! 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, & 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_what, & 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, & update_gamma, & divergence_correction, & DAMASK_NumThreadsInt, & fftw_planner_flag, & fftw_timelimit use homogenization, only: & materialpoint_sizeResults, & materialpoint_results !$ use OMP_LIB ! the openMP function library implicit none !-------------------------------------------------------------------------------------------------- ! 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, & 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 !################################################################################################## 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(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) 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(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 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 (*,'(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_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 (*,'(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 debugGeneral = iand(debug_what(debug_spectral),debug_levelBasic) /= 0 debugDivergence = iand(debug_what(debug_spectral),debug_spectralDivergence) /= 0 debugRestart = iand(debug_what(debug_spectral),debug_spectralRestart) /= 0 debugFFTW = iand(debug_what(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 !-------------------------------------------------------------------------------------------------- ! get reference material stifness and 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(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_ref = C * wgt !-------------------------------------------------------------------------------------------------- ! 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 !-------------------------------------------------------------------------------------------------- ! possible restore deformation gradient from saved state if (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 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 !-------------------------------------------------------------------------------------------------- ! 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*wgt,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 CPFEM_mode = 1_pInt ! winding forward 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) .....................................' 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() !-------------------------------------------------------------------------------------------------- ! 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 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 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?) 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) restartInc=totalIncsCounter endif if (update_gamma) then write(6,'(a)') 'update C_ref ' C_ref = C*wgt 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 call quit(0_pInt) end program DAMASK_spectral