diff --git a/code/DAMASK_spectral.f90 b/code/DAMASK_spectral.f90
index f24a00321..1545d9b16 100644
--- a/code/DAMASK_spectral.f90
+++ b/code/DAMASK_spectral.f90
@@ -585,7 +585,7 @@ program DAMASK_spectral
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
else ! precalculation of gamma_hat field
- allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source =0.0_pReal)
+ allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source = 0.0_pReal)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
diff --git a/code/DAMASK_spectralDriver.f90 b/code/DAMASK_spectralDriver.f90
new file mode 100644
index 000000000..b2c35e1c5
--- /dev/null
+++ b/code/DAMASK_spectralDriver.f90
@@ -0,0 +1,409 @@
+! Copyright 2012 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 .
+!
+!##################################################################################################
+!* $Id$
+!##################################################################################################
+! Material subroutine for BVP solution using spectral method
+!
+! Run 'DAMASK_spectral.exe --help' to get usage hints
+!
+! written by P. Eisenlohr,
+! F. Roters,
+! L. Hantcherli,
+! W.A. Counts,
+! D.D. Tjahjanto,
+! C. Kords,
+! M. Diehl,
+! R. Lebensohn
+!
+! MPI fuer Eisenforschung, Duesseldorf
+
+#include "spectral_quit.f90"
+
+program DAMASK_spectral
+ use prec, only: &
+ pInt, &
+ pReal
+
+ use IO, only: &
+ IO_error,&
+ IO_write_jobBinaryFile
+
+ use math
+
+ use FEsolving, only: &
+ restartWrite, &
+ restartInc
+
+ use homogenization, only: &
+ materialpoint_sizeResults, &
+ materialpoint_results
+
+ use DAMASK_spectralSovler
+
+ implicit none
+
+!--------------------------------------------------------------------------------------------------
+! loop variables, convergence etc.
+ integer(pInt) :: i, j, k, l, m, n, p, errorID
+
+
+ call DAMASK_interface_init
+ write(6,'(a)') ''
+ write(6,'(a)') ' <<<+- DAMASK_spectral init -+>>>'
+ write(6,'(a)') ' $Id$'
+#include "compilation_info.f90"
+ write(6,'(a)') ' Working Directory: ',trim(getSolverWorkingDirectoryName())
+ write(6,'(a)') ' Solver Job Name: ',trim(getSolverJobName())
+ write(6,'(a)') ''
+!--------------------------------------------------------------------------------------------------
+! reading the load case file and allocate data structure containing load cases
+ call IO_open_file(myUnit,trim(loadCaseFile))
+ rewind(myUnit)
+ do
+ read(myUnit,'(a1024)',END = 100) line
+ if (IO_isBlank(line)) cycle ! skip empty lines
+ positions = IO_stringPos(line,maxNchunksLoadcase)
+ do i = 1_pInt, maxNchunksLoadcase, 1_pInt ! reading compulsory parameters for loadcase
+ select case (IO_lc(IO_stringValue(line,positions,i)))
+ case('l','velocitygrad','velgrad','velocitygradient')
+ N_l = N_l + 1_pInt
+ case('fdot','dotf')
+ N_Fdot = N_Fdot + 1_pInt
+ case('t','time','delta')
+ N_t = N_t + 1_pInt
+ case('n','incs','increments','steps','logincs','logincrements','logsteps')
+ N_n = N_n + 1_pInt
+ end select
+ enddo ! count all identifiers to allocate memory and do sanity check
+ enddo
+
+100 N_Loadcases = N_n
+ if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
+ call IO_error(error_ID=837_pInt,ext_msg = trim(loadCaseFile)) ! error message for incomplete loadcase
+ allocate (bc(N_Loadcases))
+
+!--------------------------------------------------------------------------------------------------
+! reading the load case and assign values to the allocated data structure
+ rewind(myUnit)
+
+ do
+ read(myUnit,'(a1024)',END = 101) line
+ if (IO_isBlank(line)) cycle ! skip empty lines
+ loadcase = loadcase + 1_pInt
+ positions = IO_stringPos(line,maxNchunksLoadcase)
+ do j = 1_pInt,maxNchunksLoadcase
+ select case (IO_lc(IO_stringValue(line,positions,j)))
+ case('fdot','dotf','l','velocitygrad','velgrad','velocitygradient') ! assign values for the deformation BC matrix
+ bc(loadcase)%velGradApplied = &
+ (IO_lc(IO_stringValue(line,positions,j)) == 'l'.or. & ! in case of given L, set flag to true
+ IO_lc(IO_stringValue(line,positions,j)) == 'velocitygrad'.or.&
+ IO_lc(IO_stringValue(line,positions,j)) == 'velgrad'.or.&
+ IO_lc(IO_stringValue(line,positions,j)) == 'velocitygradient')
+ temp_valueVector = 0.0_pReal
+ temp_maskVector = .false.
+ forall (k = 1_pInt:9_pInt) temp_maskVector(k) = IO_stringValue(line,positions,j+k) /= '*'
+ do k = 1_pInt,9_pInt
+ if (temp_maskVector(k)) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
+ enddo
+ bc(loadcase)%maskDeformation = transpose(reshape(temp_maskVector,[ 3,3]))
+ bc(loadcase)%deformation = math_plain9to33(temp_valueVector)
+ case('p','pk1','piolakirchhoff','stress')
+ temp_valueVector = 0.0_pReal
+ forall (k = 1_pInt:9_pInt) bc(loadcase)%maskStressVector(k) =&
+ IO_stringValue(line,positions,j+k) /= '*'
+ do k = 1_pInt,9_pInt
+ if (bc(loadcase)%maskStressVector(k)) temp_valueVector(k) =&
+ IO_floatValue(line,positions,j+k) ! assign values for the bc(loadcase)%stress matrix
+ enddo
+ bc(loadcase)%maskStress = transpose(reshape(bc(loadcase)%maskStressVector,[ 3,3]))
+ bc(loadcase)%stress = math_plain9to33(temp_valueVector)
+ case('t','time','delta') ! increment time
+ bc(loadcase)%time = IO_floatValue(line,positions,j+1_pInt)
+ case('temp','temperature') ! starting temperature
+ bc(loadcase)%temperature = IO_floatValue(line,positions,j+1_pInt)
+ case('n','incs','increments','steps') ! number of increments
+ bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
+ case('logincs','logincrements','logsteps') ! number of increments (switch to log time scaling)
+ bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
+ bc(loadcase)%logscale = 1_pInt
+ case('f','freq','frequency','outputfreq') ! frequency of result writings
+ bc(loadcase)%outputfrequency = IO_intValue(line,positions,j+1_pInt)
+ case('r','restart','restartwrite') ! frequency of writing restart information
+ bc(loadcase)%restartfrequency = max(0_pInt,IO_intValue(line,positions,j+1_pInt))
+ case('guessreset','dropguessing')
+ bc(loadcase)%followFormerTrajectory = .false. ! do not continue to predict deformation along former trajectory
+ case('euler') ! rotation of loadcase given in euler angles
+ p = 0_pInt ! assuming values given in radians
+ l = 1_pInt ! assuming keyword indicating degree/radians
+ select case (IO_lc(IO_stringValue(line,positions,j+1_pInt)))
+ case('deg','degree')
+ p = 1_pInt ! for conversion from degree to radian
+ case('rad','radian')
+ case default
+ l = 0_pInt ! immediately reading in angles, assuming radians
+ end select
+ forall(k = 1_pInt:3_pInt) temp33_Real(k,1) = &
+ IO_floatValue(line,positions,j+l+k) * real(p,pReal) * inRad
+ bc(loadcase)%rotation = math_EulerToR(temp33_Real(:,1))
+ case('rotation','rot') ! assign values for the rotation of loadcase matrix
+ temp_valueVector = 0.0_pReal
+ forall (k = 1_pInt:9_pInt) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
+ bc(loadcase)%rotation = math_plain9to33(temp_valueVector)
+ end select
+ enddo; enddo
+101 close(myUnit)
+
+!-------------------------------------------------------------------------------------------------- ToDo: if temperature at CPFEM is treated properly, move this up immediately after interface init
+! initialization of all related DAMASK modules (e.g. mesh.f90 reads in geometry)
+ call CPFEM_initAll(bc(1)%temperature,1_pInt,1_pInt)
+
+!--------------------------------------------------------------------------------------------------
+! get resolution, dimension, homogenization and variables derived from resolution
+ res = mesh_spectral_getResolution()
+ geomdim = mesh_spectral_getDimension()
+ homog = mesh_spectral_getHomogenization()
+ res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
+ Npoints = res(1)*res(2)*res(3)
+ wgt = 1.0_pReal/real(Npoints, pReal)
+
+!--------------------------------------------------------------------------------------------------
+! output of geometry
+ write(6,'(a)') ''
+ write(6,'(a)') '#############################################################'
+ write(6,'(a)') 'DAMASK spectral:'
+ write(6,'(a)') 'The spectral method boundary value problem solver for'
+ write(6,'(a)') 'the Duesseldorf Advanced Material Simulation Kit'
+ write(6,'(a)') '#############################################################'
+ write(6,'(a)') 'geometry file: ',trim(geometryFile)
+ write(6,'(a)') '============================================================='
+ write(6,'(a,3(i12 ))') 'resolution a b c:', res
+ write(6,'(a,3(f12.5))') 'dimension x y z:', geomdim
+ write(6,'(a,i5)') 'homogenization: ',homog
+ write(6,'(a)') '#############################################################'
+ write(6,'(a)') 'loadcase file: ',trim(loadCaseFile)
+
+!--------------------------------------------------------------------------------------------------
+! consistency checks and output of load case
+ bc(1)%followFormerTrajectory = .false. ! cannot guess along trajectory for first inc of first loadcase
+ errorID = 0_pInt
+ do loadcase = 1_pInt, N_Loadcases
+ write (loadcase_string, '(i6)' ) loadcase
+
+ write(6,'(a)') '============================================================='
+ write(6,'(a,i6)') 'loadcase: ', loadcase
+
+ if (.not. bc(loadcase)%followFormerTrajectory) write(6,'(a)') 'drop guessing along trajectory'
+ if (bc(loadcase)%velGradApplied) then
+ do j = 1_pInt, 3_pInt
+ if (any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .true.) .and. &
+ any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .false.)) errorID = 832_pInt ! each row should be either fully or not at all defined
+ enddo
+ write(6,'(a)')'velocity gradient:'
+ else
+ write(6,'(a)')'deformation gradient rate:'
+ endif
+ write (6,'(3(3(f12.7,1x)/))',advance='no') merge(math_transpose33(bc(loadcase)%deformation),&
+ reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskDeformation))
+ write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') ' stress / GPa:',&
+ 1e-9_pReal*merge(math_transpose33(bc(loadcase)%stress),&
+ reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskStress))
+ if (any(bc(loadcase)%rotation /= math_I3)) &
+ write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',&
+ math_transpose33(bc(loadcase)%rotation)
+ write(6,'(a,f12.6)') 'temperature:', bc(loadcase)%temperature
+ write(6,'(a,f12.6)') 'time: ', bc(loadcase)%time
+ write(6,'(a,i5)') 'increments: ', bc(loadcase)%incs
+ write(6,'(a,i5)') 'output frequency: ', bc(loadcase)%outputfrequency
+ write(6,'(a,i5)') 'restart frequency: ', bc(loadcase)%restartfrequency
+
+ if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 831_pInt ! exclusive or masking only
+ if (any(bc(loadcase)%maskStress .and. transpose(bc(loadcase)%maskStress) .and. &
+ reshape([ .false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false.],[ 3,3]))) &
+ errorID = 838_pInt ! no rotation is allowed by stress BC
+ if (any(abs(math_mul33x33(bc(loadcase)%rotation,math_transpose33(bc(loadcase)%rotation))&
+ -math_I3) > reshape(spread(rotation_tol,1,9),[ 3,3]))&
+ .or. abs(math_det33(bc(loadcase)%rotation)) > 1.0_pReal + rotation_tol)&
+ errorID = 846_pInt ! given rotation matrix contains strain
+ if (bc(loadcase)%time < 0.0_pReal) errorID = 834_pInt ! negative time increment
+ if (bc(loadcase)%incs < 1_pInt) errorID = 835_pInt ! non-positive incs count
+ if (bc(loadcase)%outputfrequency < 1_pInt) errorID = 836_pInt ! non-positive result frequency
+ if (errorID > 0_pInt) call IO_error(error_ID = errorID, ext_msg = loadcase_string)
+ enddo
+!##################################################################################################
+! Loop over loadcases defined in the loadcase file
+!##################################################################################################
+ do loadcase = 1_pInt, N_Loadcases
+ time0 = time ! loadcase start time
+ if (bc(loadcase)%followFormerTrajectory .and. &
+ (restartInc < totalIncsCounter .or. &
+ restartInc > totalIncsCounter+bc(loadcase)%incs) ) then ! continue to guess along former trajectory where applicable
+ guessmode = 1.0_pReal
+ else
+ guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! arrays for mixed boundary conditions
+ mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
+ mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
+ size_reduced = int(count(bc(loadcase)%maskStressVector), pInt)
+ allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
+ allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
+
+!##################################################################################################
+! loop oper incs defined in input file for current loadcase
+!##################################################################################################
+ do inc = 1_pInt, bc(loadcase)%incs
+ totalIncsCounter = totalIncsCounter + 1_pInt
+
+!--------------------------------------------------------------------------------------------------
+! forwarding time
+ timeinc_old = timeinc
+ if (bc(loadcase)%logscale == 0_pInt) then ! linear scale
+ timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
+ else
+ if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
+ if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
+ timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
+ else ! not-1st inc of 1st loadcase of logarithmic scale
+ timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
+ endif
+ else ! not-1st loadcase of logarithmic scale
+ timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
+ real(bc(loadcase)%incs ,pReal))&
+ -(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
+ real(bc(loadcase)%incs ,pReal)) )
+ endif
+ endif
+ time = time + timeinc
+
+ if(totalIncsCounter >= restartInc) then ! do calculations (otherwise just forwarding)
+ if (bc(loadcase)%velGradApplied) then ! calculate deltaF_aim from given L and current F
+ deltaF_aim = timeinc * mask_defgrad * math_mul33x33(bc(loadcase)%deformation, F_aim)
+ else ! deltaF_aim = fDot *timeinc where applicable
+ deltaF_aim = timeinc * mask_defgrad * bc(loadcase)%deformation
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! winding forward of deformation aim in loadcase system
+ temp33_Real = F_aim
+ F_aim = F_aim &
+ + guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
+ + deltaF_aim
+ F_aim_lastInc = temp33_Real
+
+!--------------------------------------------------------------------------------------------------
+! update local deformation gradient and coordinates
+ deltaF_aim = math_rotate_backward33(deltaF_aim,bc(loadcase)%rotation)
+ call
+
+ call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,bc(loadcase)%rotation),& ! calculate current coordinates
+ 1.0_pReal,F_lastInc,coordinates)
+
+!--------------------------------------------------------------------------------------------------
+! calculate reduced compliance
+ if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
+ C_lastInc = math_rotate_forward3333(C,bc(loadcase)%rotation) ! calculate stiffness from former inc
+ temp99_Real = math_Plain3333to99(C_lastInc)
+ k = 0_pInt ! build reduced stiffness
+ do n = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(n)) then
+ k = k + 1_pInt
+ j = 0_pInt
+ do m = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(m)) then
+ j = j + 1_pInt
+ c_reduced(k,j) = temp99_Real(n,m)
+ endif; enddo; endif; enddo
+ call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
+ if(errmatinv) call IO_error(error_ID=400_pInt)
+ temp99_Real = 0.0_pReal ! build full compliance
+ k = 0_pInt
+ do n = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(n)) then
+ k = k + 1_pInt
+ j = 0_pInt
+ do m = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(m)) then
+ j = j + 1_pInt
+ temp99_Real(n,m) = s_reduced(k,j)
+ endif; enddo; endif; enddo
+ S_lastInc = (math_Plain99to3333(temp99_Real))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! report begin of new increment
+ write(6,'(a)') '##################################################################'
+ write(6,'(A,I5.5,A,es12.5)') 'Increment ', totalIncsCounter, ' Time ',time
+
+ guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
+ iter = 0_pInt
+ err_div = huge(err_div_tol) ! go into loop
+
+converged = solution(mySolver,ForwardFields(solver,deltaF_aim,timeinc/timeinc_old,guessmode))
+
+ CPFEM_mode = 1_pInt ! winding forward
+ C = C * wgt
+ write(6,'(a)') ''
+ write(6,'(a)') '=================================================================='
+ if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' NOT converged'
+ notConvergedCounter = notConvergedCounter + 1_pInt
+ else
+ convergedCounter = convergedCounter + 1_pInt
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' converged'
+ endif
+
+ if (mod(inc,bc(loadcase)%outputFrequency) == 0_pInt) then ! at output frequency
+ write(6,'(a)') ''
+ write(6,'(a)') '... writing results to file ......................................'
+ write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
+ flush(538)
+ endif
+
+ if( bc(loadcase)%restartFrequency > 0_pInt .and. &
+ mod(inc,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
+ restartInc=totalIncsCounter
+ restartWrite = .true.
+ write(6,'(a)') 'writing converged results for restart'
+ call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F)) ! writing deformation gradient field to file
+ write (777,rec=1) F
+ close (777)
+ call IO_write_jobBinaryFile(777,'C',size(C))
+ write (777,rec=1) C
+ close(777)
+ endif
+
+ endif ! end calculation/forwarding
+ enddo ! end looping over incs in current loadcase
+ deallocate(c_reduced)
+ deallocate(s_reduced)
+ enddo ! end looping over loadcases
+ write(6,'(a)') ''
+ write(6,'(a)') '##################################################################'
+ write(6,'(i6.6,a,i6.6,a,f5.1,a)') convergedCounter, ' out of ', &
+ notConvergedCounter + convergedCounter, ' (', &
+ real(convergedCounter, pReal)/&
+ real(notConvergedCounter + convergedCounter,pReal)*100.0_pReal, &
+ ' %) increments converged!'
+ close(538)
+ if (notConvergedCounter > 0_pInt) call quit(3_pInt)
+ call quit(0_pInt)
+end program DAMASK_spectral
diff --git a/code/DAMASK_spectralSolver.f90 b/code/DAMASK_spectralSolver.f90
new file mode 100644
index 000000000..082f8e5de
--- /dev/null
+++ b/code/DAMASK_spectralSolver.f90
@@ -0,0 +1,924 @@
+! Copyright 2012 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 .
+!
+!##################################################################################################
+!* $Id$
+!##################################################################################################
+! Material subroutine for BVP solution using spectral method
+!
+! Run 'DAMASK_spectral.exe --help' to get usage hints
+!
+! written by P. Eisenlohr,
+! F. Roters,
+! L. Hantcherli,
+! W.A. Counts,
+! D.D. Tjahjanto,
+! C. Kords,
+! M. Diehl,
+! R. Lebensohn
+!
+! MPI fuer Eisenforschung, Duesseldorf
+
+#include "spectral_quit.f90"
+
+program DAMASK_spectral
+ use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
+
+ use DAMASK_interface, only: &
+ DAMASK_interface_init, &
+ loadCaseFile, &
+ geometryFile, &
+ getSolverWorkingDirectoryName, &
+ getSolverJobName, &
+ appendToOutFile
+
+ use prec, only: &
+ pInt, &
+ pReal, &
+ DAMASK_NaN
+
+ use IO, only: &
+ IO_isBlank, &
+ IO_open_file, &
+ IO_stringPos, &
+ IO_stringValue, &
+ IO_floatValue, &
+ IO_intValue, &
+ IO_error, &
+ IO_lc, &
+ IO_read_jobBinaryFile, &
+ IO_write_jobBinaryFile
+
+ use debug, only: &
+ debug_level, &
+ debug_spectral, &
+ debug_levelBasic, &
+ debug_spectralDivergence, &
+ debug_spectralRestart, &
+ debug_spectralFFTW, &
+ debug_reset, &
+ debug_info
+
+ use math
+
+ use mesh, only : &
+ mesh_spectral_getResolution, &
+ mesh_spectral_getDimension, &
+ mesh_spectral_getHomogenization
+
+ use CPFEM, only: &
+ CPFEM_general, &
+ CPFEM_initAll
+
+ use FEsolving, only: &
+ restartWrite, &
+ restartInc
+
+ use numerics, only: &
+ err_div_tol, &
+ err_stress_tolrel, &
+ err_stress_tolabs, &
+ rotation_tol, &
+ itmax,&
+ itmin, &
+ memory_efficient, &
+ divergence_correction, &
+ DAMASK_NumThreadsInt, &
+ fftw_planner_flag, &
+ fftw_timelimit
+
+ use homogenization, only: &
+ materialpoint_sizeResults, &
+ materialpoint_results
+
+ implicit none
+
+#ifdef PETSC
+#include
+#include
+#include
+#include
+#include
+#endif
+!--------------------------------------------------------------------------------------------------
+! variables related to information from load case and geom file
+ real(pReal), dimension(9) :: &
+ temp_valueVector !> temporarily from loadcase file when reading in tensors
+ logical, dimension(9) :: &
+ temp_maskVector !> temporarily from loadcase file when reading in tensors
+ integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
+ (1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
+ 1_pInt, & ! dropguessing
+ maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
+ myUnit = 234_pInt
+ integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
+
+ integer(pInt) :: &
+ N_l = 0_pInt, &
+ N_t = 0_pInt, &
+ N_n = 0_pInt, &
+ N_Fdot = 0_pInt, &
+ Npoints,& ! number of Fourier points
+ homog, & ! homogenization scheme used
+ res1_red ! to store res(1)/2 +1
+
+ character(len=1024) :: &
+ line
+
+ type bc_type
+ real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
+ stress = 0.0_pReal, & ! stress BC (if applicable)
+ rotation = math_I3 ! rotation of BC (if applicable)
+ real(pReal) :: time = 0.0_pReal, & ! length of increment
+ temperature = 300.0_pReal ! isothermal starting conditions
+ integer(pInt) :: incs = 0_pInt, & ! number of increments
+ outputfrequency = 1_pInt, & ! frequency of result writes
+ restartfrequency = 0_pInt, & ! frequency of restart writes
+ logscale = 0_pInt ! linear/logaritmic time inc flag
+ logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
+ velGradApplied = .false. ! decide wether velocity gradient or fdot is given
+ logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
+ maskStress = .false. ! mask of stress boundary conditions
+ logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
+ end type
+
+ type(bc_type), allocatable, dimension(:) :: bc
+
+
+ real(pReal) :: wgt
+ real(pReal), dimension(3) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal ! physical dimension of volume element per direction
+ integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
+
+!--------------------------------------------------------------------------------------------------
+! stress, stiffness and compliance average etc.
+ real(pReal), dimension(3,3) :: &
+ P_av, &
+ F_aim = math_I3, &
+ F_aim_lastInc = math_I3, &
+ mask_stress, &
+ mask_defgrad, &
+ deltaF_aim, &
+ F_aim_lab, &
+ F_aim_lab_lastIter, &
+ P_av_lab
+
+ real(pReal), dimension(3,3,3,3) :: &
+ dPdF, &
+ C_ref = 0.0_pReal, &
+ C = 0.0_pReal, &
+ S_lastInc, &
+ C_lastInc ! stiffness and compliance
+
+ real(pReal), dimension(6) :: sigma ! cauchy stress
+ real(pReal), dimension(6,6) :: dsde
+ real(pReal), dimension(9,9) :: temp99_Real ! compliance and stiffness in matrix notation
+ real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
+ integer(pInt) :: size_reduced = 0_pInt ! number of stress BCs
+
+!--------------------------------------------------------------------------------------------------
+! pointwise data
+ type(C_PTR) :: tensorField ! field in real an fourier space
+ real(pReal), dimension(:,:,:,:,:), pointer :: P_real, deltaF_real ! field in real space (pointer)
+
+ complex(pReal), dimension(:,:,:,:,:), pointer :: P_fourier,deltaF_fourier ! field in fourier space (pointer)
+
+ real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc
+ real(pReal), dimension(:,:,:,:), allocatable :: coordinates
+ real(pReal), dimension(:,:,:), allocatable :: temperature
+
+!--------------------------------------------------------------------------------------------------
+! variables storing information for spectral method and FFTW
+ type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
+ real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
+ real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
+ real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
+ integer(pInt), dimension(3) :: k_s
+
+!--------------------------------------------------------------------------------------------------
+! loop variables, convergence etc.
+ real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
+ real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
+ real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
+ complex(pReal), dimension(3) :: temp3_Complex
+ complex(pReal), dimension(3,3) :: temp33_Complex
+ real(pReal), dimension(3,3) :: temp33_Real
+ integer(pInt) :: i, j, k, l, m, n, p, errorID
+ integer(pInt) :: N_Loadcases, loadcase = 0_pInt, inc, iter, ielem, CPFEM_mode=1_pInt, &
+ ierr, totalIncsCounter = 0_pInt,&
+ notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
+ logical :: errmatinv
+ real(pReal) :: defgradDet
+ character(len=6) :: loadcase_string
+
+!--------------------------------------------------------------------------------------------------
+!variables controlling debugging
+ logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
+
+!--------------------------------------------------------------------------------------------------
+!variables for additional output due to general debugging
+ real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
+
+!--------------------------------------------------------------------------------------------------
+! variables for additional output of divergence calculations
+ type(C_PTR) :: divergence, plan_divergence
+ real(pReal), dimension(:,:,:,:), pointer :: divergence_real
+ complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
+ real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
+ real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
+ err_div_max, err_real_div_max
+
+!--------------------------------------------------------------------------------------------------
+! variables for debugging fft using a scalar field
+ type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
+ plan_scalarField_forth, plan_scalarField_back
+ complex(pReal), dimension(:,:,:), pointer :: scalarField_real
+ complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
+ integer(pInt) :: row, column
+
+!##################################################################################################
+! reading of information from load case file and geometry file
+!##################################################################################################
+#ifdef PETSC
+ integer :: ierr_psc
+ call PetscInitialize(PETSC_NULL_CHARACTER, ierr_psc)
+#endif
+ call DAMASK_interface_init
+ write(6,'(a)') ''
+ write(6,'(a)') ' <<<+- DAMASK_spectral init -+>>>'
+ write(6,'(a)') ' $Id$'
+#include "compilation_info.f90"
+ write(6,'(a)') ''
+
+!--------------------------------------------------------------------------------------------------
+! debugging parameters
+ debugGeneral = iand(debug_level(debug_spectral),debug_levelBasic) /= 0
+ debugDivergence = iand(debug_level(debug_spectral),debug_spectralDivergence) /= 0
+ debugRestart = iand(debug_level(debug_spectral),debug_spectralRestart) /= 0
+ debugFFTW = iand(debug_level(debug_spectral),debug_spectralFFTW) /= 0
+
+!##################################################################################################
+! initialization
+!##################################################################################################
+
+ allocate (F ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
+ allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
+ allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
+ allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
+ allocate (temperature( res(1), res(2),res(3)), source = bc(1)%temperature) ! start out isothermally
+ tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
+ call c_f_pointer(tensorField, P_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
+ call c_f_pointer(tensorField, deltaF_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
+ call c_f_pointer(tensorField, P_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
+ call c_f_pointer(tensorField, deltaF_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
+
+!--------------------------------------------------------------------------------------------------
+! general initialization of fftw (see manual on fftw.org for more details)
+ if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=808_pInt) ! check for correct precision in C
+!$ if(DAMASK_NumThreadsInt > 0_pInt) then
+!$ ierr = fftw_init_threads()
+!$ if (ierr == 0_pInt) call IO_error(error_ID = 809_pInt)
+!$ call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
+!$ endif
+ call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
+
+!--------------------------------------------------------------------------------------------------
+! creating plans
+ plan_stress = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
+ P_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
+ 1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
+ P_fourier,[ res(3),res(2) ,res1_red],&
+ 1, res(3)*res(2)* res1_red,fftw_planner_flag)
+
+ plan_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
+ deltaF_fourier,[ res(3),res(2) ,res1_red],&
+ 1, res(3)*res(2)* res1_red,&
+ deltaF_real,[ res(3),res(2) ,res(1)+2_pInt],&
+ 1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
+
+!--------------------------------------------------------------------------------------------------
+! depending on (debug) options, allocate more memory and create additional plans
+ if (debugDivergence) then
+ divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
+ call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
+ call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
+ allocate (divergence_post(res(1),res(2),res(3),3)); divergence_post = 0.0_pReal
+ plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
+ divergence_fourier,[ res(3),res(2) ,res1_red],&
+ 1, res(3)*res(2)* res1_red,&
+ divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
+ 1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
+ endif
+
+ if (debugFFTW) then
+ scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
+ scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T))
+ call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)])
+ call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)])
+ plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
+ scalarField_real,scalarField_fourier,-1,fftw_planner_flag)
+ plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
+ scalarField_fourier,scalarField_real,+1,fftw_planner_flag)
+ endif
+
+ if (debugGeneral) write(6,'(a)') 'FFTW initialized'
+
+!--------------------------------------------------------------------------------------------------
+! calculation of discrete angular frequencies, ordered as in FFTW (wrap around)
+ if (divergence_correction) then
+ do i = 1_pInt, 3_pInt
+ if (i /= minloc(geomdim,1) .and. i /= maxloc(geomdim,1)) virt_dim = geomdim/geomdim(i)
+ enddo
+ else
+ virt_dim = geomdim
+ endif
+
+ do k = 1_pInt, res(3)
+ k_s(3) = k - 1_pInt
+ if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
+ do j = 1_pInt, res(2)
+ k_s(2) = j - 1_pInt
+ if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
+ do i = 1_pInt, res1_red
+ k_s(1) = i - 1_pInt
+ xi(1:3,i,j,k) = real(k_s, pReal)/virt_dim
+ enddo; enddo; enddo
+
+!--------------------------------------------------------------------------------------------------
+! in case of no restart get reference material stiffness and init fields to no deformation
+ if (restartInc == 1_pInt) then
+ ielem = 0_pInt
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ F(i,j,k,1:3,1:3) = math_I3
+ F_lastInc(i,j,k,1:3,1:3) = math_I3
+ coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) - geomdim/real(2_pInt*res,pReal)
+ call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
+ 0.0_pReal,ielem,1_pInt,sigma,dsde,P_real(i,j,k,1:3,1:3),dPdF)
+ C = C + dPdF
+ enddo; enddo; enddo
+ C = C * wgt
+ C_ref = C
+ call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
+ write (777,rec=1) C_ref
+ close(777)
+
+!--------------------------------------------------------------------------------------------------
+! restore deformation gradient and stiffness from saved state
+ elseif (restartInc > 1_pInt) then ! using old values from file
+ if (debugRestart) write(6,'(a,i6,a)') 'Reading values of increment ',&
+ restartInc - 1_pInt,' from file'
+ call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
+ trim(getSolverJobName()),size(F))
+ read (777,rec=1) F
+ close (777)
+ F_lastInc = F
+ F_aim = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ F_aim = F_aim + F(i,j,k,1:3,1:3) ! calculating old average deformation
+ enddo; enddo; enddo
+ F_aim = F_aim * wgt
+ F_aim_lastInc = F_aim
+ coordinates = 0.0 ! change it later!!!
+ call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
+ read (777,rec=1) C_ref
+ close (777)
+ call IO_read_jobBinaryFile(777,'C',trim(getSolverJobName()),size(C))
+ read (777,rec=1) C
+ close (777)
+ CPFEM_mode = 2_pInt
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! calculate the gamma operator
+ if(memory_efficient) then ! allocate just single fourth order tensor
+ allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
+ else ! precalculation of gamma_hat field
+ allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source = 0.0_pReal)
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
+ if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
+ temp33_Real = math_inv33(temp33_Real)
+ forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
+ gamma_hat(i,j,k, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
+ endif
+ enddo; enddo; enddo
+ gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! write header of output file
+ if (appendToOutFile) then
+ open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())//'.spectralOut',&
+ form='UNFORMATTED', position='APPEND', status='OLD')
+ else
+ open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())//'.spectralOut',&
+ form='UNFORMATTED',status='REPLACE')
+ write(538) 'load', trim(loadCaseFile)
+ write(538) 'workingdir', trim(getSolverWorkingDirectoryName())
+ write(538) 'geometry', trim(geometryFile)
+ write(538) 'resolution', res
+ write(538) 'dimension', geomdim
+ write(538) 'materialpoint_sizeResults', materialpoint_sizeResults
+ write(538) 'loadcases', N_Loadcases
+ write(538) 'frequencies', bc(1:N_Loadcases)%outputfrequency ! one entry per loadcase
+ write(538) 'times', bc(1:N_Loadcases)%time ! one entry per loadcase
+ write(538) 'logscales', bc(1:N_Loadcases)%logscale
+ write(538) 'increments', bc(1:N_Loadcases)%incs ! one entry per loadcase
+ write(538) 'startingIncrement', restartInc - 1_pInt ! start with writing out the previous inc
+ write(538) 'eoh' ! end of header
+ write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! initial (non-deformed or read-in) results
+ if (debugGeneral) write(6,'(a)') 'Header of result file written out'
+ endif
+
+
+!##################################################################################################
+! Loop over loadcases defined in the loadcase file
+!##################################################################################################
+ do loadcase = 1_pInt, N_Loadcases
+ time0 = time ! loadcase start time
+ if (bc(loadcase)%followFormerTrajectory .and. &
+ (restartInc < totalIncsCounter .or. &
+ restartInc > totalIncsCounter+bc(loadcase)%incs) ) then ! continue to guess along former trajectory where applicable
+ guessmode = 1.0_pReal
+ else
+ guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! arrays for mixed boundary conditions
+ mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
+ mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
+ size_reduced = int(count(bc(loadcase)%maskStressVector), pInt)
+ allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
+ allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
+
+!##################################################################################################
+! loop oper incs defined in input file for current loadcase
+!##################################################################################################
+ do inc = 1_pInt, bc(loadcase)%incs
+ totalIncsCounter = totalIncsCounter + 1_pInt
+
+!--------------------------------------------------------------------------------------------------
+! forwarding time
+ timeinc_old = timeinc
+ if (bc(loadcase)%logscale == 0_pInt) then ! linear scale
+ timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
+ else
+ if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
+ if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
+ timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
+ else ! not-1st inc of 1st loadcase of logarithmic scale
+ timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
+ endif
+ else ! not-1st loadcase of logarithmic scale
+ timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
+ real(bc(loadcase)%incs ,pReal))&
+ -(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
+ real(bc(loadcase)%incs ,pReal)) )
+ endif
+ endif
+ time = time + timeinc
+
+ if(totalIncsCounter >= restartInc) then ! do calculations (otherwise just forwarding)
+ if (bc(loadcase)%velGradApplied) then ! calculate deltaF_aim from given L and current F
+ deltaF_aim = timeinc * mask_defgrad * math_mul33x33(bc(loadcase)%deformation, F_aim)
+ else ! deltaF_aim = fDot *timeinc where applicable
+ deltaF_aim = timeinc * mask_defgrad * bc(loadcase)%deformation
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! winding forward of deformation aim in loadcase system
+ temp33_Real = F_aim
+ F_aim = F_aim &
+ + guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
+ + deltaF_aim
+ F_aim_lastInc = temp33_Real
+
+!--------------------------------------------------------------------------------------------------
+! update local deformation gradient and coordinates
+ deltaF_aim = math_rotate_backward33(deltaF_aim,bc(loadcase)%rotation)
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ temp33_Real = F(i,j,k,1:3,1:3)
+ F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ + guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
+ *timeinc/timeinc_old &
+ + (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
+ F_lastInc(i,j,k,1:3,1:3) = temp33_Real
+ enddo; enddo; enddo
+ call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,bc(loadcase)%rotation),& ! calculate current coordinates
+ 1.0_pReal,F_lastInc,coordinates)
+
+!--------------------------------------------------------------------------------------------------
+! calculate reduced compliance
+ if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
+ C_lastInc = math_rotate_forward3333(C,bc(loadcase)%rotation) ! calculate stiffness from former inc
+ temp99_Real = math_Plain3333to99(C_lastInc)
+ k = 0_pInt ! build reduced stiffness
+ do n = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(n)) then
+ k = k + 1_pInt
+ j = 0_pInt
+ do m = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(m)) then
+ j = j + 1_pInt
+ c_reduced(k,j) = temp99_Real(n,m)
+ endif; enddo; endif; enddo
+ call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
+ if(errmatinv) call IO_error(error_ID=400_pInt)
+ temp99_Real = 0.0_pReal ! build full compliance
+ k = 0_pInt
+ do n = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(n)) then
+ k = k + 1_pInt
+ j = 0_pInt
+ do m = 1_pInt,9_pInt
+ if(bc(loadcase)%maskStressVector(m)) then
+ j = j + 1_pInt
+ temp99_Real(n,m) = s_reduced(k,j)
+ endif; enddo; endif; enddo
+ S_lastInc = (math_Plain99to3333(temp99_Real))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! report begin of new increment
+ write(6,'(a)') '##################################################################'
+ write(6,'(A,I5.5,A,es12.5)') 'Increment ', totalIncsCounter, ' Time ',time
+
+ guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
+ iter = 0_pInt
+ err_div = huge(err_div_tol) ! go into loop
+
+!##################################################################################################
+! convergence loop (looping over iterations)
+!##################################################################################################
+ do while((iter < itmax .and. (err_div > err_div_tol .or. err_stress > err_stress_tol))&
+ .or. iter < itmin)
+ iter = iter + 1_pInt
+
+!--------------------------------------------------------------------------------------------------
+! report begin of new iteration
+ write(6,'(a)') ''
+ write(6,'(a)') '=================================================================='
+ write(6,'(6(a,i6.6))') 'Loadcase ',loadcase,' Inc. ',inc,'/',bc(loadcase)%incs,&
+ ' @ Iter. ',itmin,' < ',iter,' < ',itmax
+ write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
+ math_transpose33(F_aim)
+ write(6,'(a)') ''
+ write(6,'(a)') '... update stress field P(F) .....................................'
+ if (restartWrite) write(6,'(a)') 'writing restart info for last increment'
+ F_aim_lab_lastIter = math_rotate_backward33(F_aim,bc(loadcase)%rotation)
+!--------------------------------------------------------------------------------------------------
+! evaluate constitutive response
+ ielem = 0_pInt
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ call CPFEM_general(3_pInt,& ! collect cycle
+ coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),F(i,j,k,1:3,1:3), &
+ temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde,&
+ P_real(i,j,k,1:3,1:3),dPdF)
+ enddo; enddo; enddo
+
+ P_real = 0.0_pReal ! needed because of the padding for FFTW
+ C = 0.0_pReal
+ ielem = 0_pInt
+ call debug_reset()
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
+ coordinates(i,j,k,1:3),F_lastInc(i,j,k,1:3,1:3), F(i,j,k,1:3,1:3), & ! others get 2 (saves winding forward effort)
+ temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde, &
+ P_real(i,j,k,1:3,1:3),dPdF)
+ CPFEM_mode = 2_pInt
+ C = C + dPdF
+ enddo; enddo; enddo
+ call debug_info()
+! for test of regridding
+ ! if( bc(loadcase)%restartFrequency > 0_pInt .and. &
+ ! mod(inc-1,bc(loadcase)%restartFrequency) == 0_pInt .and. &
+ ! restartInc/=inc) call quit(-1*(restartInc+1)) ! trigger exit to regrid
+
+!--------------------------------------------------------------------------------------------------
+! copy one component of the stress field to to a single FT and check for mismatch
+ if (debugFFTW) then
+ row = (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
+ column = (mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
+ scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
+ cmplx(P_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! call function to calculate divergence from math (for post processing) to check results
+ if (debugDivergence) &
+ call divergence_fft(res,virt_dim,3_pInt,&
+ P_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
+
+!--------------------------------------------------------------------------------------------------
+! doing the FT because it simplifies calculation of average stress in real space also
+ call fftw_execute_dft_r2c(plan_stress,P_real,P_fourier)
+
+ P_av_lab = real(P_fourier(1,1,1,1:3,1:3),pReal)*wgt
+ P_av = math_rotate_forward33(P_av_lab,bc(loadcase)%rotation)
+ write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
+ math_transpose33(P_av)/1.e6_pReal
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 FT results
+ if (debugFFTW) then
+ call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
+ write(6,'(a,i1,1x,i1)') 'checking FT results of compontent ', row, column
+ write(6,'(a,2(es11.4,1x))') 'max FT relative error = ',&
+ maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
+ P_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
+ scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
+ maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
+ P_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
+ scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! removing highest frequencies
+ P_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+ P_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+ if(res(3)>1_pInt) &
+ P_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+
+!--------------------------------------------------------------------------------------------------
+! stress BC handling
+ if(size_reduced > 0_pInt) then ! calculate stress BC if applied
+ err_stress = maxval(abs(mask_stress * (P_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable)
+ err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
+ write(6,'(a)') ''
+ write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
+ write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
+ ' (',err_stress,' Pa)'
+ F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - bc(loadcase)%stress))) ! residual on given stress components
+ write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
+ else
+ err_stress_tol = +huge(1.0_pReal)
+ endif
+
+ F_aim_lab = math_rotate_backward33(F_aim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
+
+!--------------------------------------------------------------------------------------------------
+! actual spectral method
+ write(6,'(a)') ''
+ write(6,'(a)') '... calculating equilibrium with spectral method .................'
+
+!--------------------------------------------------------------------------------------------------
+! calculating RMS divergence criterion in Fourier space
+ pstress_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av_lab,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
+ math_transpose33(P_av_lab)))))
+ err_div_RMS = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2)
+ do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
+ err_div_RMS = err_div_RMS &
+ + 2.0_pReal*(sum (real(math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
+ xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+ +sum(aimag(math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3),&
+ xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
+ enddo
+ err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ + sum( real(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
+ xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum(aimag(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
+ xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum( real(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
+ xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum(aimag(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
+ xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
+ enddo; enddo
+
+ err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
+
+ if (err_div_RMS/pstress_av_L2 > err_div &
+ .and. err_stress < err_stress_tol &
+ .and. iter >= itmin ) then
+ write(6,'(a)') 'Increasing divergence, stopping iterations'
+ iter = itmax
+ endif
+ err_div = err_div_RMS/pstress_av_L2 ! criterion to stop iterations
+
+!--------------------------------------------------------------------------------------------------
+! calculate additional divergence criteria and report
+ if (debugDivergence) then ! calculate divergence again
+ err_div_max = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
+ temp3_Complex = math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
+ xi(1:3,i,j,k))*TWOPIIMG
+ err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
+ divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
+ enddo; enddo; enddo
+
+ call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
+
+ err_real_div_RMS = 0.0_pReal
+ err_post_div_RMS = 0.0_pReal
+ err_real_div_max = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
+ err_post_div_RMS = err_post_div_RMS + sum(divergence_post(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
+ err_real_div_max = max(err_real_div_max,sum(divergence_real(i,j,k,1:3)**2.0_pReal)) ! max of squared L_2 norm of div(stress) in real space
+ enddo; enddo; enddo
+
+ err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
+ err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
+ err_real_div_max = sqrt( err_real_div_max) ! max in real space
+ err_div_max = sqrt( err_div_max) ! max in Fourier space
+
+ write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
+ write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
+ write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
+ write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
+ write(6,'(a,es11.4)') 'error divergence Real max = ',err_real_div_max
+ endif
+ write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
+ ' (',err_div,' N/m³)'
+
+!--------------------------------------------------------------------------------------------------
+! to the actual spectral method calculation (mechanical equilibrium)
+ if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
+
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
+ if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
+ temp33_Real = math_inv33(temp33_Real)
+ forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
+ gamma_hat(1,1,1, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
+ P_fourier(i,j,k,1:3,1:3))
+ deltaF_fourier(i,j,k,1:3,1:3) = temp33_Complex
+ endif
+ enddo; enddo; enddo
+
+ else ! use precalculated gamma-operator
+
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
+ forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
+ temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
+ P_fourier(i,j,k,1:3,1:3))
+ deltaF_fourier(i,j,k, 1:3,1:3) = temp33_Complex
+ enddo; enddo; enddo
+
+ endif
+ deltaF_fourier(1,1,1,1:3,1:3) = cmplx((F_aim_lab_lastIter - F_aim_lab) & ! assign (negative) average deformation gradient change to zero frequency (real part)
+ * real(Npoints,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 inverse FT results
+ if (debugFFTW) then
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
+ scalarField_fourier(i,j,k) = deltaF_fourier(i,j,k,row,column)
+ enddo; enddo; enddo
+ do i = 0_pInt, res(1)/2_pInt-2_pInt ! unpack fft data for conj complex symmetric part
+ m = 1_pInt
+ do k = 1_pInt, res(3)
+ n = 1_pInt
+ do j = 1_pInt, res(2)
+ scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
+ if(n == 1_pInt) n = res(2) + 1_pInt
+ n = n-1_pInt
+ enddo
+ if(m == 1_pInt) m = res(3) + 1_pInt
+ m = m -1_pInt
+ enddo; enddo
+ endif
+!--------------------------------------------------------------------------------------------------
+! doing the inverse FT
+ call fftw_execute_dft_c2r(plan_correction,deltaF_fourier,deltaF_real) ! back transform of fluct deformation gradient
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 inverse FT results
+ if (debugFFTW) then
+ write(6,'(a,i1,1x,i1)') 'checking iFT results of compontent ', row, column
+ call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
+ write(6,'(a,es11.4)') 'max iFT relative error = ',&
+ maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
+ deltaF_real(1:res(1),1:res(2),1:res(3),row,column))/&
+ real(scalarField_real(1:res(1),1:res(2),1:res(3))))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! calculate some additional output
+ if(debugGeneral) then
+ maxCorrectionSkew = 0.0_pReal
+ maxCorrectionSym = 0.0_pReal
+ temp33_Real = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ maxCorrectionSym = max(maxCorrectionSym,&
+ maxval(math_symmetric33(deltaF_real(i,j,k,1:3,1:3))))
+ maxCorrectionSkew = max(maxCorrectionSkew,&
+ maxval(math_skew33(deltaF_real(i,j,k,1:3,1:3))))
+ temp33_Real = temp33_Real + deltaF_real(i,j,k,1:3,1:3)
+ enddo; enddo; enddo
+ write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
+ maxCorrectionSym*wgt
+ write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
+ maxCorrectionSkew*wgt
+ write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
+ maxval(math_symmetric33(temp33_real))/&
+ maxval(math_skew33(temp33_real))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! updated deformation gradient
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - deltaF_real(i,j,k,1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
+ enddo; enddo; enddo
+
+
+!--------------------------------------------------------------------------------------------------
+! calculate bounds of det(F) and report
+ if(debugGeneral) then
+ defgradDetMax = -huge(1.0_pReal)
+ defgradDetMin = +huge(1.0_pReal)
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ defgradDet = math_det33(F(i,j,k,1:3,1:3))
+ defgradDetMax = max(defgradDetMax,defgradDet)
+ defgradDetMin = min(defgradDetMin,defgradDet)
+ enddo; enddo; enddo
+
+ write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
+ write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
+ endif
+
+ enddo ! end looping when convergency is achieved
+
+ CPFEM_mode = 1_pInt ! winding forward
+ C = C * wgt
+ write(6,'(a)') ''
+ write(6,'(a)') '=================================================================='
+ if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' NOT converged'
+ notConvergedCounter = notConvergedCounter + 1_pInt
+ else
+ convergedCounter = convergedCounter + 1_pInt
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' converged'
+ endif
+
+ if (mod(inc,bc(loadcase)%outputFrequency) == 0_pInt) then ! at output frequency
+ write(6,'(a)') ''
+ write(6,'(a)') '... writing results to file ......................................'
+ write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
+ flush(538)
+ endif
+
+ if( bc(loadcase)%restartFrequency > 0_pInt .and. &
+ mod(inc,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
+ restartInc=totalIncsCounter
+ restartWrite = .true.
+ write(6,'(a)') 'writing converged results for restart'
+ call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F)) ! writing deformation gradient field to file
+ write (777,rec=1) F
+ close (777)
+ call IO_write_jobBinaryFile(777,'C',size(C))
+ write (777,rec=1) C
+ close(777)
+ endif
+
+ endif ! end calculation/forwarding
+ enddo ! end looping over incs in current loadcase
+ deallocate(c_reduced)
+ deallocate(s_reduced)
+ enddo ! end looping over loadcases
+ write(6,'(a)') ''
+ write(6,'(a)') '##################################################################'
+ write(6,'(i6.6,a,i6.6,a,f5.1,a)') convergedCounter, ' out of ', &
+ notConvergedCounter + convergedCounter, ' (', &
+ real(convergedCounter, pReal)/&
+ real(notConvergedCounter + convergedCounter,pReal)*100.0_pReal, &
+ ' %) increments converged!'
+ close(538)
+ call fftw_destroy_plan(plan_stress); call fftw_destroy_plan(plan_correction)
+ if (debugDivergence) call fftw_destroy_plan(plan_divergence)
+ if (debugFFTW) then
+ call fftw_destroy_plan(plan_scalarField_forth)
+ call fftw_destroy_plan(plan_scalarField_back)
+ endif
+ if (notConvergedCounter > 0_pInt) call quit(3_pInt)
+ call quit(0_pInt)
+end program DAMASK_spectral
diff --git a/code/DAMASK_spectralSolver_Basic.f90 b/code/DAMASK_spectralSolver_Basic.f90
new file mode 100644
index 000000000..008b339b2
--- /dev/null
+++ b/code/DAMASK_spectralSolver_Basic.f90
@@ -0,0 +1,710 @@
+! Copyright 2012 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 .
+!
+!##################################################################################################
+!* $Id$
+!##################################################################################################
+! Material subroutine for BVP solution using spectral method
+!
+! Run 'DAMASK_spectral.exe --help' to get usage hints
+!
+! written by P. Eisenlohr,
+! F. Roters,
+! L. Hantcherli,
+! W.A. Counts,
+! D.D. Tjahjanto,
+! C. Kords,
+! M. Diehl,
+! R. Lebensohn
+!
+! MPI fuer Eisenforschung, Duesseldorf
+
+#include "spectral_quit.f90"
+
+program DAMASK_spectral
+ use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
+
+ use DAMASK_interface, only: &
+ DAMASK_interface_init, &
+ loadCaseFile, &
+ geometryFile, &
+ getSolverWorkingDirectoryName, &
+ getSolverJobName, &
+ appendToOutFile
+
+ use prec, only: &
+ pInt, &
+ pReal, &
+ DAMASK_NaN
+
+ use IO, only: &
+ IO_isBlank, &
+ IO_open_file, &
+ IO_stringPos, &
+ IO_stringValue, &
+ IO_floatValue, &
+ IO_intValue, &
+ IO_error, &
+ IO_lc, &
+ IO_read_jobBinaryFile, &
+ IO_write_jobBinaryFile
+
+ use debug, only: &
+ debug_level, &
+ debug_spectral, &
+ debug_levelBasic, &
+ debug_spectralDivergence, &
+ debug_spectralRestart, &
+ debug_spectralFFTW, &
+ debug_reset, &
+ debug_info
+
+ use math
+
+ use mesh, only : &
+ mesh_spectral_getResolution, &
+ mesh_spectral_getDimension, &
+ mesh_spectral_getHomogenization
+
+ use CPFEM, only: &
+ CPFEM_general, &
+ CPFEM_initAll
+
+ use FEsolving, only: &
+ restartWrite, &
+ restartInc
+
+ use numerics, only: &
+ err_div_tol, &
+ err_stress_tolrel, &
+ err_stress_tolabs, &
+ rotation_tol, &
+ itmax,&
+ itmin, &
+ memory_efficient, &
+ divergence_correction, &
+ DAMASK_NumThreadsInt, &
+ fftw_planner_flag, &
+ fftw_timelimit
+
+ use homogenization, only: &
+ materialpoint_sizeResults, &
+ materialpoint_results
+
+ implicit none
+
+#ifdef PETSC
+#include
+#include
+#include
+#include
+#include
+#endif
+!--------------------------------------------------------------------------------------------------
+! variables related to information from load case and geom file
+ real(pReal), dimension(9) :: &
+ temp_valueVector !> temporarily from loadcase file when reading in tensors
+ logical, dimension(9) :: &
+ temp_maskVector !> temporarily from loadcase file when reading in tensors
+ integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
+ (1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
+ 1_pInt, & ! dropguessing
+ maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
+ myUnit = 234_pInt
+ integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
+
+ integer(pInt) :: &
+ N_l = 0_pInt, &
+ N_t = 0_pInt, &
+ N_n = 0_pInt, &
+ N_Fdot = 0_pInt, &
+ Npoints,& ! number of Fourier points
+ homog, & ! homogenization scheme used
+ res1_red ! to store res(1)/2 +1
+
+ character(len=1024) :: &
+ line
+
+ type bc_type
+ real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
+ stress = 0.0_pReal, & ! stress BC (if applicable)
+ rotation = math_I3 ! rotation of BC (if applicable)
+ real(pReal) :: time = 0.0_pReal, & ! length of increment
+ temperature = 300.0_pReal ! isothermal starting conditions
+ integer(pInt) :: incs = 0_pInt, & ! number of increments
+ outputfrequency = 1_pInt, & ! frequency of result writes
+ restartfrequency = 0_pInt, & ! frequency of restart writes
+ logscale = 0_pInt ! linear/logaritmic time inc flag
+ logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
+ velGradApplied = .false. ! decide wether velocity gradient or fdot is given
+ logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
+ maskStress = .false. ! mask of stress boundary conditions
+ logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
+ end type
+
+ type(bc_type), allocatable, dimension(:) :: bc
+
+
+ real(pReal) :: wgt
+ real(pReal), dimension(3) :: geomdim = 0.0_pReal, virt_dim = 0.0_pReal ! physical dimension of volume element per direction
+ integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
+
+!--------------------------------------------------------------------------------------------------
+! stress, stiffness and compliance average etc.
+ real(pReal), dimension(3,3) :: &
+ P_av, &
+ F_aim = math_I3, &
+ F_aim_lastInc = math_I3, &
+ mask_stress, &
+ mask_defgrad, &
+ deltaF_aim, &
+ F_aim_lab, &
+ F_aim_lab_lastIter, &
+ P_av_lab
+
+ real(pReal), dimension(3,3,3,3) :: &
+ dPdF, &
+ C_ref = 0.0_pReal, &
+ C = 0.0_pReal, &
+ S_lastInc, &
+ C_lastInc ! stiffness and compliance
+
+ real(pReal), dimension(6) :: sigma ! cauchy stress
+ real(pReal), dimension(6,6) :: dsde
+ real(pReal), dimension(9,9) :: temp99_Real ! compliance and stiffness in matrix notation
+ real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
+ integer(pInt) :: size_reduced = 0_pInt ! number of stress BCs
+
+!--------------------------------------------------------------------------------------------------
+! pointwise data
+ type(C_PTR) :: tensorField ! field in real an fourier space
+ real(pReal), dimension(:,:,:,:,:), pointer :: P_real, deltaF_real ! field in real space (pointer)
+
+ complex(pReal), dimension(:,:,:,:,:), pointer :: P_fourier,deltaF_fourier ! field in fourier space (pointer)
+
+ real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc
+ real(pReal), dimension(:,:,:,:), allocatable :: coordinates
+ real(pReal), dimension(:,:,:), allocatable :: temperature
+
+!--------------------------------------------------------------------------------------------------
+! variables storing information for spectral method and FFTW
+ type(C_PTR) :: plan_stress, plan_correction ! plans for fftw
+ real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
+ real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
+ real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
+ integer(pInt), dimension(3) :: k_s
+
+!--------------------------------------------------------------------------------------------------
+! loop variables, convergence etc.
+ real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
+ real(pReal) :: guessmode, err_div, err_stress, err_stress_tol
+ real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
+ complex(pReal), dimension(3) :: temp3_Complex
+ complex(pReal), dimension(3,3) :: temp33_Complex
+ real(pReal), dimension(3,3) :: temp33_Real
+ integer(pInt) :: i, j, k, l, m, n, p, errorID
+ integer(pInt) :: N_Loadcases, loadcase = 0_pInt, inc, iter, ielem, CPFEM_mode=1_pInt, &
+ ierr, totalIncsCounter = 0_pInt,&
+ notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
+ logical :: errmatinv
+ real(pReal) :: defgradDet
+ character(len=6) :: loadcase_string
+
+!--------------------------------------------------------------------------------------------------
+!variables controlling debugging
+ logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
+
+!--------------------------------------------------------------------------------------------------
+!variables for additional output due to general debugging
+ real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
+
+!--------------------------------------------------------------------------------------------------
+! variables for additional output of divergence calculations
+ type(C_PTR) :: divergence, plan_divergence
+ real(pReal), dimension(:,:,:,:), pointer :: divergence_real
+ complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
+ real(pReal), dimension(:,:,:,:), allocatable :: divergence_post
+ real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
+ err_div_max, err_real_div_max
+
+!--------------------------------------------------------------------------------------------------
+! variables for debugging fft using a scalar field
+ type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
+ plan_scalarField_forth, plan_scalarField_back
+ complex(pReal), dimension(:,:,:), pointer :: scalarField_real
+ complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
+ integer(pInt) :: row, column
+
+!##################################################################################################
+! reading of information from load case file and geometry file
+!##################################################################################################
+
+subroutine init
+
+#ifdef PETSC
+ integer :: ierr_psc
+ call PetscInitialize(PETSC_NULL_CHARACTER, ierr_psc)
+#endif
+ call DAMASK_interface_init
+ write(6,'(a)') ''
+ write(6,'(a)') ' <<<+- DAMASK_spectral init -+>>>'
+ write(6,'(a)') ' $Id$'
+#include "compilation_info.f90"
+ write(6,'(a)') ''
+
+
+
+!--------------------------------------------------------------------------------------------------
+! debugging parameters
+ debugGeneral = iand(debug_level(debug_spectral),debug_levelBasic) /= 0
+ debugDivergence = iand(debug_level(debug_spectral),debug_spectralDivergence) /= 0
+ debugRestart = iand(debug_level(debug_spectral),debug_spectralRestart) /= 0
+ debugFFTW = iand(debug_level(debug_spectral),debug_spectralFFTW) /= 0
+
+!##################################################################################################
+! initialization
+!##################################################################################################
+
+ call c_f_pointer(tensorField, P_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
+ call c_f_pointer(tensorField, deltaF_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for a real representation on tensorField
+ call c_f_pointer(tensorField, P_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
+ call c_f_pointer(tensorField, deltaF_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for a complex representation on tensorField
+
+
+!--------------------------------------------------------------------------------------------------
+! creating plans
+ plan_stress = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
+ P_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
+ 1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
+ P_fourier,[ res(3),res(2) ,res1_red],&
+ 1, res(3)*res(2)* res1_red,fftw_planner_flag)
+
+ plan_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
+ deltaF_fourier,[ res(3),res(2) ,res1_red],&
+ 1, res(3)*res(2)* res1_red,&
+ deltaF_real,[ res(3),res(2) ,res(1)+2_pInt],&
+ 1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
+
+
+!--------------------------------------------------------------------------------------------------
+! in case of no restart get reference material stiffness and init fields to no deformation
+ if (restartInc == 1_pInt) then
+ ielem = 0_pInt
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ F(i,j,k,1:3,1:3) = math_I3
+ F_lastInc(i,j,k,1:3,1:3) = math_I3
+ coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) - geomdim/real(2_pInt*res,pReal)
+ call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
+ 0.0_pReal,ielem,1_pInt,sigma,dsde,P_real(i,j,k,1:3,1:3),dPdF)
+ C = C + dPdF
+ enddo; enddo; enddo
+ C = C * wgt
+ C_ref = C
+ call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
+ write (777,rec=1) C_ref
+ close(777)
+
+!--------------------------------------------------------------------------------------------------
+! restore deformation gradient and stiffness from saved state
+ elseif (restartInc > 1_pInt) then ! using old values from file
+ if (debugRestart) write(6,'(a,i6,a)') 'Reading values of increment ',&
+ restartInc - 1_pInt,' from file'
+ call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
+ trim(getSolverJobName()),size(F))
+ read (777,rec=1) F
+ close (777)
+ F_lastInc = F
+ F_aim = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ F_aim = F_aim + F(i,j,k,1:3,1:3) ! calculating old average deformation
+ enddo; enddo; enddo
+ F_aim = F_aim * wgt
+ F_aim_lastInc = F_aim
+ coordinates = 0.0 ! change it later!!!
+ call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
+ read (777,rec=1) C_ref
+ close (777)
+ call IO_read_jobBinaryFile(777,'C',trim(getSolverJobName()),size(C))
+ read (777,rec=1) C
+ close (777)
+ CPFEM_mode = 2_pInt
+ endif
+
+end subroutine init
+
+
+ subroutine solution(guessmode, F_aim,F_aimLastInc, BC_stress, mask_stress)
+!--------------------------------------------------------------------------------------------------
+! update local deformation gradient and coordinates
+
+ deltaF_aim = math_rotate_backward33(deltaF_aim,bc(loadcase)%rotation)
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ temp33_Real = F(i,j,k,1:3,1:3)
+ F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ + guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
+ *timeinc/timeinc_old &
+ + (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
+ F_lastInc(i,j,k,1:3,1:3) = temp33_Real
+ enddo; enddo; enddo
+ call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,bc(loadcase)%rotation),& ! calculate current coordinates
+ 1.0_pReal,F_lastInc,coordinates)
+
+
+
+ guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
+ iter = 0_pInt
+ err_div = huge(err_div_tol) ! go into loop
+
+!##################################################################################################
+! convergence loop (looping over iterations)
+!##################################################################################################
+ do while((iter < itmax .and. (err_div > err_div_tol .or. err_stress > err_stress_tol))&
+ .or. iter < itmin)
+ iter = iter + 1_pInt
+
+!--------------------------------------------------------------------------------------------------
+! report begin of new iteration
+ write(6,'(a)') ''
+ write(6,'(a)') '=================================================================='
+ write(6,'(6(a,i6.6))') 'Loadcase ',loadcase,' Inc. ',inc,'/',bc(loadcase)%incs,&
+ ' @ Iter. ',itmin,' < ',iter,' < ',itmax
+ write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
+ math_transpose33(F_aim)
+ write(6,'(a)') ''
+ write(6,'(a)') '... update stress field P(F) .....................................'
+ if (restartWrite) write(6,'(a)') 'writing restart info for last increment'
+ F_aim_lab_lastIter = math_rotate_backward33(F_aim,bc(loadcase)%rotation)
+!--------------------------------------------------------------------------------------------------
+! evaluate constitutive response
+ ielem = 0_pInt
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ call CPFEM_general(3_pInt,& ! collect cycle
+ coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),F(i,j,k,1:3,1:3), &
+ temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde,&
+ P_real(i,j,k,1:3,1:3),dPdF)
+ enddo; enddo; enddo
+
+ P_real = 0.0_pReal ! needed because of the padding for FFTW
+ C = 0.0_pReal
+ ielem = 0_pInt
+ call debug_reset()
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ ielem = ielem + 1_pInt
+ call CPFEM_general(CPFEM_mode,& ! first element in first iteration retains CPFEM_mode 1,
+ coordinates(i,j,k,1:3),F_lastInc(i,j,k,1:3,1:3), F(i,j,k,1:3,1:3), & ! others get 2 (saves winding forward effort)
+ temperature(i,j,k),timeinc,ielem,1_pInt,sigma,dsde, &
+ P_real(i,j,k,1:3,1:3),dPdF)
+ CPFEM_mode = 2_pInt
+ C = C + dPdF
+ enddo; enddo; enddo
+ call debug_info()
+! for test of regridding
+ ! if( bc(loadcase)%restartFrequency > 0_pInt .and. &
+ ! mod(inc-1,bc(loadcase)%restartFrequency) == 0_pInt .and. &
+ ! restartInc/=inc) call quit(-1*(restartInc+1)) ! trigger exit to regrid
+
+!--------------------------------------------------------------------------------------------------
+! copy one component of the stress field to to a single FT and check for mismatch
+ if (debugFFTW) then
+ row = (mod(totalIncsCounter+iter-2_pInt,9_pInt))/3_pInt + 1_pInt ! go through the elements of the tensors, controlled by totalIncsCounter and iter, starting at 1
+ column = (mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
+ scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
+ cmplx(P_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! call function to calculate divergence from math (for post processing) to check results
+ if (debugDivergence) &
+ call divergence_fft(res,virt_dim,3_pInt,&
+ P_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
+
+!--------------------------------------------------------------------------------------------------
+! doing the FT because it simplifies calculation of average stress in real space also
+ call fftw_execute_dft_r2c(plan_stress,P_real,P_fourier)
+
+ P_av_lab = real(P_fourier(1,1,1,1:3,1:3),pReal)*wgt
+ P_av = math_rotate_forward33(P_av_lab,bc(loadcase)%rotation)
+ write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
+ math_transpose33(P_av)/1.e6_pReal
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 FT results
+ if (debugFFTW) then
+ call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
+ write(6,'(a,i1,1x,i1)') 'checking FT results of compontent ', row, column
+ write(6,'(a,2(es11.4,1x))') 'max FT relative error = ',&
+ maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
+ P_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
+ scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
+ maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
+ P_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
+ scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! removing highest frequencies
+ P_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+ P_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+ if(res(3)>1_pInt) &
+ P_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
+ = cmplx(0.0_pReal,0.0_pReal,pReal)
+
+!--------------------------------------------------------------------------------------------------
+! stress BC handling
+ if(size_reduced > 0_pInt) then ! calculate stress BC if applied
+ err_stress = maxval(abs(mask_stress * (P_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable)
+ err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
+ write(6,'(a)') ''
+ write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
+ write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
+ ' (',err_stress,' Pa)'
+ F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - bc(loadcase)%stress))) ! residual on given stress components
+ write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
+ else
+ err_stress_tol = +huge(1.0_pReal)
+ endif
+
+ F_aim_lab = math_rotate_backward33(F_aim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
+
+!--------------------------------------------------------------------------------------------------
+! actual spectral method
+ write(6,'(a)') ''
+ write(6,'(a)') '... calculating equilibrium with spectral method .................'
+
+!--------------------------------------------------------------------------------------------------
+! calculating RMS divergence criterion in Fourier space
+ pstress_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av_lab,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
+ math_transpose33(P_av_lab)))))
+ err_div_RMS = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2)
+ do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
+ err_div_RMS = err_div_RMS &
+ + 2.0_pReal*(sum (real(math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
+ xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+ +sum(aimag(math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3),&
+ xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
+ enddo
+ err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ + sum( real(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
+ xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum(aimag(math_mul33x3_complex(P_fourier(1 ,j,k,1:3,1:3),&
+ xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum( real(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
+ xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
+ + sum(aimag(math_mul33x3_complex(P_fourier(res1_red,j,k,1:3,1:3),&
+ xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
+ enddo; enddo
+
+ err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
+
+ if (err_div_RMS/pstress_av_L2 > err_div &
+ .and. err_stress < err_stress_tol &
+ .and. iter >= itmin ) then
+ write(6,'(a)') 'Increasing divergence, stopping iterations'
+ iter = itmax
+ endif
+ err_div = err_div_RMS/pstress_av_L2 ! criterion to stop iterations
+
+!--------------------------------------------------------------------------------------------------
+! calculate additional divergence criteria and report
+ if (debugDivergence) then ! calculate divergence again
+ err_div_max = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
+ temp3_Complex = math_mul33x3_complex(P_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
+ xi(1:3,i,j,k))*TWOPIIMG
+ err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
+ divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
+ enddo; enddo; enddo
+
+ call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
+
+ err_real_div_RMS = 0.0_pReal
+ err_post_div_RMS = 0.0_pReal
+ err_real_div_max = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
+ err_post_div_RMS = err_post_div_RMS + sum(divergence_post(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
+ err_real_div_max = max(err_real_div_max,sum(divergence_real(i,j,k,1:3)**2.0_pReal)) ! max of squared L_2 norm of div(stress) in real space
+ enddo; enddo; enddo
+
+ err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
+ err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
+ err_real_div_max = sqrt( err_real_div_max) ! max in real space
+ err_div_max = sqrt( err_div_max) ! max in Fourier space
+
+ write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
+ write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
+ write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
+ write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
+ write(6,'(a,es11.4)') 'error divergence Real max = ',err_real_div_max
+ endif
+ write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
+ ' (',err_div,' N/m³)'
+
+!--------------------------------------------------------------------------------------------------
+! to the actual spectral method calculation (mechanical equilibrium)
+ if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
+
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
+ if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
+ temp33_Real = math_inv33(temp33_Real)
+ forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, p=1_pInt:3_pInt)&
+ gamma_hat(1,1,1, l,m,n,p) = temp33_Real(l,n)*xiDyad(m,p)
+ forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
+ temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
+ P_fourier(i,j,k,1:3,1:3))
+ deltaF_fourier(i,j,k,1:3,1:3) = temp33_Complex
+ endif
+ enddo; enddo; enddo
+
+ else ! use precalculated gamma-operator
+
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
+ forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
+ temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
+ P_fourier(i,j,k,1:3,1:3))
+ deltaF_fourier(i,j,k, 1:3,1:3) = temp33_Complex
+ enddo; enddo; enddo
+
+ endif
+ deltaF_fourier(1,1,1,1:3,1:3) = cmplx((F_aim_lab_lastIter - F_aim_lab) & ! assign (negative) average deformation gradient change to zero frequency (real part)
+ * real(Npoints,pReal),0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 inverse FT results
+ if (debugFFTW) then
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
+ scalarField_fourier(i,j,k) = deltaF_fourier(i,j,k,row,column)
+ enddo; enddo; enddo
+ do i = 0_pInt, res(1)/2_pInt-2_pInt ! unpack fft data for conj complex symmetric part
+ m = 1_pInt
+ do k = 1_pInt, res(3)
+ n = 1_pInt
+ do j = 1_pInt, res(2)
+ scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
+ if(n == 1_pInt) n = res(2) + 1_pInt
+ n = n-1_pInt
+ enddo
+ if(m == 1_pInt) m = res(3) + 1_pInt
+ m = m -1_pInt
+ enddo; enddo
+ endif
+!--------------------------------------------------------------------------------------------------
+! doing the inverse FT
+ call fftw_execute_dft_c2r(plan_correction,deltaF_fourier,deltaF_real) ! back transform of fluct deformation gradient
+
+!--------------------------------------------------------------------------------------------------
+! comparing 1 and 3x3 inverse FT results
+ if (debugFFTW) then
+ write(6,'(a,i1,1x,i1)') 'checking iFT results of compontent ', row, column
+ call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
+ write(6,'(a,es11.4)') 'max iFT relative error = ',&
+ maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
+ deltaF_real(1:res(1),1:res(2),1:res(3),row,column))/&
+ real(scalarField_real(1:res(1),1:res(2),1:res(3))))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! calculate some additional output
+ if(debugGeneral) then
+ maxCorrectionSkew = 0.0_pReal
+ maxCorrectionSym = 0.0_pReal
+ temp33_Real = 0.0_pReal
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ maxCorrectionSym = max(maxCorrectionSym,&
+ maxval(math_symmetric33(deltaF_real(i,j,k,1:3,1:3))))
+ maxCorrectionSkew = max(maxCorrectionSkew,&
+ maxval(math_skew33(deltaF_real(i,j,k,1:3,1:3))))
+ temp33_Real = temp33_Real + deltaF_real(i,j,k,1:3,1:3)
+ enddo; enddo; enddo
+ write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
+ maxCorrectionSym*wgt
+ write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
+ maxCorrectionSkew*wgt
+ write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
+ maxval(math_symmetric33(temp33_real))/&
+ maxval(math_skew33(temp33_real))
+ endif
+
+!--------------------------------------------------------------------------------------------------
+! updated deformation gradient
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - deltaF_real(i,j,k,1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
+ enddo; enddo; enddo
+
+
+!--------------------------------------------------------------------------------------------------
+! calculate bounds of det(F) and report
+ if(debugGeneral) then
+ defgradDetMax = -huge(1.0_pReal)
+ defgradDetMin = +huge(1.0_pReal)
+ do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
+ defgradDet = math_det33(F(i,j,k,1:3,1:3))
+ defgradDetMax = max(defgradDetMax,defgradDet)
+ defgradDetMin = min(defgradDetMin,defgradDet)
+ enddo; enddo; enddo
+
+ write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
+ write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
+ endif
+
+ enddo ! end looping when convergency is achieved
+
+ CPFEM_mode = 1_pInt ! winding forward
+ C = C * wgt
+ write(6,'(a)') ''
+ write(6,'(a)') '=================================================================='
+ if(err_div > err_div_tol .or. err_stress > err_stress_tol) then
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' NOT converged'
+ notConvergedCounter = notConvergedCounter + 1_pInt
+ else
+ convergedCounter = convergedCounter + 1_pInt
+ write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' converged'
+ endif
+
+ if (mod(inc,bc(loadcase)%outputFrequency) == 0_pInt) then ! at output frequency
+ write(6,'(a)') ''
+ write(6,'(a)') '... writing results to file ......................................'
+ write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
+ flush(538)
+ endif
+
+ if( bc(loadcase)%restartFrequency > 0_pInt .and. &
+ mod(inc,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
+ restartInc=totalIncsCounter
+ restartWrite = .true.
+ write(6,'(a)') 'writing converged results for restart'
+ call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F)) ! writing deformation gradient field to file
+ write (777,rec=1) F
+ close (777)
+ call IO_write_jobBinaryFile(777,'C',size(C))
+ write (777,rec=1) C
+ close(777)
+ endif
+
+ endif ! end calculation/forwarding
+ enddo ! end looping over incs in current loadcase
+
diff --git a/code/DAMASK_spectral_AL.f90 b/code/DAMASK_spectral_AL.f90
deleted file mode 100644
index 589ee3635..000000000
--- a/code/DAMASK_spectral_AL.f90
+++ /dev/null
@@ -1,889 +0,0 @@
-! Copyright 2011 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 .
-!
-!##################################################################################################
-!* $Id$
-!##################################################################################################
-! Material subroutine for BVP solution using spectral method
-!
-! Run 'DAMASK_spectral.exe --help' to get usage hints
-!
-! written by P. Eisenlohr,
-! F. Roters,
-! L. Hantcherli,
-! W.A. Counts,
-! D.D. Tjahjanto,
-! C. Kords,
-! M. Diehl,
-! R. Lebensohn
-!
-! MPI fuer Eisenforschung, Duesseldorf
-#include "spectral_quit.f90"
-
-program DAMASK_spectral_AL
- use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment)
-
- use DAMASK_interface, only: &
- DAMASK_interface_init, &
- getLoadcaseName, &
- getSolverWorkingDirectoryName, &
- getSolverJobName, &
- getModelName, &
- inputFileExtension
-
- use prec, only: &
- pInt, &
- pReal, &
- DAMASK_NaN
-
- use IO, only: &
- IO_isBlank, &
- IO_open_file, &
- IO_stringPos, &
- IO_stringValue, &
- IO_floatValue, &
- IO_intValue, &
- IO_error, &
- IO_lc, &
- IO_read_jobBinaryFile, &
- IO_write_jobBinaryFile
-
- use debug, only: &
- debug_level, &
- debug_spectral, &
- debug_levelBasic, &
- debug_spectralDivergence, &
- debug_spectralRestart, &
- debug_spectralFFTW, &
- debug_reset, &
- debug_info
-
- use math
-
- use mesh, only : &
- mesh_spectral_getResolution, &
- mesh_spectral_getDimension, &
- mesh_spectral_getHomogenization
-
- use CPFEM, only: &
- CPFEM_general, &
- CPFEM_initAll
-
- use FEsolving, only: &
- restartWrite, &
- restartInc
-
- use numerics, only: &
- err_stress_tolrel, &
- err_stress_tolabs, &
- rotation_tol, &
- itmax,&
- itmin, &
- memory_efficient, &
- update_gamma, &
- divergence_correction, &
- DAMASK_NumThreadsInt, &
- fftw_planner_flag, &
- fftw_timelimit
-
- use homogenization, only: &
- materialpoint_sizeResults, &
- materialpoint_results
-
- implicit none
-!--------------------------------------------------------------------------------------------------
-! variables to read from load case and geom file
- real(pReal), dimension(9) :: temp_valueVector ! stores information temporarily from loadcase file
- logical, dimension(9) :: temp_maskVector
- integer(pInt), parameter :: maxNchunksLoadcase = (1_pInt + 9_pInt)*3_pInt +& ! deformation, rotation, and stress
- (1_pInt + 1_pInt)*5_pInt +& ! time, (log)incs, temp, restartfrequency, and outputfrequency
- 1_pInt, & ! dropguessing
- maxNchunksGeom = 7_pInt, & ! 4 identifiers, 3 values
- myUnit = 234_pInt
- integer(pInt), dimension(1_pInt + maxNchunksLoadcase*2_pInt) :: positions ! this is longer than needed for geometry parsing
- integer(pInt) :: &
- N_l = 0_pInt,&
- N_t = 0_pInt,&
- N_n = 0_pInt,&
- N_Fdot = 0_pInt
- character(len=1024) :: line
-
-!--------------------------------------------------------------------------------------------------
-! variable storing information from load case file
- type bc_type
- real(pReal), dimension (3,3) :: deformation = 0.0_pReal, & ! applied velocity gradient or time derivative of deformation gradient
- P = 0.0_pReal, & ! stress BC (if applicable)
- rotation = math_I3 ! rotation of BC (if applicable)
- real(pReal) :: time = 0.0_pReal, & ! length of increment
- temperature = 300.0_pReal ! isothermal starting conditions
- integer(pInt) :: incs = 0_pInt, & ! number of increments
- outputfrequency = 1_pInt, & ! frequency of result writes
- restartfrequency = 0_pInt, & ! frequency of restart writes
- logscale = 0_pInt ! linear/logaritmic time inc flag
- logical :: followFormerTrajectory = .true., & ! follow trajectory of former loadcase
- velGradApplied = .false. ! decide wether velocity gradient or fdot is given
- logical, dimension(3,3) :: maskDeformation = .false., & ! mask of deformation boundary conditions
- maskStress = .false. ! mask of stress boundary conditions
- logical, dimension(9) :: maskStressVector = .false. ! linear mask of boundary conditions
- end type
-
- type(bc_type), allocatable, dimension(:) :: bc
-
-!--------------------------------------------------------------------------------------------------
-! variables storing information from geom file
- real(pReal) :: wgt
- real(pReal), dimension(3) :: geomdim = 0.0_pReal ! physical dimension of volume element per direction
- integer(pInt) :: Npoints,& ! number of Fourier points
- homog ! homogenization scheme used
- integer(pInt), dimension(3) :: res = 1_pInt ! resolution (number of Fourier points) in each direction
- integer(pInt) :: res1_red ! to store res(1)/2 +1
-
-!--------------------------------------------------------------------------------------------------
-! stress, stiffness and compliance average etc.
- real(pReal), dimension(3,3) :: P_av = 0.0_pReal, &
- F_aim = math_I3, F_aim_lastInc = math_I3, lambda_av, &
- mask_stress, mask_defgrad, deltaF, F_star_av, &
- F_aim_lab ! quantities rotated to other coordinate system
- real(pReal), dimension(3,3,3,3) :: C_inc0, C=0.0_pReal, S_inc0, S_lastInc, C_lastInc ! stiffness and compliance
- real(pReal), dimension(6) :: sigma ! cauchy stress
- real(pReal), dimension(6,6) :: dsde ! small strain stiffness
- real(pReal), dimension(9,9) :: s_prev99, c_prev99 ! compliance and stiffness in matrix notation
- real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
- integer(pInt) :: size_reduced = 0_pInt ! number of stress BCs
-
-!--------------------------------------------------------------------------------------------------
-! pointwise data
- type(C_PTR) :: tensorField ! fields in real an fourier space
- real(pReal), dimension(:,:,:,:,:), pointer :: tau_real, F_real ! fields in real space (pointer)
- complex(pReal), dimension(:,:,:,:,:), pointer :: tau_fourier, F_fourier ! fields in fourier space (pointer)
- real(pReal), dimension(:,:,:,:,:), allocatable :: F_lastInc, lambda, P, F_star
- real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: dPdF
- real(pReal), dimension(:,:,:,:), allocatable :: coordinates
- real(pReal), dimension(:,:,:), allocatable :: temperature
-
-!--------------------------------------------------------------------------------------------------
-! variables storing information for spectral method and FFTW
- type(C_PTR) :: plan_correction, plan_tau ! plans for fftw
- real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
- real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
- real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
- integer(pInt), dimension(3) :: k_s
-
-!--------------------------------------------------------------------------------------------------
-! loop variables, convergence etc.
- real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc = 1.0_pReal, timeinc_old = 0.0_pReal ! elapsed time, begin of interval, time interval
- real(pReal) :: guessmode, err_stress, err_stress_tol, err_f, err_p, err_crit, &
- err_f_point, err_p_point, err_nl, err_nl_point
- real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
- complex(pReal), dimension(3,3) :: temp33_Complex
- real(pReal), dimension(3,3) :: temp33_Real
- integer(pInt) :: i, j, k, l, u, v, w, errorID = 0_pInt, ierr
- integer(pInt) :: N_Loadcases, loadcase, inc, iter, ielem, CPFEM_mode, guesses, guessmax=10_pInt,&
- totalIncsCounter = 0_pInt,notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
- logical :: errmatinv, callCPFEM
- character(len=6) :: loadcase_string
-
-!--------------------------------------------------------------------------------------------------
-!variables controlling debugging
- logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW
-
-!##################################################################################################
-! reading of information from load case file and geometry file
-!##################################################################################################
- open (6, encoding='UTF-8')
- call DAMASK_interface_init
-
- write(6,'(a)') ''
- write(6,'(a)') ' <<<+- DAMASK_spectral_AL init -+>>>'
- write(6,'(a)') ' $Id$'
-#include "compilation_info.f90"
- write(6,'(a)') ' Working Directory: ',trim(getSolverWorkingDirectoryName())
- write(6,'(a)') ' Solver Job Name: ',trim(getSolverJobName())
- write(6,'(a)') ''
-!--------------------------------------------------------------------------------------------------
-! reading the load case file and allocate data structure containing load cases
- call IO_open_file(myUnit,getLoadcaseName())
- rewind(myUnit)
- do
- read(myUnit,'(a1024)',END = 100) line
- if (IO_isBlank(line)) cycle ! skip empty lines
- positions = IO_stringPos(line,maxNchunksLoadcase)
- do i = 1_pInt, maxNchunksLoadcase, 1_pInt ! reading compulsory parameters for loadcase
- select case (IO_lc(IO_stringValue(line,positions,i)))
- case('l','velocitygrad','velgrad','velocitygradient')
- N_l = N_l + 1_pInt
- case('fdot','dotf')
- N_Fdot = N_Fdot + 1_pInt
- case('t','time','delta')
- N_t = N_t + 1_pInt
- case('n','incs','increments','steps','logincs','logsteps')
- N_n = N_n + 1_pInt
- end select
- enddo ! count all identifiers to allocate memory and do sanity check
- enddo
-
-100 N_Loadcases = N_n
- if ((N_l + N_Fdot /= N_n) .or. (N_n /= N_t)) & ! sanity check
- call IO_error(error_ID=837_pInt,ext_msg = trim(getLoadcaseName())) ! error message for incomplete loadcase
- allocate (bc(N_Loadcases))
-
-!--------------------------------------------------------------------------------------------------
-! reading the load case and assign values to the allocated data structure
- rewind(myUnit)
- loadcase = 0_pInt
- do
- read(myUnit,'(a1024)',END = 101) line
- if (IO_isBlank(line)) cycle ! skip empty lines
- loadcase = loadcase + 1_pInt
- positions = IO_stringPos(line,maxNchunksLoadcase)
- do j = 1_pInt,maxNchunksLoadcase
- select case (IO_lc(IO_stringValue(line,positions,j)))
- case('fdot','dotf','l','velocitygrad','velgrad','velocitygradient') ! assign values for the deformation BC matrix
- bc(loadcase)%velGradApplied = &
- (IO_lc(IO_stringValue(line,positions,j)) == 'l'.or. & ! in case of given L, set flag to true
- IO_lc(IO_stringValue(line,positions,j)) == 'velocitygrad'.or.&
- IO_lc(IO_stringValue(line,positions,j)) == 'velgrad'.or.&
- IO_lc(IO_stringValue(line,positions,j)) == 'velocitygradient')
- temp_valueVector = 0.0_pReal
- temp_maskVector = .false.
- forall (k = 1_pInt:9_pInt) temp_maskVector(k) = IO_stringValue(line,positions,j+k) /= '*'
- do k = 1_pInt,9_pInt
- if (temp_maskVector(k)) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
- enddo
- bc(loadcase)%maskDeformation = transpose(reshape(temp_maskVector,[ 3,3]))
- bc(loadcase)%deformation = math_plain9to33(temp_valueVector)
- case('p','pk1','piolakirchhoff','stress')
- temp_valueVector = 0.0_pReal
- forall (k = 1_pInt:9_pInt) bc(loadcase)%maskStressVector(k) =&
- IO_stringValue(line,positions,j+k) /= '*'
- do k = 1_pInt,9_pInt
- if (bc(loadcase)%maskStressVector(k)) temp_valueVector(k) =&
- IO_floatValue(line,positions,j+k) ! assign values for the bc(loadcase)%P matrix
- enddo
- bc(loadcase)%maskStress = transpose(reshape(bc(loadcase)%maskStressVector,[ 3,3]))
- bc(loadcase)%P = math_plain9to33(temp_valueVector)
- case('t','time','delta') ! increment time
- bc(loadcase)%time = IO_floatValue(line,positions,j+1_pInt)
- case('temp','temperature') ! starting temperature
- bc(loadcase)%temperature = IO_floatValue(line,positions,j+1_pInt)
- case('n','incs','increments','steps') ! number of increments
- bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
- case('logincs','logincrements','logsteps') ! number of increments (switch to log time scaling)
- bc(loadcase)%incs = IO_intValue(line,positions,j+1_pInt)
- bc(loadcase)%logscale = 1_pInt
- case('f','freq','frequency','outputfreq') ! frequency of result writings
- bc(loadcase)%outputfrequency = IO_intValue(line,positions,j+1_pInt)
- case('r','restart','restartwrite') ! frequency of writing restart information
- bc(loadcase)%restartfrequency = max(0_pInt,IO_intValue(line,positions,j+1_pInt))
- case('guessreset','dropguessing')
- bc(loadcase)%followFormerTrajectory = .false. ! do not continue to predict deformation along former trajectory
- case('euler') ! rotation of loadcase given in euler angles
- u = 0_pInt ! assuming values given in radians
- v = 1_pInt ! assuming keyword indicating degree/radians
- select case (IO_lc(IO_stringValue(line,positions,j+1_pInt)))
- case('deg','degree')
- u = 1_pInt ! for conversion from degree to radian
- case('rad','radian')
- case default
- v = 0_pInt ! immediately reading in angles, assuming radians
- end select
- forall(k = 1_pInt:3_pInt) temp33_Real(k,1) = &
- IO_floatValue(line,positions,j+v+k) * real(u,pReal) * inRad
- bc(loadcase)%rotation = math_EulerToR(temp33_Real(:,1))
- case('rotation','rot') ! assign values for the rotation of loadcase matrix
- temp_valueVector = 0.0_pReal
- forall (k = 1_pInt:9_pInt) temp_valueVector(k) = IO_floatValue(line,positions,j+k)
- bc(loadcase)%rotation = math_plain9to33(temp_valueVector)
- end select
- enddo; enddo
-101 close(myUnit)
-
-!-------------------------------------------------------------------------------------------------- ToDo: if temperature at CPFEM is treated properly, move this up immediately after interface init
-! initialization of all related DAMASK modules (e.g. mesh.f90 reads in geometry)
- call CPFEM_initAll(bc(1)%temperature,1_pInt,1_pInt)
-
-!--------------------------------------------------------------------------------------------------
-! get resolution, dimension, homogenization and variables derived from resolution
- res = mesh_spectral_getResolution()
- geomdim = mesh_spectral_getDimension()
- homog = mesh_spectral_getHomogenization()
-
-
- res1_red = res(1)/2_pInt + 1_pInt ! size of complex array in first dimension (c2r, r2c)
- Npoints = res(1)*res(2)*res(3)
- wgt = 1.0_pReal/real(Npoints, pReal)
-
-!--------------------------------------------------------------------------------------------------
-! output of geometry
- write(6,'(a)') ''
- write(6,'(a)') '#############################################################'
- write(6,'(a)') 'DAMASK spectral_AL:'
- write(6,'(a)') 'The AL spectral method boundary value problem solver for'
- write(6,'(a)') 'the Duesseldorf Advanced Material Simulation Kit'
- write(6,'(a)') '#############################################################'
- write(6,'(a)') 'geometry file: ',trim(getModelName())//InputFileExtension
- write(6,'(a)') '============================================================='
- write(6,'(a,3(i12 ))') 'resolution a b c:', res
- write(6,'(a,3(f12.5))') 'dimension x y z:', geomdim
- write(6,'(a,i5)') 'homogenization: ',homog
- write(6,'(a)') '#############################################################'
- write(6,'(a)') 'loadcase file: ',trim(getLoadcaseName())
-
-!--------------------------------------------------------------------------------------------------
-! consistency checks and output of load case
- bc(1)%followFormerTrajectory = .false. ! cannot guess along trajectory for first inc of first loadcase
-
- do loadcase = 1_pInt, N_Loadcases
- write (loadcase_string, '(i6)' ) loadcase
-
- write(6,'(a)') '============================================================='
- write(6,'(a,i6)') 'loadcase: ', loadcase
-
- if (.not. bc(loadcase)%followFormerTrajectory) write(6,'(a)') 'drop guessing along trajectory'
- if (bc(loadcase)%velGradApplied) then
- do j = 1_pInt, 3_pInt
- if (any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .true.) .and. &
- any(bc(loadcase)%maskDeformation(j,1:3) .eqv. .false.)) errorID = 832_pInt ! each row should be either fully or not at all defined
- enddo
- write(6,'(a)') 'velocity gradient:'
- else
- write(6,'(a)') 'deformation gradient rate:'
- endif
- write (6,'(3(3(f12.7,1x)/))',advance='no') merge(math_transpose33(bc(loadcase)%deformation),&
- reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskDeformation))
- write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'stress / GPa:',&
- 1e-9_pReal*merge(math_transpose33(bc(loadcase)%P),&
- reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskStress))
- if (any(bc(loadcase)%rotation /= math_I3)) &
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',&
- math_transpose33(bc(loadcase)%rotation)
- write(6,'(a,f12.6)') 'temperature:',bc(loadcase)%temperature
- write(6,'(a,f12.6)') 'time: ',bc(loadcase)%time
- write(6,'(a,i5)') 'increments: ',bc(loadcase)%incs
- write(6,'(a,i5)') 'output frequency: ',bc(loadcase)%outputfrequency
- write(6,'(a,i5)') 'restart frequency: ',bc(loadcase)%restartfrequency
- if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 831_pInt ! exclusive or masking only
- if (any(bc(loadcase)%maskStress .and. transpose(bc(loadcase)%maskStress) .and. &
- reshape([ .false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false.],[ 3,3]))) &
- errorID = 838_pInt ! no rotation is allowed by stress BC
- if (any(abs(math_mul33x33(bc(loadcase)%rotation,math_transpose33(bc(loadcase)%rotation))&
- -math_I3) > reshape(spread(rotation_tol,1,9),[ 3,3]))&
- .or. abs(math_det33(bc(loadcase)%rotation)) > 1.0_pReal + rotation_tol)&
- errorID = 846_pInt ! given rotation matrix contains strain
- if (bc(loadcase)%time < 0.0_pReal) errorID = 834_pInt ! negative time increment
- if (bc(loadcase)%incs < 1_pInt) errorID = 835_pInt ! non-positive incs count
- if (bc(loadcase)%outputfrequency < 1_pInt) errorID = 836_pInt ! non-positive result frequency
- if (errorID > 0_pInt) call IO_error(error_ID = errorID, ext_msg = loadcase_string)
- enddo
-
-!--------------------------------------------------------------------------------------------------
-! debugging parameters
- debugRestart = iand(debug_spectral,debug_spectralRestart) > 0_pInt
- debugFFTW = iand(debug_spectral,debug_spectralFFTW) > 0_pInt
- debugGeneral = .true.
-
-!##################################################################################################
-! initialization
-!##################################################################################################
-
-!--------------------------------------------------------------------------------------------------
-! allocate more memory
- allocate (P ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
- allocate (dPdF ( res(1), res(2),res(3),3,3,3,3), source = 0.0_pReal)
- allocate (F_star ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
- allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
- allocate (lambda ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
- allocate (xi (3,res1_red,res(2),res(3)), source = 0.0_pReal)
- allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
- allocate (temperature( res(1), res(2),res(3)), source = bc(1)%temperature) ! start out isothermally
- tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
- call c_f_pointer(tensorField, tau_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation
- call c_f_pointer(tensorField, F_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation
- call c_f_pointer(tensorField, tau_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
- call c_f_pointer(tensorField, F_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
-
-!--------------------------------------------------------------------------------------------------
-! general initialization of fftw (see manual on fftw.org for more details)
- if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=808_pInt) ! check for correct precision in C
-!$ if(DAMASK_NumThreadsInt > 0_pInt) then
-!$ ierr = fftw_init_threads()
-!$ if (ierr == 0_pInt) call IO_error(error_ID = 809_pInt)
-!$ call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
-!$ endif
- call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
-
-!--------------------------------------------------------------------------------------------------
-! creating plans
- plan_tau = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
- tau_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
- 1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
- tau_fourier,[ res(3),res(2) ,res1_red],&
- 1, res(3)*res(2)* res1_red,fftw_planner_flag)
-
- plan_correction = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
- F_fourier,[ res(3),res(2) ,res1_red],&
- 1, res(3)*res(2)* res1_red,&
- F_real,[ res(3),res(2) ,res(1)+2_pInt],&
- 1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
- if (debugGeneral) write(6,'(a)') 'FFTW initialized'
-
-!--------------------------------------------------------------------------------------------------
-! init fields to no deformation
- ielem = 0_pInt
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- F_star(i,j,k,1:3,1:3) = math_I3
- F_lastInc(i,j,k,1:3,1:3) = math_I3
- coordinates(i,j,k,1:3) = geomdim/real(res * [i,j,k], pReal) - geomdim/real(2_pInt*res,pReal)
- call CPFEM_general(3_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
- 0.0_pReal,ielem,1_pInt,sigma,dsde,P(i,j,k,1:3,1:3),dPdF(i,j,k,1:3,1:3,1:3,1:3))
- enddo; enddo; enddo
-
- ielem = 0_pInt
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
- 0.0_pReal,ielem,1_pInt,sigma,dsde,P(i,j,k,1:3,1:3),dPdF(i,j,k,1:3,1:3,1:3,1:3))
- C = C + dPdF(i,j,k,1:3,1:3,1:3,1:3)
- enddo; enddo; enddo
- C_inc0 = C * wgt *3.0_pReal ! linear reference material stiffness
-
-!--------------------------------------------------------------------------------------------------
-! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) and remove the given highest frequencies
- do k = 1_pInt, res(3)
- k_s(3) = k - 1_pInt
- if(k > res(3)/2_pInt + 1_pInt) k_s(3) = k_s(3) - res(3)
- do j = 1_pInt, res(2)
- k_s(2) = j - 1_pInt
- if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
- do i = 1_pInt, res1_red
- k_s(1) = i - 1_pInt
- xi(1:3,i,j,k) = real(k_s, pReal)/geomdim
- enddo; enddo; enddo
-
-!--------------------------------------------------------------------------------------------------
-! calculate the gamma operator
- if(memory_efficient) then ! allocate just single fourth order tensor
- allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
- else ! precalculation of gamma_hat field
- allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source =0.0_pReal)
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
- if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
- forall(l = 1_pInt:3_pInt, u = 1_pInt:3_pInt) &
- xiDyad(l,u) = xi(l, i,j,k)*xi(u, i,j,k)
- forall(l = 1_pInt:3_pInt, u = 1_pInt:3_pInt) &
- temp33_Real(l,u) = sum(C_inc0(l,1:3,u,1:3)*xiDyad)
- temp33_Real = math_inv33(temp33_Real)
- forall(l=1_pInt:3_pInt, u=1_pInt:3_pInt, v=1_pInt:3_pInt, w=1_pInt:3_pInt)&
- gamma_hat(i,j,k, l,u,v,w) = temp33_Real(l,v)*xiDyad(u,w)
- endif
- enddo; enddo; enddo
- gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
- endif
-
-
-!--------------------------------------------------------------------------------------------------
-! write header of output file
- open(538,file=trim(getSolverWorkingDirectoryName())//trim(getSolverJobName())&
- //'.spectralOut',form='UNFORMATTED',status='REPLACE')
- write(538) 'load', trim(getLoadcaseName())
- write(538) 'workingdir', trim(getSolverWorkingDirectoryName())
- write(538) 'geometry', trim(getSolverJobName())//InputFileExtension
- write(538) 'resolution', res
- write(538) 'dimension', geomdim
- write(538) 'materialpoint_sizeResults', materialpoint_sizeResults
- write(538) 'loadcases', N_Loadcases
- write(538) 'frequencies', bc(1:N_Loadcases)%outputfrequency ! one entry per loadcase
- write(538) 'times', bc(1:N_Loadcases)%time ! one entry per loadcase
- write(538) 'logscales', bc(1:N_Loadcases)%logscale
- write(538) 'increments', bc(1:N_Loadcases)%incs ! one entry per loadcase
- write(538) 'startingIncrement', restartInc - 1_pInt ! start with writing out the previous inc
- write(538) 'eoh' ! end of header
- write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! initial (non-deformed or read-in) results
- if (debugGeneral) write(6,'(a)') 'Header of result file written out'
-
-!##################################################################################################
-! Loop over loadcases defined in the loadcase file
-!##################################################################################################
- do loadcase = 1_pInt, N_Loadcases
- time0 = time ! loadcase start time
- if (bc(loadcase)%followFormerTrajectory .and. &
- (restartInc < totalIncsCounter .or. &
- restartInc > totalIncsCounter+bc(loadcase)%incs) ) then ! continue to guess along former trajectory where applicable
- guessmode = 1.0_pReal
- else
- guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
- endif
-
-!--------------------------------------------------------------------------------------------------
-! arrays for mixed boundary conditions
- mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
- mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
- size_reduced = int(count(bc(loadcase)%maskStressVector), pInt)
- allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
- allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
-
-!##################################################################################################
-! loop oper incs defined in input file for current loadcase
-!##################################################################################################
- do inc = 1_pInt, bc(loadcase)%incs
- totalIncsCounter = totalIncsCounter + 1_pInt
- if(totalIncsCounter >= restartInc) then ! do calculations (otherwise just forwarding)
-!--------------------------------------------------------------------------------------------------
-! forwarding time
- timeinc_old = timeinc
- if (bc(loadcase)%logscale == 0_pInt) then ! linear scale
- timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
- else
- if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
- if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
- timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
- else ! not-1st inc of 1st loadcase of logarithmic scale
- timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
- endif
- else ! not-1st loadcase of logarithmic scale
- timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
- real(bc(loadcase)%incs ,pReal))&
- -(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
- real(bc(loadcase)%incs ,pReal)) )
- endif
- endif
- time = time + timeinc
-
- if (bc(loadcase)%velGradApplied) then ! calculate deltaF from given L and current F
- deltaF = timeinc * mask_defgrad * math_mul33x33(bc(loadcase)%deformation, F_aim)
- else ! deltaF = fDot *timeinc where applicable
- deltaF = timeinc * mask_defgrad * bc(loadcase)%deformation
- endif
-
-!--------------------------------------------------------------------------------------------------
-! coordinates at beginning of inc
- !call deformed_fft(res,geomdim,1.0_pReal,F_real(1:res(1),1:res(2),1:res(3),1:3,1:3),coordinates)! calculate current coordinates
-
-!--------------------------------------------------------------------------------------------------
-! winding forward of deformation aim in loadcase system
- temp33_Real = F_aim
- F_aim = F_aim &
- + guessmode * mask_stress * (F_aim - F_aim_lastInc)*timeinc/timeinc_old &
- + deltaF
- F_aim_lastInc = temp33_Real
-
-!--------------------------------------------------------------------------------------------------
-! update local deformation gradient
- deltaF = math_rotate_backward33(deltaF,bc(loadcase)%rotation)
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- temp33_Real = F_star(i,j,k,1:3,1:3)
- F_star(i,j,k,1:3,1:3) = F_star(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
- + guessmode * (F_star(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))& ! guessing...
- *timeinc/timeinc_old &
- + (1.0_pReal-guessmode) * deltaF ! if not guessing, use prescribed average deformation where applicable
- F_lastInc(i,j,k,1:3,1:3) = temp33_Real
- enddo; enddo; enddo
-
-!--------------------------------------------------------------------------------------------------
-! Initialize / Update lambda to useful value
- P_av = P_av + math_mul3333xx33(C*wgt, F_aim-F_aim_lastInc)
-
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- lambda(i,j,k,1:3,1:3) = lambda(i,j,k,1:3,1:3) + math_mul3333xx33(C*wgt, F_aim-F_aim_lastInc)
- enddo; enddo; enddo
-!--------------------------------------------------------------------------------------------------
-!Initialize pointwise data for AL scheme: ToDo: good choice?
-
- F_star_av = 0.0_pReal
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- F_star_av = F_star_av + F_star(i,j,k,1:3,1:3)
- enddo; enddo; enddo
-
- F_star_av = F_star_av *wgt
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'F* =',&
- math_transpose33(F_star_av)
-!
-!--------------------------------------------------------------------------------------------------
-! calculate reduced compliance
- if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
- C_lastInc = math_rotate_forward3333(C*wgt,bc(loadcase)%rotation) ! calculate stiffness from former inc
- c_prev99 = math_Plain3333to99(C_lastInc)
- k = 0_pInt ! build reduced stiffness
- do v = 1_pInt,9_pInt
- if(bc(loadcase)%maskStressVector(v)) then
- k = k + 1_pInt
- j = 0_pInt
- do u = 1_pInt,9_pInt
- if(bc(loadcase)%maskStressVector(u)) then
- j = j + 1_pInt
- c_reduced(k,j) = c_prev99(v,u)
- endif; enddo; endif; enddo
- call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
- if(errmatinv) call IO_error(error_ID=400_pInt)
- s_prev99 = 0.0_pReal ! build full compliance
- k = 0_pInt
- do v = 1_pInt,9_pInt
- if(bc(loadcase)%maskStressVector(v)) then
- k = k + 1_pInt
- j = 0_pInt
- do u = 1_pInt,9_pInt
- if(bc(loadcase)%maskStressVector(u)) then
- j = j + 1_pInt
- s_prev99(v,u) = s_reduced(k,j)
- endif; enddo; endif; enddo
- S_lastInc = (math_Plain99to3333(s_prev99))
- endif
- S_inc0 = math_invSym3333(C*wgt)
-!--------------------------------------------------------------------------------------------------
-! report begin of new increment
- write(6,'(a)') '##################################################################'
- write(6,'(A,I5.5,A,es12.5)') 'Increment ', totalIncsCounter, ' Time ',time
-
- guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
- CPFEM_mode = 1_pInt ! winding forward
- iter = 0_pInt
- err_crit = huge(1.0_pReal) ! go into loop
- callCPFEM=.true.
- guessmax = 3
- guesses = 0
-
-!##################################################################################################
-! convergence loop (looping over iterations)
-!##################################################################################################
- do while((iter < itmax .and. (err_crit > 1.0_pReal)) .or. iter < itmin)
- iter = iter + 1_pInt
-
-!--------------------------------------------------------------------------------------------------
-! report begin of new iteration
- write(6,'(a)') ''
- write(6,'(a)') '=================================================================='
- write(6,'(5(a,i6.6))') 'Loadcase ',loadcase,' Increment ',inc,'/',bc(loadcase)%incs,&
- ' @ Iteration ',iter,'/',itmax
-
-!--------------------------------------------------------------------------------------------------
-! stress BC handling
- if(size_reduced > 0_pInt) then ! calculate stress BC if applied
- err_stress = maxval(abs(mask_stress * (P_av - bc(loadcase)%P))) ! maximum deviaton (tensor norm not applicable)
- F_aim = F_aim + math_mul3333xx33(S_lastInc,bc(loadcase)%P- P_av)
- err_stress_tol = maxval(abs(P_av)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent
- else
- err_stress_tol = + huge(1.0_pReal)
- endif
- F_aim_lab = math_rotate_backward33(F_aim,bc(loadcase)%rotation)
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'F aim =',&
- math_transpose33(F_aim)
-
-!--------------------------------------------------------------------------------------------------
-! doing Fourier transform
- write(6,'(a)') '... spectral method ...............................................'
- tau_real = 0.0_pReal
- do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res(1)
- tau_real(i,j,k,1:3,1:3) = lambda(i,j,k,1:3,1:3) - math_mul3333xx33(C_inc0,F_star(i,j,k,1:3,1:3))
- enddo; enddo; enddo
- call fftw_execute_dft_r2c(plan_tau,tau_real,tau_fourier)
- tau_fourier( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
- = cmplx(0.0_pReal,0.0_pReal,pReal)
- tau_fourier(1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
- = cmplx(0.0_pReal,0.0_pReal,pReal)
- if(res(3)>1_pInt) &
- tau_fourier(1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
- = cmplx(0.0_pReal,0.0_pReal,pReal)
-!--------------------------------------------------------------------------------------------------
-! using gamma operator to update F
- if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
- do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
- if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
- forall(l = 1_pInt:3_pInt, u = 1_pInt:3_pInt) &
- xiDyad(l,u) = xi(l, i,j,k)*xi(u, i,j,k)
- forall(l = 1_pInt:3_pInt, u = 1_pInt:3_pInt) &
- temp33_Real(l,u) = sum(C_inc0(l,1:3,u,1:3)*xiDyad)
- temp33_Real = math_inv33(temp33_Real)
- forall(l=1_pInt:3_pInt, u=1_pInt:3_pInt, v=1_pInt:3_pInt, w=1_pInt:3_pInt)&
- gamma_hat(1,1,1, l,u,v,w) = temp33_Real(l,v)*xiDyad(u,w)
- forall(l = 1_pInt:3_pInt, u = 1_pInt:3_pInt) &
- temp33_Complex(l,u) = sum(gamma_hat(1,1,1, l,u, 1:3,1:3) *&
- tau_fourier(i,j,k,1:3,1:3))
- F_fourier(i,j,k,1:3,1:3) = - temp33_Complex
- endif
- enddo; enddo; enddo
- else ! use precalculated gamma-operator
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
- forall( u = 1_pInt:3_pInt, v = 1_pInt:3_pInt) &
- temp33_Complex(u,v) = sum(gamma_hat(i,j,k, u,v, 1:3,1:3) *&
- tau_fourier(i,j,k,1:3,1:3))
- F_fourier(i,j,k, 1:3,1:3) = - temp33_Complex
- enddo; enddo; enddo
- endif
- F_fourier(1,1,1,1:3,1:3) = cmplx((F_aim_lab)*real(Npoints,pReal),0.0_pReal,pReal)
-
-!--------------------------------------------------------------------------------------------------
-! doing inverse Fourier transform
- call fftw_execute_dft_c2r(plan_correction,F_fourier,F_real) ! back transform of fluct deformation gradient
- F_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = F_real(1:res(1),1:res(2),1:res(3),1:3,1:3) * wgt
-
- F_star_av = 0.0_pReal
- temp33_real = 0.0_pReal
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- F_star_av = F_star_av + F_star(i,j,k,1:3,1:3)
- temp33_real = temp33_real + F_real(i,j,k,1:3,1:3)
- enddo; enddo; enddo
-
- F_star_av = F_star_av *wgt
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'F* =',&
- math_transpose33(F_star_av)
- temp33_real = temp33_real *wgt
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'F =',&
- math_transpose33(temp33_real)
-!--------------------------------------------------------------------------------------------------
- write(6,'(a)') '... calling CPFEM to update P(F*) and F*.........................'
- err_nl_point = huge(1.0_pReal)
- u = 0_pInt
- do while (err_nl_point>1.0e6_pReal .or. u<2_pInt)
- u = u + 1_pInt
- ielem = 0_pInt
- err_nl_point = 0.0_pReal
- err_nl = 0.0_pReal
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- call CPFEM_general(3_pInt,& ! collect cycle
- coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),&
- F_star(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
- sigma,dsde, P(i,j,k,1:3,1:3), dPdF(i,j,k,1:3,1:3,1:3,1:3))
- enddo; enddo; enddo
- ielem = 0_pInt
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- call CPFEM_general(CPFEM_mode,&
- coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),&
- F_star(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
- sigma,dsde, P(i,j,k,1:3,1:3), dPdF(i,j,k,1:3,1:3,1:3,1:3))
- CPFEM_mode = 2_pInt ! winding forward
- temp33_Real = P(i,j,k,1:3,1:3) - lambda(i,j,k,1:3,1:3) &
- + math_mul3333xx33(C_inc0,F_star(i,j,k,1:3,1:3)-F_real(i,j,k,1:3,1:3))
-
- err_nl_point = max(err_nl_point, maxval(abs(temp33_real)))
- err_nl = max(err_nl, sqrt(math_mul33xx33(temp33_real,temp33_real)))
-
- ! temp33_Real = lambda(i,j,k,1:3,1:3) - P(i,j,k,1:3,1:3) &
- ! + math_mul3333xx33(C_inc0,F_real(i,j,k,1:3,1:3)- F_star(i,j,k,1:3,1:3))
- ! F_star(i,j,k,1:3,1:3) = F_star(i,j,k,1:3,1:3) + math_mul3333xx33(math_invSym3333(&
- ! C_inc0 + dPdF(i,j,k,1:3,1:3,1:3,1:3)), temp33_Real)
- F_star(i,j,k,1:3,1:3) = F_star(i,j,k,1:3,1:3) - 0.1_pReal * math_mul3333xx33(S_inc0, temp33_Real)
- enddo; enddo; enddo
-
- if(u>1) print*, 'comp wise error of nl eq last it:', err_nl_point/1.0e6_pReal
- if(u>1) print*, 'norm error: last it ', err_nl/1.0e6_pReal
-
- enddo
-
-
- write(6,'(a)') '... update λ..........................'
-
- err_f = 0.0_pReal
- err_f_point = 0.0_pReal
- err_p = 0.0_pReal
- err_p_point = 0.0_pReal
-
- F_star_av = 0.0_pReal
- lambda_av = 0.0_pReal
-
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- lambda(i,j,k,1:3,1:3) = lambda(i,j,k,1:3,1:3) + math_mul3333xx33(C_inc0,F_real(i,j,k,1:3,1:3) &
- - F_star(i,j,k,1:3,1:3))
- F_star_av = F_star_av + F_star(i,j,k,1:3,1:3)
- lambda_av = lambda_av + lambda(i,j,k,1:3,1:3)
-
- temp33_real = F_star(i,j,k,1:3,1:3) - F_real(i,j,k,1:3,1:3)
- err_f_point = max(err_f_point, maxval(abs(temp33_real)))
- err_f = max(err_f, sqrt(math_mul33xx33(temp33_real,temp33_real)))
-
- enddo; enddo; enddo
-
- ielem = 0_pInt
- P_av = 0.0_pReal
- C = 0.0_pReal
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- call CPFEM_general(3_pInt,& ! collect cycle
- coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),&
- F_real(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
- sigma,dsde, P(i,j,k,1:3,1:3), dPdF(i,j,k,1:3,1:3,1:3,1:3))
- enddo; enddo; enddo
- ielem = 0_pInt
- do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
- ielem = ielem + 1_pInt
- call CPFEM_general(2_pInt,&
- coordinates(i,j,k,1:3), F_lastInc(i,j,k,1:3,1:3),&
- F_real(i,j,k,1:3,1:3),temperature(i,j,k),timeinc,ielem,1_pInt,&
- sigma,dsde, P(i,j,k,1:3,1:3), dPdF(i,j,k,1:3,1:3,1:3,1:3))
- P_av = P_av + P(i,j,k,1:3,1:3)
- temp33_real = lambda(i,j,k,1:3,1:3) - P(i,j,k,1:3,1:3)
- err_p_point = max(err_p_point, maxval(abs(temp33_real)))
- err_p = max(err_p, sqrt(math_mul33xx33(temp33_real,temp33_real)))
- C = C + dPdF(i,j,k,1:3,1:3,1:3,1:3)
- enddo; enddo; enddo
-
- F_star_av = F_star_av *wgt
- write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'F* =',&
- math_transpose33(F_star_av)
- P_av = P_av *wgt
- write (*,'(a,/,3(3(es14.7,1x)/))',advance='no') 'P(F) / GPa =',&
- math_transpose33(P_av) /1.e6_pReal
- lambda_av = lambda_av *wgt
- write (*,'(a,/,3(3(es14.7,1x)/))',advance='no') 'λ / GPa =',&
- math_transpose33(lambda_av) /1.e6_pReal
-
- err_f = err_f/sqrt(math_mul33xx33(F_star_av,F_star_av))
- err_p = err_p/sqrt(math_mul33xx33(P_av,P_av))
-
- write(6,'(a,es14.7,es14.7)') 'error F', err_f/1e-4, err_f
- write(6,'(a,es14.7,es14.7)') 'error P', err_p/1e-3, err_p
- write(6,'(a,es14.7,es14.7)') 'error stress = ',err_stress/err_stress_tol, err_stress
- write(6,*) ' '
- write(6,'(a,es14.7)') 'max abs err F', err_f_point
- write(6,'(a,es14.7)') 'max abs err P', err_p_point
- err_crit = max(err_p/1e-3, err_f/1e-4,err_stress/err_stress_tol)
- write(6,'(a,es14.7)') 'critical error', err_crit
-
-
- enddo ! end looping when convergency is achieved
- write(6,'(a)') ' '
- write(6,'(a)') '=================================================================='
- if(err_crit > 1.0_pReal) then
- write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' NOT converged'
- notConvergedCounter = notConvergedCounter + 1_pInt
- else
- convergedCounter = convergedCounter + 1_pInt
- write(6,'(A,I5.5,A)') 'increment ', totalIncsCounter, ' converged'
- endif
-
- if (mod(totalIncsCounter -1_pInt,bc(loadcase)%outputfrequency) == 0_pInt) then ! at output frequency
- write(6,'(a)') ' '
- write(6,'(a)') '... writing results to file ......................................'
- write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
- endif
-
- endif ! end calculation/forwarding
- enddo ! end looping over incs in current loadcase
- deallocate(c_reduced)
- deallocate(s_reduced)
- enddo ! end looping over loadcases
- write(6,'(a)') ''
- write(6,'(a)') '##################################################################'
- write(6,'(i6.6,a,i6.6,a)') notConvergedCounter, ' out of ', &
- notConvergedCounter + convergedCounter, ' increments did not converge!'
- close(538)
- call fftw_destroy_plan(plan_tau); call fftw_destroy_plan(plan_correction)
- call quit(1_pInt)
-end program DAMASK_spectral_AL