!-------------------------------------------------------------------------------------------------- !* $Id$ !-------------------------------------------------------------------------------------------------- !> @author Pratheek Shanthraj, Max-Planck-Institut für Eisenforschung GmbH !> @author Martin Diehl, Max-Planck-Institut für Eisenforschung GmbH !> @author Philip Eisenlohr, Max-Planck-Institut für Eisenforschung GmbH !> @brief Basic scheme solver !-------------------------------------------------------------------------------------------------- module DAMASK_spectral_SolverBasic use, intrinsic :: iso_fortran_env ! to get compiler_version and compiler_options (at least for gfortran >4.6 at the moment) use DAMASK_spectral_Utilities use math, only: & math_I3, & math_mul33x33, use mesh, only : & mesh_spectral_getResolution, & mesh_spectral_getDimension, & math_rotate_backward33, & math_transpose33,& math_mul3333xx33, & math_eigenvalues33 implicit none character (len=*), parameter, public :: & DAMASK_spectral_SolverBasic_label = 'basic' !-------------------------------------------------------------------------------------------------- ! common pointwise data real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc, P real(pReal), dimension(:,:,:,:), allocatable :: coordinates real(pReal), dimension(:,:,:), allocatable :: temperature !-------------------------------------------------------------------------------------------------- ! stress, stiffness and compliance average etc. real(pReal), dimension(3,3) :: & F_aim = math_I3, & F_aim_lastInc = math_I3 real(pReal), dimension(3,3,3,3) :: & C = 0.0_pReal contains subroutine basic_init() use IO, only: & IO_read_JobBinaryFile, & IO_write_JobBinaryFile use FEsolving, only: & restartInc use DAMASK_interface, only: & getSolverJobName implicit none integer(pInt) :: i,j,k real(pReal), dimension(3,3) :: temp33_Real write(6,'(a)') '' write(6,'(a)') ' <<<+- DAMASK_spectral_solverBasic init -+>>>' write(6,'(a)') ' $Id$' #include "compilation_info.f90" write(6,'(a)') '' call Utilities_Init() 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 (P ( res(1), res(2),res(3),3,3), 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 = 0.0_pReal) !-------------------------------------------------------------------------------------------------- ! init fields if (restartInc == 1_pInt) then ! no deformation (no restart) 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) = 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) enddo; enddo; enddo elseif (restartInc > 1_pInt) then ! using old values from file if (debugRestart) write(6,'(a,i6,a)') 'Reading values of increment ',& restartInc - 1_pInt,' from file' call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',& trim(getSolverJobName()),size(F)) read (777,rec=1) F close (777) call IO_read_jobBinaryFile(777,'convergedSpectralDefgrad_lastInc',& trim(getSolverJobName()),size(F_lastInc)) read (777,rec=1) F_lastInc close (777) call IO_read_jobBinaryFile(777,'F_aim',trim(getSolverJobName()),size(F_aim)) read (777,rec=1) F_aim close (777) call IO_read_jobBinaryFile(777,'F_aim_lastInc',trim(getSolverJobName()),size(F_aim_lastInc)) read (777,rec=1) F_aim_lastInc close (777) coordinates = 0.0 ! change it later!!! endif call Utilities_constitutiveResponse(coordinates,F,F_lastInc,temperature,0.0_pReal,& P,C,temp33_Real,.false.,math_I3) !-------------------------------------------------------------------------------------------------- ! reference stiffness if (restartInc == 1_pInt) then call IO_write_jobBinaryFile(777,'C_ref',size(C)) write (777,rec=1) C close(777) elseif (restartInc > 1_pInt) then call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C)) read (777,rec=1) C close (777) endif call Utilities_updateGamma(C) end subroutine basic_init type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC,mask_stressVector,velgrad,rotation_BC) use numerics, only: & itmax, & itmin, & update_gamma use IO, only: & IO_write_JobBinaryFile use FEsolving, only: & restartWrite implicit none !-------------------------------------------------------------------------------------------------- ! input data for solution real(pReal), intent(in) :: timeinc, timeinc_old real(pReal), intent(in) :: guessmode logical, intent(in) :: velgrad real(pReal), dimension(3,3), intent(in) :: P_BC,F_BC,rotation_BC logical, dimension(9), intent(in) :: mask_stressVector !-------------------------------------------------------------------------------------------------- ! loop variables, convergence etc. real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal real(pReal), dimension(3,3) :: temp33_Real real(pReal), dimension(3,3,3,3) :: S real(pReal), dimension(3,3) :: mask_stress, & mask_defgrad, & deltaF_aim, & F_aim_lab, & F_aim_lab_lastIter, & P_av real(pReal) :: err_div, err_stress integer(pInt) :: iter integer(pInt) :: i, j, k logical :: ForwardData real(pReal) :: defgradDet real(pReal) :: defgradDetMax, defgradDetMin mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3])) mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3])) if (restartWrite) then write(6,'(a)') 'writing converged results for restart' call IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(F_lastInc)) ! writing deformation gradient field to file write (777,rec=1) F_LastInc close (777) call IO_write_jobBinaryFile(777,'C',size(C)) write (777,rec=1) C close(777) endif ForwardData = .True. if (velgrad) then ! calculate deltaF_aim from given L and current F deltaF_aim = timeinc * mask_defgrad * math_mul33x33(F_BC, F_aim) else ! deltaF_aim = fDot *timeinc where applicable deltaF_aim = timeinc * mask_defgrad * F_BC 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 F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame !-------------------------------------------------------------------------------------------------- ! update local deformation gradient and coordinates deltaF_aim = math_rotate_backward33(deltaF_aim,rotation_BC) 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))*timeinc/timeinc_old& ! guessing... + (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,rotation_BC),& ! calculate current coordinates 1.0_pReal,F_lastInc,coordinates) iter = 0_pInt S = Utilities_maskedCompliance(rotation_BC,mask_stressVector,C) if (update_gamma) call Utilities_updateGamma(C) convergenceLoop: do iter = iter + 1_pInt !-------------------------------------------------------------------------------------------------- ! report begin of new iteration write(6,'(a)') '' write(6,'(a)') '==================================================================' write(6,'(3(a,i6.6))') ' Iter. ',itmin,' < ',iter,' < ',itmax + 1_pInt write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',& math_transpose33(F_aim) F_aim_lab_lastIter = math_rotate_backward33(F_aim,rotation_BC) !-------------------------------------------------------------------------------------------------- ! evaluate constitutive response print*, 'FLast 111', F_lastInc(1,1,1,1:3,1:3) call Utilities_constitutiveResponse(coordinates,F_lastInc,F,temperature,timeinc,& P,C,P_av,ForwardData,rotation_BC) ForwardData = .False. !-------------------------------------------------------------------------------------------------- ! stress BC handling F_aim = F_aim - math_mul3333xx33(S, ((P_av - P_BC))) !S = 0.0 for no bc err_stress = maxval(mask_stress * (P_av - P_BC)) ! mask = 0.0 for no bc F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame !-------------------------------------------------------------------------------------------------- ! updated deformation gradient field_real = 0.0_pReal field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = P call Utilities_forwardFFT() err_div = Utilities_divergenceRMS() call Utilities_fourierConvolution(F_aim_lab_lastIter - F_aim_lab) call Utilities_backwardFFT() temp33_real =0.0_pReal 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) - field_real(i,j,k,1:3,1:3) ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization temp33_real = temp33_real + field_real(i,j,k,1:3,1:3) enddo; enddo; enddo if (Convergenced(err_div,P_av,err_stress,P_av,iter)) exit enddo convergenceLoop end function basic_solution logical function Convergenced(err_div,P_av,err_stress,P_av2,iter) use numerics, only: & itmax, & itmin, & err_div_tol, & err_stress_tolrel, & err_stress_tolabs implicit none real(pReal), dimension(3,3) :: P_av, P_av2 real(pReal) :: err_div, err_stress, field_av_L2 integer(pInt) :: iter field_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html) math_transpose33(P_av))))) Convergenced = (iter < itmax) .and. (iter > itmin) .and. & all([err_div/field_av_L2/err_div_tol,& err_stress/min(maxval(abs(P_av2))*err_stress_tolrel,err_stress_tolabs)] < 1.0_pReal) write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/min(maxval(abs(P_av2))*err_stress_tolrel,err_stress_tolabs), & ' (',err_stress,' Pa)' write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/field_av_L2/err_div_tol,& ' (',err_div,' N/m³)' end function Convergenced subroutine basic_destroy() implicit none call Utilities_destroy() end subroutine basic_destroy end module DAMASK_spectral_SolverBasic !-------------------------------------------------------------------------------------------------- ! 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(field_real(i,j,k,1:3,1:3)))) ! maxCorrectionSkew = max(maxCorrectionSkew,& ! maxval(math_skew33(field_real(i,j,k,1:3,1:3)))) ! temp33_Real = temp33_Real + field_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 !-------------------------------------------------------------------------------------------------- ! 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