! Copyright 2012 Max-Planck-Institut fuer Eisenforschung GmbH ! ! This file is part of DAMASK, ! the Duesseldorf 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 !################################################################################################## ! used modules !################################################################################################## program DAMASK_spectral use DAMASK_interface use prec, only: pInt, pReal, DAMASK_NaN use IO use debug, only: debug_spectral, & debug_spectralGeneral, & debug_spectralDivergence, & debug_spectralRestart, & debug_spectralFFTW use math use kdtree2_module use CPFEM, only: CPFEM_general, CPFEM_initAll use FEsolving, only: restartWrite, restartInc use numerics, only: err_div_tol, err_stress_tolrel, rotation_tol, itmax, & memory_efficient, update_gamma, & simplified_algorithm, divergence_correction, & cut_off_value, & DAMASK_NumThreadsInt, & fftw_planner_flag, fftw_timelimit use homogenization, only: materialpoint_sizeResults, materialpoint_results !$ use OMP_LIB ! the openMP function library !################################################################################################## ! variable declaration !################################################################################################## 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) :: headerLength,& N_l = 0_pInt,& N_t = 0_pInt,& N_n = 0_pInt,& N_Fdot = 0_pInt character(len=1024) :: path, line, keyword logical :: gotResolution = .false.,& gotDimension = .false.,& gotHomogenization = .false. 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_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 character(len=6) :: loadcase_string !-------------------------------------------------------------------------------------------------- ! 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) :: pstress, pstress_av, & defgradAim = math_I3, defgradAimOld = math_I3,& mask_stress, mask_defgrad, deltaF, & pstress_av_lab, defgradAim_lab, defgrad_av_lab ! quantities rotated to other coordinate system real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current = 0.0_pReal, s_prev, c_prev,& ! stiffness and compliance s0_reference real(pReal), dimension(6) :: cstress ! cauchy stress real(pReal), dimension(6,6) :: dsde, c0_66, s0_66 ! small strain stiffness real(pReal), dimension(9,9) :: s_prev99, c_prev99, c0_99, s0_99 ! compliance and stiffness in matrix notation real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC) real(pReal), dimension(6,6) :: mask_inversion = reshape([& 1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,& 1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,& 1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,& 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal,& 0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal,& 0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal],& [ 6_pInt, 6_pInt]) real(pReal), dimension(3,3,3,3) :: temp_3333 = 0.0_pReal integer(pInt) :: size_reduced = 0.0_pReal ! number of stress BCs !-------------------------------------------------------------------------------------------------- ! pointwise data type(C_PTR) :: tensorField, tau ! fields in real an fourier space real(pReal), dimension(:,:,:,:,:), pointer :: tensorField_real ! fields in real space (pointer) real(pReal), dimension(:,:,:,:,:), pointer :: tau_real complex(pReal), dimension(:,:,:,:,:), pointer :: tensorField_fourier ! fields in fourier space (pointer) complex(pReal), dimension(:,:,:,:,:), pointer :: tau_fourier real(pReal), dimension(:,:,:,:,:), allocatable :: defgrad, defgradold 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, 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, cutting_freq !-------------------------------------------------------------------------------------------------- ! 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, inc, iter, ielem, CPFEM_mode, & ierr, totalIncsCounter = 0_pInt,& notConvergedCounter = 0_pInt, convergedCounter = 0_pInt logical :: errmatinv real(pReal) :: defgradDet, correctionFactor !-------------------------------------------------------------------------------------------------- !variables controlling debugging logical :: debugGeneral, debugDivergence, debugRestart, debugFFTW !-------------------------------------------------------------------------------------------------- !variables for additional output due to general debugging real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew, max_diag, max_offdiag !-------------------------------------------------------------------------------------------------- ! 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_postProc real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS,& err_div_max, err_real_div_max,& max_div_error !-------------------------------------------------------------------------------------------------- ! 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 !################################################################################################## !$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS call DAMASK_interface_init() print '(a)', '' print '(a)', ' <<<+- DAMASK_spectral init -+>>>' print '(a)', ' $Id$' #include "compilation_info.f90" print '(a,a)', ' Working Directory: ',trim(getSolverWorkingDirectoryName()) print '(a,a)', ' Solver Job Name: ',trim(getSolverJobName()) print '(a)', '' !-------------------------------------------------------------------------------------------------- ! reading the load case file and allocate data structure containing load cases path = getLoadcaseName() if (.not. IO_open_file(myUnit,path)) call IO_error(error_ID = 30_pInt,ext_msg = trim(path)) 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=37_pInt,ext_msg = trim(path)) ! 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)%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) if (update_gamma .and. .not. memory_efficient) call IO_error(error_ID = 47_pInt) !-------------------------------------------------------------------------------------------------- ! read header of geom file to get size information. complete geom file is intepretated by mesh.f90 path = getModelName() if (.not. IO_open_file(myUnit,trim(path)//InputFileExtension))& call IO_error(error_ID=101_pInt,ext_msg = trim(path)//InputFileExtension) rewind(myUnit) read(myUnit,'(a1024)') line positions = IO_stringPos(line,2_pInt) keyword = IO_lc(IO_StringValue(line,positions,2_pInt)) if (keyword(1:4) == 'head') then headerLength = IO_intValue(line,positions,1_pInt) + 1_pInt else call IO_error(error_ID=42_pInt) endif rewind(myUnit) do i = 1_pInt, headerLength read(myUnit,'(a1024)') line positions = IO_stringPos(line,maxNchunksGeom) select case ( IO_lc(IO_StringValue(line,positions,1)) ) case ('dimension') gotDimension = .true. do j = 2_pInt,6_pInt,2_pInt select case (IO_lc(IO_stringValue(line,positions,j))) case('x') geomdim(1) = IO_floatValue(line,positions,j+1_pInt) case('y') geomdim(2) = IO_floatValue(line,positions,j+1_pInt) case('z') geomdim(3) = IO_floatValue(line,positions,j+1_pInt) end select enddo case ('homogenization') gotHomogenization = .true. homog = IO_intValue(line,positions,2_pInt) case ('resolution') gotResolution = .true. do j = 2_pInt,6_pInt,2_pInt select case (IO_lc(IO_stringValue(line,positions,j))) case('a') res(1) = IO_intValue(line,positions,j+1_pInt) case('b') res(2) = IO_intValue(line,positions,j+1_pInt) case('c') res(3) = IO_intValue(line,positions,j+1_pInt) end select enddo end select enddo close(myUnit) !-------------------------------------------------------------------------------------------------- ! sanity checks of geometry parameters if (.not.(gotDimension .and. gotHomogenization .and. gotResolution))& call IO_error(error_ID = 45_pInt) if (any(geomdim<=0.0_pReal)) call IO_error(error_ID = 102_pInt) if(mod(res(1),2_pInt)/=0_pInt .or.& mod(res(2),2_pInt)/=0_pInt .or.& (mod(res(3),2_pInt)/=0_pInt .and. res(3)/= 1_pInt))& call IO_error(error_ID = 103_pInt) !-------------------------------------------------------------------------------------------------- ! variables derived from resolution 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) if (cut_off_value <0.0_pReal .or. cut_off_value >0.9_pReal) stop cutting_freq = nint(real(res,pReal)*cut_off_value,pInt) ! for cut_off_value=0.0 just the highest freq. is removed !-------------------------------------------------------------------------------------------------- ! output of geometry print '(a)', '' print '(a)', '#############################################################' print '(a)', 'DAMASK spectral:' print '(a)', 'The spectral method boundary value problem solver for' print '(a)', 'the Duesseldorf Advanced Material Simulation Kit' print '(a)', '#############################################################' print '(a,a)', 'geometry file: ',trim(path)//'.geom' print '(a)', '=============================================================' print '(a,3(i12 ))','resolution a b c:', res print '(a,3(f12.5))','dimension x y z:', geomdim print '(a,i5)','homogenization: ',homog if(cut_off_value/=0.0_pReal) print '(a,3(i12),a)', 'cutting away ', cutting_freq, ' frequencies' print '(a)', '#############################################################' print '(a,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 errorID = 0_pInt do loadcase = 1_pInt, N_Loadcases write (loadcase_string, '(i6)' ) loadcase print '(a)', '=============================================================' print '(a,i6)', 'loadcase: ', loadcase if (.not. bc(loadcase)%followFormerTrajectory) print '(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 = 32_pInt ! each row should be either fully or not at all defined enddo print '(a)','velocity gradient:' else print '(a)','deformation gradient rate:' endif write (*,'(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 (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' stress / GPa:',& 1e-9*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 (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',& math_transpose33(bc(loadcase)%rotation) print '(a,f12.6)','temperature:',bc(loadcase)%temperature print '(a,f12.6)','time: ',bc(loadcase)%time print '(a,i5)' ,'increments: ',bc(loadcase)%incs print '(a,i5)','output frequency: ',bc(loadcase)%outputfrequency print '(a,i5)','restart frequency: ',bc(loadcase)%restartfrequency if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 31 ! 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 = 38_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 = 46_pInt ! given rotation matrix contains strain if (bc(loadcase)%time < 0.0_pReal) errorID = 34_pInt ! negative time increment if (bc(loadcase)%incs < 1_pInt) errorID = 35_pInt ! non-positive incs count if (bc(loadcase)%outputfrequency < 1_pInt) errorID = 36_pInt ! non-positive result frequency if (errorID > 0_pInt) call IO_error(error_ID = errorID, ext_msg = loadcase_string) enddo !-------------------------------------------------------------------------------------------------- ! debugging parameters debugGeneral = iand(debug_spectral,debug_spectralGeneral) > 0_pInt debugDivergence = iand(debug_spectral,debug_spectralDivergence) > 0_pInt debugRestart = iand(debug_spectral,debug_spectralRestart) > 0_pInt debugFFTW = iand(debug_spectral,debug_spectralFFTW) > 0_pInt !################################################################################################## ! initialization !################################################################################################## allocate (defgrad ( res(1), res(2),res(3),3,3)); defgrad = 0.0_pReal allocate (defgradold ( res(1), res(2),res(3),3,3)); defgradold = 0.0_pReal allocate (coordinates( res(1), res(2),res(3),3)); coordinates = 0.0_pReal allocate (temperature( res(1), res(2),res(3))); temperature = bc(1)%temperature ! start out isothermally allocate (xi (3,res1_red,res(2),res(3))); xi = 0.0_pReal 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, tensorField_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation call c_f_pointer(tensorField, tensorField_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation !-------------------------------------------------------------------------------------------------- ! 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 defgrad(i,j,k,1:3,1:3) = math_I3 defgradold(i,j,k,1:3,1:3) = math_I3 coordinates(i,j,k,1:3) = geomdim/real(res, pReal)*[i,j,k] - 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,cstress,dsde,pstress,dPdF) c_current = c_current + dPdF enddo; enddo; enddo c0_reference = c_current * wgt ! linear reference material stiffness c0_66 = math_Mandel3333to66(c0_reference) call math_invert(6_pInt, c0_66, s0_66, i, errmatinv) ! invert in mandel notation if(errmatinv) call IO_error(error_ID=800_pInt) s0_reference = math_Mandel66to3333(s0_66) !-------------------------------------------------------------------------------------------------- ! possible restore deformation gradient from saved state if (restartInc > 1_pInt) then ! using old values from file if (debugRestart) print '(a,i6,a)' , 'Reading values of increment ',& restartInc - 1_pInt,' from file' if (IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',& trim(getSolverJobName()),size(defgrad))) then read (777,rec=1) defgrad close (777) endif defgradold = defgrad defgradAim = 0.0_pReal do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1) defgradAim = defgradAim + defgrad(i,j,k,1:3,1:3) ! calculating old average deformation enddo; enddo; enddo defgradAim = defgradAim * wgt defgradAimOld = defgradAim endif !-------------------------------------------------------------------------------------------------- ! 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, 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)); gamma_hat = 0.0_pReal else ! precalculation of gamma_hat field allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3)); gamma_hat = 0.0_pReal do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red ! if(k==res(3)/2 .or. k==res(3)/2+2 .or.& ! j==res(2)/2 .or. j==res(2)/2+2 .or.& ! i==res(1)/2 .or. i==res(1)/2+2) then ! gamma_hat(i,j,k,1:3,1:3,1:3,1:3) = s0_reference ! else 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(c0_reference(l,1:3,m,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 !-------------------------------------------------------------------------------------------------- ! 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=108_pInt) ! check for correct precision in C #ifdef _OPENMP if(DAMASK_NumThreadsInt > 0_pInt) then ierr = fftw_init_threads() if (ierr == 0_pInt) call IO_error(error_ID = 109_pInt) call fftw_plan_with_nthreads(DAMASK_NumThreadsInt) endif #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 tensorField_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 tensorField_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,& tensorField_fourier,[ res(3),res(2) ,res1_red],& 1, res(3)*res(2)* res1_red,& tensorField_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 (.not. simplified_algorithm) then print*, 'using polarization field based algorithm' tau = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) call c_f_pointer(tau, tau_real, [ res(1)+2_pInt,res(2),res(3),3,3]) call c_f_pointer(tau, tau_fourier, [ res1_red, res(2),res(3),3,3]) plan_tau = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& tau_real,[ res(3),res(2) ,res(1)+2_pInt],& 1, res(3)*res(2)*(res(1)+2_pInt),& tau_fourier,[ res(3),res(2) ,res1_red],& 1, res(3)*res(2)* res1_red,fftw_planner_flag) endif 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_postProc(res(1),res(2),res(3),3)); divergence_postProc= 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) print '(a)' , 'FFTW initialized' !-------------------------------------------------------------------------------------------------- ! do not correct divergence criterion (usefull to kill dimension and resolution dependenc) correctionFactor = 1.0_pReal !-------------------------------------------------------------------------------------------------- ! 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) print '(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 = count(bc(loadcase)%maskStressVector) allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 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, defgradAim) else ! deltaF = fDot *timeinc where applicable deltaF = timeinc * mask_defgrad * bc(loadcase)%deformation endif !-------------------------------------------------------------------------------------------------- ! winding forward of deformation aim in loadcase system temp33_Real = defgradAim defgradAim = defgradAim & + guessmode * mask_stress * (defgradAim - defgradAimOld)*timeinc/timeinc_old & + deltaF defgradAimOld = 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 = defgrad(i,j,k,1:3,1:3) defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon + guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(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 defgradold(i,j,k,1:3,1:3) = temp33_Real enddo; enddo; enddo !-------------------------------------------------------------------------------------------------- ! calculate reduced compliance c_prev = math_rotate_forward3333(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former inc if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied c_prev99 = math_Plain3333to99(c_prev) 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) = c_prev99(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=800_pInt) s_prev99 = 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 s_prev99(n,m) = s_reduced(k,j) endif; enddo; endif; enddo s_prev = (math_Plain99to3333(s_prev99)) endif !-------------------------------------------------------------------------------------------------- ! report begin of new increment print '(a)', '##################################################################' print '(A,I5.5,A,es12.6)', '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_div = 2.0_pReal * 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)) iter = iter + 1_pInt !-------------------------------------------------------------------------------------------------- ! report begin of new iteration print '(a)', '' print '(a)', '==================================================================' print '(5(a,i6.6))', 'Loadcase ',loadcase,' Increment ',inc,'/',bc(loadcase)%incs,& ' @ Iteration ',iter,'/',itmax do n = 1_pInt,3_pInt; do m = 1_pInt,3_pInt defgrad_av_lab(m,n) = sum(defgrad(1:res(1),1:res(2),1:res(3),m,n)) * wgt enddo; enddo write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient:',& math_transpose33(math_rotate_forward33(defgrad_av_lab,bc(loadcase)%rotation)) print '(a)', '' print '(a)', '... update stress field P(F) .....................................' !-------------------------------------------------------------------------------------------------- ! evaluate constitutive response call deformed_fft(res,geomdim,defgrad_av_lab,1.0_pReal,defgrad,coordinates) ! calculate current coordinates 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), defgradold(i,j,k,1:3,1:3), defgrad(i,j,k,1:3,1:3),& temperature(i,j,k),timeinc,ielem,1_pInt,& cstress,dsde, pstress, dPdF) enddo; enddo; enddo tensorField_real = 0.0_pReal ! needed because of the padding for FFTW c_current = 0.0_pReal 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,& ! first element in first iteration retains CPFEM_mode 1, coordinates(i,j,k,1:3),& defgradold(i,j,k,1:3,1:3), defgrad(i,j,k,1:3,1:3),& ! others get 2 (saves winding forward effort) temperature(i,j,k),timeinc,ielem,1_pInt,& cstress,dsde, pstress,dPdF) CPFEM_mode = 2_pInt tensorField_real(i,j,k,1:3,1:3) = pstress c_current = c_current + dPdF enddo; enddo; enddo !-------------------------------------------------------------------------------------------------- ! 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 tensorField_real(1:res(1),1:res(2),1:res(3),row,column) endif !-------------------------------------------------------------------------------------------------- ! build polarization field if (.not. simplified_algorithm) then tau_real = 0.0_pReal ! padding 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)& = tensorField_real(i,j,k,1:3,1:3) & - math_mul3333xx33(c0_reference,defgrad(i,j,k,1:3,1:3)) enddo; enddo; enddo call fftw_execute_dft_r2c(plan_tau,tau_real,tau_fourier) endif !-------------------------------------------------------------------------------------------------- ! call function to calculate divergence from math (for post processing) to check results if (debugDivergence) & call divergence_fft(res,geomdim,3_pInt,& tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_postProc) !padding !-------------------------------------------------------------------------------------------------- ! doing the FT because it simplifies calculation of average stress in real space also call fftw_execute_dft_r2c(plan_stress,tensorField_real,tensorField_fourier) pstress_av_lab = real(tensorField_fourier(1,1,1,1:3,1:3),pReal)*wgt pstress_av = math_rotate_forward33(pstress_av_lab,bc(loadcase)%rotation) write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa:',& math_transpose33(pstress_av)/1.e6 !-------------------------------------------------------------------------------------------------- ! comparing 1 and 3x3 FT results if (debugFFTW) then call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier) print '(a,i1,1x,i1)', 'checking FT results of compontent ', row, column print '(a,2(es10.4,1x))', 'max FT relative error ',& maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-& tensorField_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))-& tensorField_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 tensorField_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)& = cmplx(0.0_pReal,0.0_pReal,pReal) tensorField_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) & tensorField_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 * (pstress_av - bc(loadcase)%stress))) ! maximum deviaton (tensor norm not applicable) err_stress_tol = maxval(abs(pstress_av)) * err_stress_tolrel ! don't use any tensor norm because the comparison should be coherent print '(a)', '' print '(a)', '... correcting deformation gradient to fulfill BCs ...............' print '(a,f6.2,a,es10.4,a)', 'error stress = ', err_stress/err_stress_tol, & ' (',err_stress,' Pa)' defgradAim = defgradAim - math_mul3333xx33(s_prev, ((pstress_av - bc(loadcase)%stress))) ! residual on given stress components if(debugGeneral) write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'new deformation aim:',& math_transpose33(defgradAim) print '(a,1x,es10.4)' , 'determinant of new deformation: ', math_det33(defgradAim) else err_stress_tol = +huge(1.0_pReal) endif defgradAim_lab = math_rotate_backward33(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame !-------------------------------------------------------------------------------------------------- ! actual spectral method print '(a)', '' print '(a)', '... calculating equilibrium with spectral method .................' !-------------------------------------------------------------------------------------------------- ! calculating RMS divergence criterion in Fourier space pstress_av_L2 = sqrt(maxval (math_eigenvalues33(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress math_transpose33(pstress_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(tensorField_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))*two_pi_img)**2.0_pReal)& ! --> sum squared L_2 norm of vector +sum(aimag(math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),& xi(1:3,i,j,k))*two_pi_img)**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(tensorField_fourier(1 ,j,k,1:3,1:3),& xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)& + sum(aimag(math_mul33x3_complex(tensorField_fourier(1 ,j,k,1:3,1:3),& xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)& + sum(real(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),& xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)& + sum(aimag(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),& xi(1:3,res1_red,j,k))*two_pi_img)**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*sqrt(wgt) * correctionFactor>err_div& .and.iter >2_pInt& .and.err_stress < err_stress_tol) then print*, 'Increasing divergence, stopping iterations' iter = itmax endif err_div = err_div_RMS/pstress_av_L2*sqrt(wgt) * correctionFactor ! 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(tensorField_fourier(i,j,k,1:3,1:3),& xi(1:3,i,j,k))*two_pi_img err_div_max = max(err_div_max,sqrt(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) divergence_real = divergence_real*wgt err_real_div_RMS = 0.0_pReal err_real_div_max = 0.0_pReal max_div_error = 0.0_pReal do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1) max_div_error= max(max_div_error,maxval((divergence_real(i,j,k,1:3)& -divergence_postProc(i,j,k,1:3))/divergence_real(i,j,k,1:3))) err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of L_2 norm of div(stress) in real space err_real_div_max = max(err_real_div_max, sqrt(sum(divergence_real(i,j,k,1:3)**2.0_pReal))) ! maximum of L two 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_div_max = err_div_max*sqrt(wgt) print '(a,es10.4)', 'error divergence FT RMS = ',err_div_RMS print '(a,es10.4)', 'error divergence FT max = ',err_div_max print '(a,es10.4)', 'error divergence Real RMS = ',err_real_div_RMS print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max print '(a,es10.4)', 'divergence RMS FT/real = ',err_div_RMS/err_real_div_RMS print '(a,es10.4)', 'divergence max FT/real = ',err_div_max/err_real_div_max print '(a,es10.4)', 'max deviat. from postProc = ',max_div_error endif print '(a,f6.2,a,es10.4,a)', 'error divergence = ', err_div/err_div_tol, ' (',err_div,' 1/m)' !-------------------------------------------------------------------------------------------------- ! divergence is calculated from FT(stress), depending on algorithm use field for spectral method if (.not. simplified_algorithm) tensorField_fourier = tau_fourier max_diag = tiny(1.0_pReal) max_offdiag = tiny(1.0_pReal) !-------------------------------------------------------------------------------------------------- ! 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(k==res(3)/2 .or. k==res(3)/2+2 .or.& ! j==res(2)/2 .or. j==res(2)/2+2 .or.& ! i==res(1)/2 .or. i==res(1)/2+2) then ! forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt)& ! temp33_Complex(m,n) = sum(s0_reference(m,n, 1:3,1:3)* tensorField_fourier(i,j,k,1:3,1:3)) ! else 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(c0_reference(l,1:3,m,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) * tensorField_fourier(i,j,k,1:3,1:3)) tensorField_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) * tensorField_fourier(i,j,k,1:3,1:3)) tensorField_fourier(i,j,k, 1:3,1:3) = temp33_Complex enddo; enddo; enddo endif if (simplified_algorithm) then ! do not use the polarization field based algorithm tensorField_fourier(1,1,1,1:3,1:3) = (defgrad_av_lab - defgradAim_lab) & ! assign (negative) average deformation gradient change to zero frequency (real part) * real(Npoints,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1 else tensorField_fourier(1,1,1,1:3,1:3) = defgradAim_lab * real(Npoints,pReal) ! assign deformation aim to zero frequency (real part) endif !-------------------------------------------------------------------------------------------------- ! 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) = tensorField_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. can be directly used in calculation of cstress_field 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,tensorField_fourier,tensorField_real) ! back transform of fluct deformation gradient !-------------------------------------------------------------------------------------------------- ! comparing 1 and 3x3 inverse FT results if (debugFFTW) then print '(a,i1,1x,i1)', 'checking iFT results of compontent ', row, column call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real) print '(a,es10.4)', 'max iFT relative error ',& maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-& tensorField_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(tensorField_real(i,j,k,1:3,1:3)))) maxCorrectionSkew = max(maxCorrectionSkew,& maxval(math_skew33(tensorField_real(i,j,k,1:3,1:3)))) temp33_Real = temp33_Real + tensorField_real(i,j,k,1:3,1:3) enddo; enddo; enddo print '(a,1x,es10.4)' , 'max symmetrix correction of deformation:',& maxCorrectionSym*wgt print '(a,1x,es10.4)' , 'max skew correction of deformation:',& maxCorrectionSkew*wgt print '(a,1x,es10.4)' , 'max sym/skew of avg correction: ',& maxval(math_symmetric33(temp33_real))/& maxval(math_skew33(temp33_real)) endif !-------------------------------------------------------------------------------------------------- ! updated deformation gradient defgrad = defgrad - tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization !-------------------------------------------------------------------------------------------------- ! updated deformation gradient in case of fluctuation field algorithm if (.not.simplified_algorithm) then defgrad = tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3) * wgt endif !-------------------------------------------------------------------------------------------------- ! 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(defgrad(i,j,k,1:3,1:3)) defgradDetMax = max(defgradDetMax,defgradDet) defgradDetMin = min(defgradDetMin,defgradDet) enddo; enddo; enddo print '(a,1x,es10.4)' , 'max determinant of deformation:', defgradDetMax print '(a,1x,es10.4)' , 'min determinant of deformation:', defgradDetMin endif enddo ! end looping when convergency is achieved print '(a)', '' print '(a)', '==================================================================' if(err_div > err_div_tol .or. err_stress > err_stress_tol) then print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' NOT converged' notConvergedCounter = notConvergedCounter + 1_pInt else convergedCounter = convergedCounter + 1_pInt print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' converged' endif if (mod(totalIncsCounter -1_pInt,bc(loadcase)%outputfrequency) == 0_pInt) then ! at output frequency print '(a)', '' print '(a)', '... writing results to file ......................................' write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file endif if( bc(loadcase)%restartFrequency > 0_pInt .and. & mod(inc - 1_pInt,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?) restartWrite = .true. print '(A)', 'writing converged results for restart' if(IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(defgrad))) then ! writing deformation gradient field to file write (777,rec=1) defgrad close (777) endif restartInc=totalIncsCounter endif if (update_gamma) then print*, 'update c0_reference ' c0_reference = c_current*wgt ! s0_reference = math_Plain99to3333(s0_99) !c0_99 = math_Plain3333to99(c0_reference) ! call math_invert(9_pInt, s0_99, c0_99, i, errmatinv) ! invert reduced stiffness ! if(errmatinv) call IO_error(error_ID=800_pInt) ! print*, (c0_reference - math_Plain99to3333(c0_99))/c0_reference ! pause endif endif ! end calculation/forwarding enddo ! end looping over incs in current loadcase deallocate(c_reduced) deallocate(s_reduced) enddo ! end looping over loadcases print '(a)', '' print '(a)', '##################################################################' print '(i6.6,a,i6.6,a)', notConvergedCounter, ' out of ', & notConvergedCounter + convergedCounter, ' increments did not converge!' 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 stop 0 end program DAMASK_spectral !******************************************************************** ! quit subroutine to satisfy IO_error ! !******************************************************************** subroutine quit(id) use prec implicit none integer(pInt) id stop end subroutine