cutBack) then 
    F_aim = F_aim_lastInc
-   F_tau= reshape(F_tau_lastInc,[9,grid(1),grid(2),grid(3)]) 
+   F_lambda= reshape(F_lambda_lastInc,[9,grid(1),grid(2),grid(3)]) 
    F    = reshape(F_lastInc,    [9,grid(1),grid(2),grid(3)]) 
    C_volAvg = C_volAvgLastInc
  else
@@ -377,11 +378,11 @@ type(tSolutionState) function &
                                             F,[3,3,grid(1),grid(2),grid(3)])),[3,1,product(grid)])
    Fdot =  Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
                   timeinc_old,guess,F_lastInc,reshape(F,[3,3,grid(1),grid(2),grid(3)]))
-   F_tauDot =  Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
+   F_lambdaDot =  Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
-                  timeinc_old,guess,F_tau_lastInc,reshape(F_tau,[3,3,grid(1),grid(2),grid(3)]))  
+                  timeinc_old,guess,F_lambda_lastInc,reshape(F_lambda,[3,3,grid(1),grid(2),grid(3)]))  
                 
    F_lastInc     = reshape(F,       [3,3,grid(1),grid(2),grid(3)])
-   F_tau_lastInc = reshape(F_tau,[3,3,grid(1),grid(2),grid(3)])
+   F_lambda_lastInc = reshape(F_lambda,[3,3,grid(1),grid(2),grid(3)])
  endif
  F_aim = F_aim + f_aimDot * timeinc
 
@@ -389,7 +390,7 @@ type(tSolutionState) function &
 ! update local deformation gradient
  F     = reshape(Utilities_forwardField(timeinc,F_lastInc,Fdot, &                                   ! ensure that it matches rotated F_aim
                                math_rotate_backward33(F_aim,rotation_BC)),[9,grid(1),grid(2),grid(3)])
- F_tau = reshape(Utilities_forwardField(timeinc,F_tau_lastInc,F_taudot),  [9,grid(1),grid(2),grid(3)]) ! does not have any average value as boundary condition
+ F_lambda = reshape(Utilities_forwardField(timeinc,F_lambda_lastInc,F_lambdadot),  [9,grid(1),grid(2),grid(3)]) ! does not have any average value as boundary condition
  call DMDAVecRestoreArrayF90(da,solution_vec,xx_psc,ierr)
  CHKERRQ(ierr)
 
@@ -415,9 +416,8 @@ type(tSolutionState) function &
 
 !--------------------------------------------------------------------------------------------------
 ! solve BVP 
-   call SNESSolve(snes,PETSC_NULL_OBJECT,solution_vec,ierr)
+ call SNESSolve(snes,PETSC_NULL_OBJECT,solution_vec,ierr)
-   CHKERRQ(ierr)
+ CHKERRQ(ierr)
-
 !--------------------------------------------------------------------------------------------------
 ! stress BC handling
    err_stress = maxval(abs(mask_stress * (P_av - params%P_BC)))                                     ! mask = 0.0 for no bc
@@ -430,11 +430,11 @@ type(tSolutionState) function &
 
 !--------------------------------------------------------------------------------------------------
 ! check convergence
-   call SNESGetConvergedReason(snes,reason,ierr)
+ call SNESGetConvergedReason(snes,reason,ierr)
-   CHKERRQ(ierr)
+ CHKERRQ(ierr)
  
-   AL_solution%termIll = terminallyIll
+ AL_solution%termIll = terminallyIll
-   terminallyIll = .false.
+ terminallyIll = .false.
    AL_solution%converged = .true.
    if (reason < 1 ) AL_solution%converged = .false.
    AL_solution%iterationsNeeded = totalIter
@@ -489,24 +489,24 @@ subroutine AL_formResidual(in,x_scal,f_scal,dummy,ierr)
    f_scal
  PetscScalar, pointer, dimension(:,:,:,:,:) :: &
    F, &
-   F_tau, &
+   F_lambda, &
    residual_F, &
-   residual_F_tau
+   residual_F_lambda
  PetscInt :: &
    PETScIter, &
    nfuncs
  PetscObject :: dummy
  PetscErrorCode :: ierr
  integer(pInt) :: &
-   i, j, k, e
+   i, j, k
 
  F              => x_scal(1:3,1:3,1,&
   XG_RANGE,YG_RANGE,ZG_RANGE)
- F_tau          => x_scal(1:3,1:3,2,&
+ F_lambda          => x_scal(1:3,1:3,2,&
   XG_RANGE,YG_RANGE,ZG_RANGE)
  residual_F     => f_scal(1:3,1:3,1,&
   X_RANGE,Y_RANGE,Z_RANGE)
- residual_F_tau => f_scal(1:3,1:3,2,&
+ residual_F_lambda => f_scal(1:3,1:3,2,&
   X_RANGE,Y_RANGE,Z_RANGE)
  
  call SNESGetNumberFunctionEvals(snes,nfuncs,ierr); CHKERRQ(ierr)
@@ -533,8 +533,8 @@ subroutine AL_formResidual(in,x_scal,f_scal,dummy,ierr)
 ! 
  field_real = 0.0_pReal
  do k = 1_pInt, grid(3); do j = 1_pInt, grid(2); do i = 1_pInt, grid(1)
-   field_real(i,j,k,1:3,1:3) = math_mul3333xx33(C_scale,(polarAlpha + polarBeta)*F(1:3,1:3,i,j,k) - &
+   field_real(i,j,k,1:3,1:3) = math_mul3333xx33(C_scale,polarBeta*F(1:3,1:3,i,j,k) - &
-                                                               (polarAlpha)*F_tau(1:3,1:3,i,j,k))
+                                                        polarAlpha*F_lambda(1:3,1:3,i,j,k))
  enddo; enddo; enddo
  
 !--------------------------------------------------------------------------------------------------
@@ -545,33 +545,30 @@ subroutine AL_formResidual(in,x_scal,f_scal,dummy,ierr)
  
 !--------------------------------------------------------------------------------------------------
 ! constructing residual                         
- residual_F_tau = polarBeta*F - reshape(field_real(1:grid(1),1:grid(2),1:grid(3),1:3,1:3),&
+ residual_F_lambda = polarBeta*F - reshape(field_real(1:grid(1),1:grid(2),1:grid(3),1:3,1:3),&
                                       [3,3,grid(1),grid(2),grid(3)],order=[3,4,5,1,2])
 
 !--------------------------------------------------------------------------------------------------
 ! evaluate constitutive response
- call Utilities_constitutiveResponse(F_lastInc,F - residual_F_tau/polarBeta,params%temperature,params%timeinc, &
+ call Utilities_constitutiveResponse(F_lastInc,F - residual_F_lambda/polarBeta,params%temperature,params%timeinc, &
                                      residual_F,C_volAvg,C_minMaxAvg,P_av,ForwardData,params%rotation_BC)
  ForwardData = .False.
   
+ 
 !--------------------------------------------------------------------------------------------------
 ! constructing residual
- e = 0_pInt
  err_p = 0.0_pReal
  do k = 1_pInt, grid(3); do j = 1_pInt, grid(2); do i = 1_pInt, grid(1)
-   e = e + 1_pInt
+   err_p = err_p + sum((math_I3 + math_mul3333xx33(S_scale,residual_F(1:3,1:3,i,j,k)) - &
-   err_p = err_p + sum((math_mul3333xx33(S_scale,residual_F(1:3,1:3,i,j,k)) - &
+                        F_lambda(1:3,1:3,i,j,k))**2.0_pReal)
-                        (F_tau(1:3,1:3,i,j,k) - &
+   residual_F(1:3,1:3,i,j,k) = math_I3 + math_mul3333xx33(S_scale,residual_F(1:3,1:3,i,j,k)) - &
-                         F(1:3,1:3,i,j,k) + residual_F_tau(1:3,1:3,i,j,k)/polarBeta))**2.0_pReal)
+                               F_lambda(1:3,1:3,i,j,k) &
-   residual_F(1:3,1:3,i,j,k) = math_mul3333xx33(math_invSym3333(materialpoint_dPdF(:,:,:,:,1,e) + C_scale), &
+                               + residual_F_lambda(1:3,1:3,i,j,k)
-                                                residual_F(1:3,1:3,i,j,k) - &
-                                                math_mul3333xx33(C_scale,F_tau(1:3,1:3,i,j,k) - F(1:3,1:3,i,j,k))) &
-                               + residual_F_tau(1:3,1:3,i,j,k)
  enddo; enddo; enddo
  
 !--------------------------------------------------------------------------------------------------
 ! calculating errors  
- err_f = wgt*sqrt(sum(residual_F_tau**2.0_pReal))/polarBeta
+ err_f = wgt*sqrt(sum(residual_F_lambda**2.0_pReal))/polarBeta
  err_p = wgt*sqrt(err_p) 
    
 end subroutine AL_formResidual
@@ -601,19 +598,7 @@ subroutine AL_converged(snes_local,PETScIter,xnorm,snorm,fnorm,reason,dummy,ierr
  SNESConvergedReason :: reason
  PetscObject :: dummy
  PetscErrorCode ::ierr
- logical :: Converged
+
- Converged = (totalIter >= itmin .and. &
-               all([ err_f/err_f_tol, &
-                     err_p/err_p_tol  ] < 1.0_pReal)) &
-             .or.    terminallyIll     
- 
- if (Converged) then
-   reason = 1
- elseif (totalIter >= itmax) then
-   reason = -1
- else  
-   reason = 0
- endif 
  write(6,'(1/,a)') ' ... reporting .............................................................'
  write(6,'(/,a,f8.2,a,es11.5,a,es11.4,a)') ' mismatch F =      ', &
                      err_f/err_f_tol, &
@@ -621,8 +606,18 @@ subroutine AL_converged(snes_local,PETScIter,xnorm,snorm,fnorm,reason,dummy,ierr
  write(6,'(a,f8.2,a,es11.5,a,es11.4,a)')   ' mismatch P =      ', &
                      err_p/err_p_tol, &
                 ' (',err_p,' -,  tol =',err_p_tol,')'
- if(err_p/err_p_tol>1.0_pReal .or. err_f/err_f_tol>1.0_pReal) &                                     ! if not converged, write line for end of iteration (otherwise stress BC check will be done)
+ converged: if ((totalIter >= itmin .and. &
-   write(6,'(/,a)') ' ==========================================================================='
+               all([ err_f/err_f_tol, &
+                     err_p/err_p_tol  ] < 1.0_pReal)) &
+             .or.    terminallyIll) then
+   reason = 1
+ elseif (totalIter >= itmax) then converged 
+   reason = -1
+   write(6,'(/,a)') ' ===========================================================================' ! if leaving, write line for end of iteration (otherwise stress BC check will be done)
+ else converged
+   reason = 0
+   write(6,'(/,a)') ' ===========================================================================' ! if leaving, write line for end of iteration (otherwise stress BC check will be done)
+ endif converged
  flush(6)
 
 end subroutine AL_converged

code/DAMASK_spectral_solverPolarisation.f90

@@ -0,0 +1,648 @@
+! Copyright 2011-13 Max-Planck-Institut für Eisenforschung GmbH
+!
+! This file is part of DAMASK,
+! the Düsseldorf Advanced MAterial Simulation Kit.
+!
+! 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/>.
+!
+!--------------------------------------------------------------------------------------------------
+! $Id$
+!--------------------------------------------------------------------------------------------------
+!> @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 Polarisation scheme solver
+!--------------------------------------------------------------------------------------------------
+module DAMASK_spectral_solverPolarisation
+ use prec, only: & 
+   pInt, &
+   pReal
+ use math, only: &
+   math_I3
+ use DAMASK_spectral_utilities, only: &
+   tSolutionState
+ 
+ implicit none
+ private
+#include <finclude/petscsys.h>
+#include <finclude/petscdmda.h>
+#include <finclude/petscsnes.h>
+
+ character (len=*), parameter, public :: &
+   DAMASK_spectral_solverPolarisation_label = 'polarisation'
+   
+!--------------------------------------------------------------------------------------------------
+! derived types 
+ type tSolutionParams                                                                               !< @todo use here the type definition for a full loadcase including mask
+   real(pReal), dimension(3,3) :: P_BC, rotation_BC
+   real(pReal) :: timeinc
+   real(pReal) :: temperature
+ end type tSolutionParams
+ 
+ type(tSolutionParams), private :: params
+ real(pReal), private, dimension(3,3) :: mask_stress = 0.0_pReal
+
+!--------------------------------------------------------------------------------------------------
+! PETSc data
+ DM,   private :: da
+ SNES, private :: snes
+ Vec,  private :: solution_vec
+ 
+!--------------------------------------------------------------------------------------------------
+! common pointwise data
+ real(pReal), private, dimension(:,:,:,:,:), allocatable :: &
+   F_lastInc, &                                                                                     !< field of previous compatible deformation gradients
+   F_tau_lastInc, &                                                                                 !< field of previous incompatible deformation gradient 
+   Fdot, &                                                                                          !< field of assumed rate of compatible deformation gradient
+   F_tauDot                                                                                         !< field of assumed rate of incopatible deformation gradient
+
+!--------------------------------------------------------------------------------------------------
+! stress, stiffness and compliance average etc.
+ real(pReal), private, dimension(3,3) :: &
+   F_aimDot, &                                                                                      !< 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
+ character(len=1024), private :: incInfo                                                            !< time and increment information
+ real(pReal), private, 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
+   S = 0.0_pReal, &                                                                                 !< current compliance (filled up with zeros)
+   C_scale = 0.0_pReal, &                             
+   S_scale = 0.0_pReal
+ 
+ real(pReal), private :: &
+   err_stress, &                                                                                    !< deviation from stress BC
+   err_f, &                                                                                         !< difference between compatible and incompatible deformation gradient
+   err_p                                                                                            !< difference of stress resulting from compatible and incompatible F
+ logical, private :: ForwardData
+ integer(pInt), private :: &
+   currIter = 0_pInt, &                                                                             !< helper to count total iteration correctly
+   totalIter = 0_pInt                                                                               !< total iteration in current increment
+ 
+ public :: &
+   Polarisation_init, &
+   Polarisation_solution, &
+   Polarisation_destroy
+ external :: &
+   VecDestroy, &
+   DMDestroy, &
+   DMDACreate3D, &
+   DMCreateGlobalVector, &
+   DMDASetLocalFunction, &
+   PETScFinalize, &
+   SNESDestroy, &
+   SNESGetNumberFunctionEvals, &
+   SNESGetIterationNumber, &
+   SNESSolve, &
+   SNESSetDM, &
+   SNESGetConvergedReason, &
+   SNESSetConvergenceTest, &
+   SNESSetFromOptions, &
+   SNESCreate, &
+   MPI_Abort
+
+contains
+
+!--------------------------------------------------------------------------------------------------
+!> @brief allocates all neccessary fields and fills them with data, potentially from restart info
+!> @todo use sourced allocation, e.g. allocate(Fdot,source = F_lastInc)
+!--------------------------------------------------------------------------------------------------
+subroutine Polarisation_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_intOut, &
+   IO_read_JobBinaryFile, &
+   IO_write_JobBinaryFile, &
+   IO_timeStamp
+ use debug, only : &
+  debug_level, &
+  debug_spectral, &
+  debug_spectralRestart
+ use FEsolving, only: &
+   restartInc
+ use DAMASK_interface, only: &
+   getSolverJobName
+ use DAMASK_spectral_Utilities, only: &
+   Utilities_init, &
+   Utilities_constitutiveResponse, &
+   Utilities_updateGamma, &
+   grid, &
+   geomSize, &
+   wgt
+ use mesh, only: &
+   mesh_ipCoordinates, &
+   mesh_deformedCoordsFFT
+ use math, only: &
+   math_invSym3333
+   
+ implicit none
+ real(pReal), intent(inout) :: &
+   temperature
+#include <finclude/petscdmda.h90>
+#include <finclude/petscsnes.h90>
+ real(pReal), dimension(:,:,:,:,:), allocatable :: P
+ real(pReal), dimension(3,3) :: &
+   temp33_Real = 0.0_pReal
+ real(pReal), dimension(3,3,3,3) :: &
+   temp3333_Real = 0.0_pReal, &
+   temp3333_Real2 = 0.0_pReal
+
+ PetscErrorCode :: ierr
+ PetscObject :: dummy
+ PetscScalar, pointer, dimension(:,:,:,:) :: xx_psc, F, F_tau
+ 
+ call Utilities_init()
+ write(6,'(/,a)') ' <<<+-  DAMASK_spectral_solverPolarisation init  -+>>>'
+ write(6,'(a)') ' $Id$'
+ write(6,'(a16,a)')   ' Current time : ',IO_timeStamp()
+#include "compilation_info.f90"
+
+ allocate (P            (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+!--------------------------------------------------------------------------------------------------
+! allocate global fields
+ allocate (F_lastInc    (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+ allocate (Fdot         (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+ allocate (F_tau_lastInc(3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+ allocate (F_tauDot     (3,3,grid(1),grid(2),grid(3)),source = 0.0_pReal)
+    
+!--------------------------------------------------------------------------------------------------
+! PETSc Init
+ call SNESCreate(PETSC_COMM_WORLD,snes,ierr); CHKERRQ(ierr)
+ call DMDACreate3d(PETSC_COMM_WORLD,                               &
+           DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, &
+           DMDA_STENCIL_BOX,grid(1),grid(2),grid(3),PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE, &
+           18,1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr)
+ CHKERRQ(ierr)
+ call DMCreateGlobalVector(da,solution_vec,ierr); CHKERRQ(ierr)
+ call DMDASetLocalFunction(da,Polarisation_formResidual,ierr); CHKERRQ(ierr)
+ call SNESSetDM(snes,da,ierr); CHKERRQ(ierr)
+ call SNESSetConvergenceTest(snes,Polarisation_converged,dummy,PETSC_NULL_FUNCTION,ierr)
+ CHKERRQ(ierr)
+ call SNESSetFromOptions(snes,ierr); CHKERRQ(ierr)
+
+!--------------------------------------------------------------------------------------------------
+! init fields                 
+ call DMDAVecGetArrayF90(da,solution_vec,xx_psc,ierr); CHKERRQ(ierr)                                ! places pointer xx_psc on PETSc data
+ F => xx_psc(0:8,:,:,:)
+ F_tau => xx_psc(9:17,:,:,:)
+ if (restartInc == 1_pInt) then                                                                     ! no deformation (no restart)
+   F_lastInc     = spread(spread(spread(math_I3,3,grid(1)),4,grid(2)),5,grid(3))                    ! initialize to identity
+   F_tau_lastInc = F_lastInc
+   F = reshape(F_lastInc,[9,grid(1),grid(2),grid(3)])
+   F_tau = F
+ elseif (restartInc > 1_pInt) then 
+   if (iand(debug_level(debug_spectral),debug_spectralRestart)/= 0) &
+     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         = reshape(sum(sum(sum(F,dim=4),dim=3),dim=2) * wgt, [3,3])                         ! 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_tau',&
+                                           trim(getSolverJobName()),size(F_tau))
+   read (777,rec=1) F_tau
+   close (777)
+   call IO_read_jobBinaryFile(777,'F_tau_lastInc',&
+                                        trim(getSolverJobName()),size(F_tau_lastInc))
+   read (777,rec=1) F_tau_lastInc
+   close (777)
+   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_volAvg',trim(getSolverJobName()),size(C_volAvg))
+   read (777,rec=1) C_volAvg
+   close (777)
+   call IO_read_jobBinaryFile(777,'C_volAvgLastInc',trim(getSolverJobName()),size(C_volAvgLastInc))
+   read (777,rec=1) C_volAvgLastInc
+   close (777)
+   call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(temp3333_Real))
+   read (777,rec=1) C_minMaxAvg
+   close (777)
+ endif
+ mesh_ipCoordinates = reshape(mesh_deformedCoordsFFT(geomSize,reshape(&
+                                              F,[3,3,grid(1),grid(2),grid(3)])),[3,1,product(grid)])
+ call Utilities_constitutiveResponse(F,F,temperature,0.0_pReal,P,temp3333_Real,temp3333_Real2,&
+                                temp33_Real,.false.,math_I3)
+ call DMDAVecRestoreArrayF90(da,solution_vec,xx_psc,ierr); CHKERRQ(ierr)
+
+!--------------------------------------------------------------------------------------------------
+! reference stiffness
+ if (restartInc == 1_pInt) then                                                                     ! use initial stiffness as reference stiffness
+   C_minMaxAvg = temp3333_Real2
+   C_volAvg = temp3333_Real
+ endif 
+
+ call Utilities_updateGamma(temp3333_Real2,.True.)
+ C_scale = temp3333_Real2
+ S_scale = math_invSym3333(temp3333_Real2)
+ 
+end subroutine Polarisation_init
+
+
+!--------------------------------------------------------------------------------------------------
+!> @brief solution for the Polarisation scheme with internal iterations
+!--------------------------------------------------------------------------------------------------
+type(tSolutionState) function &
+  Polarisation_solution(incInfoIn,guess,timeinc,timeinc_old,loadCaseTime,P_BC,F_BC,temperature_bc,rotation_BC)
+ use numerics, only: &
+   update_gamma, &
+   itmax, &
+   err_stress_tolrel, &
+   err_stress_tolabs
+ use math, only: &
+   math_mul33x33 ,&
+   math_mul3333xx33, &
+   math_rotate_backward33, &
+   math_invSym3333
+ use mesh, only: &
+   mesh_ipCoordinates, &
+   mesh_deformedCoordsFFT
+ use IO, only: &
+   IO_write_JobBinaryFile
+ use DAMASK_spectral_Utilities, only: &
+   grid, &
+   geomSize, &
+   tBoundaryCondition, &
+   Utilities_forwardField, &
+   Utilities_calculateRate, &
+   Utilities_maskedCompliance, &
+   Utilities_updateGamma, &
+   cutBack
+ use FEsolving, only: &
+   restartWrite, &
+   terminallyIll
+ 
+ implicit none
+#include <finclude/petscdmda.h90>
+#include <finclude/petscsnes.h90>
+
+!--------------------------------------------------------------------------------------------------
+! input data for solution
+  real(pReal), intent(in) :: &
+   timeinc, &                                                                                       !< increment in time for current solution
+   timeinc_old, &                                                                                   !< increment in time of last increment
+   loadCaseTime, &                                                                                  !< remaining time of current load case
+   temperature_bc
+ logical, intent(in) :: &
+   guess
+ type(tBoundaryCondition),      intent(in) :: &
+   P_BC, &
+   F_BC
+ character(len=*), intent(in) :: &
+   incInfoIn
+ real(pReal), dimension(3,3), intent(in) :: rotation_BC
+ real(pReal) :: err_stress_tol
+!--------------------------------------------------------------------------------------------------
+! PETSc Data
+ PetscScalar, dimension(:,:,:,:), pointer :: xx_psc, F, F_tau
+ PetscErrorCode :: ierr   
+ SNESConvergedReason :: reason
+
+ incInfo = incInfoIn                                                                                ! set global variable to incoming one
+ call DMDAVecGetArrayF90(da,solution_vec,xx_psc,ierr)
+ F => xx_psc(0:8,:,:,:)
+ F_tau => xx_psc(9:17,:,:,:)
+ 
+!--------------------------------------------------------------------------------------------------
+! 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_tau',size(F_tau))                                             ! writing deformation gradient field to file
+   write (777,rec=1) F_tau
+   close (777)
+   call IO_write_jobBinaryFile(777,'F_tau_lastInc',size(F_tau_lastInc))                             ! writing F_lastInc field to file
+   write (777,rec=1) F_tau_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_volAvg',size(C_volAvg))
+   write (777,rec=1) C_volAvg
+   close(777)
+   call IO_write_jobBinaryFile(777,'C_volAvgLastInc',size(C_volAvgLastInc))
+   write (777,rec=1) C_volAvgLastInc
+   close(777)
+ endif 
+ Polarisation_solution%converged =.false.
+
+ if (cutBack) then 
+   F_aim = F_aim_lastInc
+   F_tau= reshape(F_tau_lastInc,[9,grid(1),grid(2),grid(3)]) 
+   F    = reshape(F_lastInc,    [9,grid(1),grid(2),grid(3)]) 
+   C_volAvg = C_volAvgLastInc
+ else
+   C_volAvgLastInc = C_volAvg
+!--------------------------------------------------------------------------------------------------
+! 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
+   elseif(F_BC%myType=='f') then                                                                    ! aim at end of load case is prescribed
+     f_aimDot = F_BC%maskFloat * (F_BC%values -F_aim)/loadCaseTime
+   endif
+   if (guess) f_aimDot  = f_aimDot + P_BC%maskFloat * (F_aim - F_aim_lastInc)/timeinc_old
+   F_aim_lastInc = F_aim
+
+!--------------------------------------------------------------------------------------------------
+! update coordinates and rate and forward last inc
+   mesh_ipCoordinates = reshape(mesh_deformedCoordsFFT(geomSize,reshape(&
+                                            F,[3,3,grid(1),grid(2),grid(3)])),[3,1,product(grid)])
+   Fdot =  Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
+                  timeinc_old,guess,F_lastInc,reshape(F,[3,3,grid(1),grid(2),grid(3)]))
+   F_tauDot =  Utilities_calculateRate(math_rotate_backward33(f_aimDot,rotation_BC), &
+                  timeinc_old,guess,F_tau_lastInc,reshape(F_tau,[3,3,grid(1),grid(2),grid(3)]))  
+                
+   F_lastInc     = reshape(F,       [3,3,grid(1),grid(2),grid(3)])
+   F_tau_lastInc = reshape(F_tau,[3,3,grid(1),grid(2),grid(3)])
+ endif
+ F_aim = F_aim + f_aimDot * timeinc
+
+!--------------------------------------------------------------------------------------------------
+! update local deformation gradient
+ F     = reshape(Utilities_forwardField(timeinc,F_lastInc,Fdot, &                                   ! ensure that it matches rotated F_aim
+                               math_rotate_backward33(F_aim,rotation_BC)),[9,grid(1),grid(2),grid(3)])
+ F_tau = reshape(Utilities_forwardField(timeinc,F_tau_lastInc,F_taudot),  [9,grid(1),grid(2),grid(3)]) ! does not have any average value as boundary condition
+ call DMDAVecRestoreArrayF90(da,solution_vec,xx_psc,ierr)
+ CHKERRQ(ierr)
+
+!--------------------------------------------------------------------------------------------------
+! update stiffness (and gamma operator)
+ S = Utilities_maskedCompliance(rotation_BC,P_BC%maskLogical,C_volAvg)
+ if (update_gamma) then
+   call Utilities_updateGamma(C_minMaxAvg,restartWrite)
+   C_scale = C_minMaxAvg
+   S_scale = math_invSym3333(C_minMaxAvg)
+ endif  
+ 
+ ForwardData = .True.
+ mask_stress = P_BC%maskFloat
+ params%P_BC = P_BC%values
+ params%rotation_BC = rotation_BC
+ params%timeinc = timeinc
+ params%temperature = temperature_bc
+
+ err_stress_tol = 1.0_pReal; err_stress = 2.0_pReal * err_stress_tol                                ! ensure to start loop
+ totalIter = -1_pInt
+ do while(err_stress/err_stress_tol > 1.0_pReal)                                                    ! solve BVP and Stress RB
+
+!--------------------------------------------------------------------------------------------------
+! solve BVP 
+   call SNESSolve(snes,PETSC_NULL_OBJECT,solution_vec,ierr)
+   CHKERRQ(ierr)
+
+!--------------------------------------------------------------------------------------------------
+! stress BC handling
+   err_stress = maxval(abs(mask_stress * (P_av - params%P_BC)))                                     ! mask = 0.0 for no bc
+   err_stress_tol = max(maxval(abs(P_av))*err_stress_tolrel,err_stress_tolabs)
+   F_aim = F_aim - math_mul3333xx33(S, ((P_av - params%P_BC)))                                      ! S = 0.0 for no bc
+   write(6,'(1/,a)') ' ... correcting stress boundary condition  .................................'
+   write(6,'(1/,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,')' 
+   write(6,'(/,a)') ' ==========================================================================='
+
+!--------------------------------------------------------------------------------------------------
+! check convergence
+   call SNESGetConvergedReason(snes,reason,ierr)
+   CHKERRQ(ierr)
+ 
+   Polarisation_solution%termIll = terminallyIll
+   terminallyIll = .false.
+   Polarisation_solution%converged = .true.
+   if (reason < 1 ) Polarisation_solution%converged = .false.
+   Polarisation_solution%iterationsNeeded = totalIter
+ end do
+
+end function Polarisation_solution
+
+
+!--------------------------------------------------------------------------------------------------
+!> @brief forms the Polarisation residual vector
+!--------------------------------------------------------------------------------------------------
+subroutine Polarisation_formResidual(in,x_scal,f_scal,dummy,ierr)
+ use numerics, only: &
+   itmax, &
+   itmin, &
+   polarAlpha, &
+   polarBeta
+ use IO, only: &
+   IO_intOut
+ use math, only: &
+   math_rotate_backward33, &
+   math_transpose33, &
+   math_mul3333xx33, &
+   math_invSym3333
+ use DAMASK_spectral_Utilities, only: &
+   grid, &
+   wgt, &
+   field_real, &
+   Utilities_FFTforward, &
+   Utilities_fourierConvolution, &
+   Utilities_FFTbackward, &
+   Utilities_constitutiveResponse
+ use debug, only: &
+   debug_level, &
+   debug_spectral, &
+   debug_spectralRotation
+ use homogenization, only: &
+   materialpoint_P, &
+   materialpoint_dPdF
+
+ implicit none
+!--------------------------------------------------------------------------------------------------
+! strange syntax in the next line because otherwise macros expand beyond 132 character limit 
+ DMDALocalInfo,        dimension(&
+   DMDA_LOCAL_INFO_SIZE) :: &
+   in
+ PetscScalar, target, dimension(3,3,2, &
+   XG_RANGE,YG_RANGE,ZG_RANGE) :: &
+   x_scal
+ PetscScalar, target, dimension(3,3,2, &
+   X_RANGE,Y_RANGE,Z_RANGE) :: &
+   f_scal
+ PetscScalar, pointer, dimension(:,:,:,:,:) :: &
+   F, &
+   F_tau, &
+   residual_F, &
+   residual_F_tau
+ PetscInt :: &
+   PETScIter, &
+   nfuncs
+ PetscObject :: dummy
+ PetscErrorCode :: ierr
+ integer(pInt) :: &
+   i, j, k, e
+
+ F              => x_scal(1:3,1:3,1,&
+  XG_RANGE,YG_RANGE,ZG_RANGE)
+ F_tau          => x_scal(1:3,1:3,2,&
+  XG_RANGE,YG_RANGE,ZG_RANGE)
+ residual_F     => f_scal(1:3,1:3,1,&
+  X_RANGE,Y_RANGE,Z_RANGE)
+ residual_F_tau => f_scal(1:3,1:3,2,&
+  X_RANGE,Y_RANGE,Z_RANGE)
+ 
+ call SNESGetNumberFunctionEvals(snes,nfuncs,ierr); CHKERRQ(ierr)
+ call SNESGetIterationNumber(snes,PETScIter,ierr); CHKERRQ(ierr)
+
+ if(nfuncs== 0 .and. PETScIter == 0) currIter = -1_pInt                                             ! new increment
+
+ if (PETScIter == currIter .or. currIter == -1 ) then                                                    ! new iteration
+!--------------------------------------------------------------------------------------------------
+! report begin of new iteration
+   currIter = currIter + 1_pInt
+   totalIter = totalIter + 1_pInt
+   write(6,'(1x,a,3(a,'//IO_intOut(itmax)//'))') 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) =', &
+                                 math_transpose33(math_rotate_backward33(F_aim,params%rotation_BC))
+   write(6,'(/,a,/,3(3(f12.7,1x)/))',advance='no') ' deformation gradient aim =', &
+                                 math_transpose33(F_aim)
+   flush(6)
+ endif
+  
+!--------------------------------------------------------------------------------------------------
+! 
+ field_real = 0.0_pReal
+ do k = 1_pInt, grid(3); do j = 1_pInt, grid(2); do i = 1_pInt, grid(1)
+   field_real(i,j,k,1:3,1:3) = math_mul3333xx33(C_scale,(polarAlpha + polarBeta)*F(1:3,1:3,i,j,k) - &
+                                                               (polarAlpha)*F_tau(1:3,1:3,i,j,k))
+ enddo; enddo; enddo
+ 
+!--------------------------------------------------------------------------------------------------
+! doing convolution in Fourier space 
+ call Utilities_FFTforward()
+ call Utilities_fourierConvolution(math_rotate_backward33(polarBeta*F_aim,params%rotation_BC)) 
+ call Utilities_FFTbackward()
+ 
+!--------------------------------------------------------------------------------------------------
+! constructing residual                         
+ residual_F_tau = polarBeta*F - reshape(field_real(1:grid(1),1:grid(2),1:grid(3),1:3,1:3),&
+                                      [3,3,grid(1),grid(2),grid(3)],order=[3,4,5,1,2])
+
+!--------------------------------------------------------------------------------------------------
+! evaluate constitutive response
+ call Utilities_constitutiveResponse(F_lastInc,F - residual_F_tau/polarBeta,params%temperature,params%timeinc, &
+                                     residual_F,C_volAvg,C_minMaxAvg,P_av,ForwardData,params%rotation_BC)
+ ForwardData = .False.
+  
+!--------------------------------------------------------------------------------------------------
+! constructing residual
+ e = 0_pInt
+ err_p = 0.0_pReal
+ do k = 1_pInt, grid(3); do j = 1_pInt, grid(2); do i = 1_pInt, grid(1)
+   e = e + 1_pInt
+   err_p = err_p + sum((math_mul3333xx33(S_scale,residual_F(1:3,1:3,i,j,k)) - &
+                        (F_tau(1:3,1:3,i,j,k) - &
+                         F(1:3,1:3,i,j,k) + residual_F_tau(1:3,1:3,i,j,k)/polarBeta))**2.0_pReal)
+   residual_F(1:3,1:3,i,j,k) = math_mul3333xx33(math_invSym3333(materialpoint_dPdF(:,:,:,:,1,e) + C_scale), &
+                                                residual_F(1:3,1:3,i,j,k) - &
+                                                math_mul3333xx33(C_scale,F_tau(1:3,1:3,i,j,k) - F(1:3,1:3,i,j,k))) &
+                               + residual_F_tau(1:3,1:3,i,j,k)
+ enddo; enddo; enddo
+ 
+!--------------------------------------------------------------------------------------------------
+! calculating errors  
+ err_f = wgt*sqrt(sum(residual_F_tau**2.0_pReal))/polarBeta
+ err_p = wgt*sqrt(err_p) 
+   
+end subroutine Polarisation_formResidual
+
+
+!--------------------------------------------------------------------------------------------------
+!> @brief convergence check
+!--------------------------------------------------------------------------------------------------
+subroutine Polarisation_converged(snes_local,PETScIter,xnorm,snorm,fnorm,reason,dummy,ierr)
+ use numerics, only: &
+  itmax, &
+  itmin, &
+  err_f_tol, &
+  err_p_tol, &
+  err_stress_tolrel, &
+  err_stress_tolabs
+ use FEsolving, only: &
+   terminallyIll
+
+ implicit none
+ SNES :: snes_local
+ PetscInt :: PETScIter
+ PetscReal :: &
+   xnorm, &
+   snorm, &
+   fnorm
+ SNESConvergedReason :: reason
+ PetscObject :: dummy
+ PetscErrorCode ::ierr
+ logical :: Converged
+ Converged = (totalIter >= itmin .and. &
+               all([ err_f/err_f_tol, &
+                     err_p/err_p_tol  ] < 1.0_pReal)) &
+             .or.    terminallyIll     
+ 
+ if (Converged) then
+   reason = 1
+ elseif (totalIter >= itmax) then
+   reason = -1
+ else  
+   reason = 0
+ endif 
+ write(6,'(1/,a)') ' ... reporting .............................................................'
+ write(6,'(/,a,f8.2,a,es11.5,a,es11.4,a)') ' mismatch F =      ', &
+                     err_f/err_f_tol, &
+                ' (',err_f,' -,  tol =',err_f_tol,')'
+ write(6,'(a,f8.2,a,es11.5,a,es11.4,a)')   ' mismatch P =      ', &
+                     err_p/err_p_tol, &
+                ' (',err_p,' -,  tol =',err_p_tol,')'
+ if(err_p/err_p_tol>1.0_pReal .or. err_f/err_f_tol>1.0_pReal) &                                     ! if not converged, write line for end of iteration (otherwise stress BC check will be done)
+   write(6,'(/,a)') ' ==========================================================================='
+ flush(6)
+
+end subroutine Polarisation_converged
+
+!--------------------------------------------------------------------------------------------------
+!> @brief destroy routine
+!--------------------------------------------------------------------------------------------------
+subroutine Polarisation_destroy()
+ use DAMASK_spectral_Utilities, only: &
+   Utilities_destroy
+ 
+ implicit none
+ PetscErrorCode :: ierr
+
+ call VecDestroy(solution_vec,ierr); CHKERRQ(ierr)
+ call SNESDestroy(snes,ierr); CHKERRQ(ierr)
+ call DMDestroy(da,ierr); CHKERRQ(ierr)
+ call PetscFinalize(ierr); CHKERRQ(ierr)
+ call Utilities_destroy()
+
+end subroutine Polarisation_destroy
+
+end module DAMASK_spectral_SolverPolarisation

code/Makefile

@@ -350,7 +350,9 @@ COMPILED_FILES = prec.o DAMASK_spectral_interface.o IO.o libs.o numerics.o debug
                  DAMASK_spectral_utilities.o DAMASK_spectral_solverBasic.o 
 
 ifdef PETSC_DIR
-PETSC_FILES = DAMASK_spectral_solverAL.o DAMASK_spectral_solverBasicPETSc.o
+PETSC_FILES = DAMASK_spectral_solverAL.o \
+                        DAMASK_spectral_solverBasicPETSc.o \
+                        DAMASK_spectral_solverPolarisation.o
 COMPILED_FILES += $(PETSC_FILES)
 endif
 
@@ -369,6 +371,9 @@ DAMASK_spectral_solverAL.o:    DAMASK_spectral_solverAL.f90\
 DAMASK_spectral_solverBasic.o: DAMASK_spectral_solverBasic.f90\
                                DAMASK_spectral_utilities.o
   
+DAMASK_spectral_solverPolarisation.o:    DAMASK_spectral_solverPolarisation.f90\
+                               DAMASK_spectral_utilities.o
+  
 DAMASK_spectral_solverBasicPETSc.o: DAMASK_spectral_solverBasicPETSc.f90\
                                DAMASK_spectral_utilities.o