diff --git a/code/DAMASK_spectral.f90 b/code/DAMASK_spectral.f90 index 8393d0618..3bf9ad6e3 100644 --- a/code/DAMASK_spectral.f90 +++ b/code/DAMASK_spectral.f90 @@ -122,13 +122,15 @@ program DAMASK_spectral ! variables storing information for spectral method and 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 + real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator integer(pInt), dimension(3) :: k_s integer*8, dimension(3) :: fftw_plan ! plans for fftw (forward and backward) ! loop variables, convergence etc. real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc ! elapsed time, begin of interval, time interval real(pReal) :: guessmode, err_div, err_stress, err_stress_tol, p_hat_avg + complex(pReal) :: err_div_avg_complex + complex(pReal), dimension(3) :: divergence_complex complex(pReal), parameter :: img = cmplx(0.0_pReal,1.0_pReal) real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal complex(pReal), dimension(3,3) :: temp33_Complex @@ -139,6 +141,7 @@ program DAMASK_spectral logical :: errmatinv, regrid = .false. real(pReal) :: defgradDet, defgradDetMax, defgradDetMin real(pReal) :: correctionFactor + integer(pInt), dimension(3) :: cutting_freq ! --- debugging variables real(pReal), dimension(:,:,:,:), allocatable :: divergence @@ -156,12 +159,10 @@ program DAMASK_spectral bc_init%rotation = math_I3 ! assume no rotation ! --- initializing model size independed parameters - !$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS - if (.not.(command_argument_count()==4 .or. command_argument_count()==6)) &! check for correct number of given arguments - call IO_error(error_ID=102_pInt) + !$ 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,a)', ' <<<+- DAMASK_spectral init -+>>>' print '(a,a)', ' $Id$' @@ -474,11 +475,12 @@ program DAMASK_spectral allocate (defgradold ( res(1),res(2),res(3),3,3)); defgradold = 0.0_pReal allocate (coordinates(3,res(1),res(2),res(3))); coordinates = 0.0_pReal allocate (temperature( res(1),res(2),res(3))); temperature = bc(1)%temperature ! start out isothermally - allocate (xi (3,res(1)/2+1,res(2),res(3))); xi =0.0_pReal + allocate (xi (3,res(1)/2+1,res(2),res(3))); xi =0.0_pReal allocate (workfft(res(1)+2,res(2),res(3),3,3)); workfft = 0.0_pReal if (debugDivergence) allocate (divergence(res(1)+2,res(2),res(3),3)); divergence = 0.0_pReal wgt = 1.0_pReal/real(Npoints, pReal) + call dfftw_plan_many_dft_r2c(fftw_plan(1),3,(/res(1),res(2),res(3)/),9,& workfft,(/res(1) +2_pInt,res(2),res(3)/),1,(res(1) +2_pInt)*res(2)*res(3),& workfft,(/res(1)/2_pInt+1_pInt,res(2),res(3)/),1,(res(1)/2_pInt+1_pInt)*res(2)*res(3),fftw_planner_flag) @@ -538,24 +540,26 @@ program DAMASK_spectral if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2) do i = 1, res(1)/2_pInt + 1_pInt k_s(1) = i - 1_pInt - xi(3,i,j,k) = 0.0_pReal ! 2D case - if(res(3) > 1_pInt) xi(3,i,j,k) = real(k_s(3), pReal)/geomdimension(3) ! 3D case - xi(2,i,j,k) = real(k_s(2), pReal)/geomdimension(2) - xi(1,i,j,k) = real(k_s(1), pReal)/geomdimension(1) + xi(3,i,j,k) = 0.0_pReal ! 2D case + if(res(3) > 1_pInt) xi(3,i,j,k) = real(k_s(3), pReal)/geomdimension(3) ! 3D case + xi(2,i,j,k) = real(k_s(2), pReal)/geomdimension(2) ! 2D and 3D case + xi(1,i,j,k) = real(k_s(1), pReal)/geomdimension(1) ! 2D and 3D case enddo; enddo; enddo - !remove highest frequencies for calculation of divergence (CAREFULL, they will be used for pre calculatet gamma operator!) + + !remove the given highest frequencies for calculation of the gamma operator + cutting_freq = (/0_pInt,0_pInt,0_pInt/) ! for 0,0,0, just the highest freq. is removed do k = 1_pInt ,res(3); do j = 1_pInt ,res(2); do i = 1_pInt,res(1)/2_pInt + 1_pInt - if(k==res(3)/2_pInt+1_pInt) xi(3,i,j,k)= 0.0_pReal - if(j==res(2)/2_pInt+1_pInt) xi(2,i,j,k)= 0.0_pReal - if(i==res(1)/2_pInt+1_pInt) xi(1,i,j,k)= 0.0_pReal + if((k .gt. res(3)/2_pInt - cutting_freq(3)).and.(k .le. res(3)/2_pInt + 1_pInt + cutting_freq(3))) xi(3,i,j,k)= 0.0_pReal + if((j .gt. res(2)/2_pInt - cutting_freq(2)).and.(j .le. res(2)/2_pInt + 1_pInt + cutting_freq(2))) xi(2,i,j,k)= 0.0_pReal + if((i .gt. res(1)/2_pInt - cutting_freq(1)).and.(i .le. res(2)/2_pInt + 1_pInt + cutting_freq(1))) xi(1,i,j,k)= 0.0_pReal enddo; enddo; enddo - + 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(res(1)/2_pInt + 1_pInt ,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, res(1)/2_pInt + 1_pInt - if (any(xi(:,i,j,k) /= 0.0_pReal)) then + if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then do l = 1_pInt ,3_pInt; do m = 1_pInt,3_pInt xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k) enddo; enddo @@ -651,7 +655,7 @@ program DAMASK_spectral iter = 0_pInt err_div = 2.0_pReal * err_div_tol ! go into loop - c_prev = math_rotate_forward3x3x3x3(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former step + c_prev = math_rotate_forward3x3x3x3(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former step 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 @@ -731,7 +735,7 @@ program DAMASK_spectral cstress,dsde, pstress,dPdF) CPFEM_mode = 2_pInt - workfft(i,j,k,1:3,1:3) = pstress ! build up average P-K stress + workfft(i,j,k,1:3,1:3) = pstress ! build up average P-K stress c_current = c_current + dPdF enddo; enddo; enddo @@ -742,32 +746,60 @@ program DAMASK_spectral print '(a)', '' print '(a)', '... calculating equilibrium with spectral method ............' - call dfftw_execute_dft_r2c(fftw_plan(1),workfft,workfft) ! FFT of pstress - - p_hat_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(workfft(1,1,1,1:3,1:3),& ! L_2 norm of average stress in fourier space, - math_transpose3x3(workfft(1,1,1,1:3,1:3)))))) ! ignore imaginary part as it is always zero for real only input)) - err_div = 0.0_pReal - err_div_max = 0.0_pReal ! only if if(debugDivergence) == .true. of importace + call dfftw_execute_dft_r2c(fftw_plan(1),workfft,workfft) ! FFT of pstress + + p_hat_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(workfft(1,1,1,1:3,1:3),& ! L_2 norm of average stress (freq 0,0,0) in fourier space, + math_transpose3x3(workfft(1,1,1,1:3,1:3)))))) ! ignore imaginary part as it is always zero for real only input + err_div_avg_complex = 0.0_pReal + err_div_max = 0.0_pReal ! only if debugDivergence == .true. of importance + divergence = 0.0_pReal ! - '' - + do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)/2_pInt+1_pInt - err_div = err_div + sqrt(sum((& ! avg of L_2 norm of div(stress) in fourier space (Suquet small strain) - math_mul33x3_complex(workfft(i*2_pInt-1_pInt,j,k,1:3,1:3) + & - workfft(i*2_pInt ,j,k,1:3,1:3)*img,& - xi(1:3,i,j,k))& - )**2.0_pReal)) - if(debugDivergence) & - err_div_max = max(err_div_max,abs(sqrt(sum((& ! maximum of L two norm of div(stress) in fourier space (Suquet large strain) - math_mul33x3_complex(workfft(i*2_pInt-1_pInt,j,k,1:3,1:3)+& - workfft(i*2_pInt ,j,k,1:3,1:3)*img,& - xi(1:3,i,j,k))& - )**2.0_pReal)))) + divergence_complex = math_mul33x3_complex(workfft(i*2_pInt-1_pInt,j,k,1:3,1:3)& ! calculate divergence out of the real and imaginary part of the stress + + workfft(i*2_pInt ,j,k,1:3,1:3)*img,xi(1:3,i,j,k)) + if(i==1_pInt .or. i == res(1)/2_pInt + 1_pInt) then ! We are on one of the two slides without conjg. complex counterpart + err_div_avg_complex = err_div_avg_complex + sum(divergence_complex**2.0_pReal) ! Avg of L_2 norm of div(stress) in fourier space (Suquet small strain) + else ! Has somewhere a conj. complex counterpart. Therefore count it twice. + err_div_avg_complex = err_div_avg_complex +2.0*real(sum(divergence_complex**2.0_pReal)) ! Ignore img part (conjg. complex sum will end up 0). This and the different order + endif ! compared to c2c transform results in slight numerical deviations. + if(debugDivergence) then + err_div_max = max(err_div_max,abs(sqrt(sum(divergence_complex**2.0_pReal)))) ! maximum of L two norm of div(stress) in fourier space (Suquet large strain) + divergence(i*2_pInt-1_pInt,j,k,1:3) = -aimag(divergence_complex)*pi*2.0_pReal ! real part at i*2-1, imaginary part at i*2, multiply by i + divergence(i*2_pInt ,j,k,1:3) = real(divergence_complex)*pi*2.0_pReal ! ==> switch order and change sign of img part + endif enddo; enddo; enddo - err_div = err_div*wgt/p_hat_avg*correctionFactor ! weighting by points and average stress and multiplying with correction factor - err_div_max = err_div_max/p_hat_avg*correctionFactor ! weighting by average stress and multiplying with correction factor, only if if(debugDivergence) == .true. of importace + err_div = abs(sqrt (err_div_avg_complex*wgt)) ! weighting by and taking square root. abs(...) because result is a complex number + err_div = err_div *correctionFactor/p_hat_avg ! weighting by average stress and multiplying with correction factor + err_div_max = err_div_max*correctionFactor/p_hat_avg ! - '' - only if debugDivergence == .true. of importance + ! calculate additional divergence criteria and report ------------- + if(debugDivergence) then + call dfftw_execute_dft_c2r(fftw_plan(3),divergence,divergence) + divergence = divergence * wgt + + err_real_div_avg = 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_avg = err_real_div_avg + sum(divergence(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(i,j,k,1:3)**2.0_pReal))) ! maximum of L two norm of div(stress) in real space + enddo; enddo; enddo + p_real_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space, + math_transpose3x3(pstress_av_lab))))) + err_real_div_avg = sqrt(wgt*err_real_div_avg)*correctionFactor/p_hat_avg + err_real_div_max = err_real_div_max *correctionFactor/p_hat_avg + + print '(a,es10.4,a,f6.2)', 'error divergence FT avg = ',err_div, ', ', err_div/err_div_tol + print '(a,es10.4)', 'error divergence FT max = ',err_div_max + print '(a,es10.4)', 'error divergence Real avg = ',err_real_div_avg + print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max + else + print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', ', err_div/err_div_tol + endif + ! -------------------------- 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, res(1)/2_pInt+1_pInt - if (any(xi(:,i,j,k) /= 0.0_pReal)) then + if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k) enddo; enddo @@ -798,53 +830,17 @@ program DAMASK_spectral enddo; enddo; enddo endif - ! calculate additional divergence criteria and report ------------- - if(debugDivergence) then - divergence = 0.0_pReal - do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)/2_pInt+1_pInt - ! real part at i*2-1, imaginary part at i*2 and multiply by i ==> switch and change sign - divergence(i*2_pInt-1_pInt,j,k,1:3) = workfft(i*2_pInt ,j,k,1:3,1)*xi(1:3,i,j,k)*pi*2.0_pReal& - + workfft(i*2_pInt ,j,k,1:3,2)*xi(1:3,i,j,k)*pi*2.0_pReal& - + workfft(i*2_pInt ,j,k,1:3,3)*xi(1:3,i,j,k)*pi*2.0_pReal - divergence(i*2_pInt,j,k,1:3) = - workfft(i*2_pInt-1_pInt,j,k,1:3,1)*xi(1:3,i,j,k)*pi*2.0_pReal& - - workfft(i*2_pInt-1_pInt,j,k,1:3,2)*xi(1:3,i,j,k)*pi*2.0_pReal& - - workfft(i*2_pInt-1_pInt,j,k,1:3,3)*xi(1:3,i,j,k)*pi*2.0_pReal - enddo; enddo; enddo - divergence = divergence*correctionFactor - call dfftw_execute_dft_c2r(fftw_plan(3),divergence,divergence) - divergence = divergence * wgt - err_real_div_avg = 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_avg = err_real_div_avg + sqrt(sum((divergence(i,j,k,1:3))**2.0_pReal)) ! avg of L_2 norm of div(stress) in fourier space (Suquet small strain) - err_real_div_max = max(err_real_div_max,abs(sqrt(sum((divergence(i,j,k,1:3))**2.0_pReal)))) ! maximum of L two norm of div(stress) in fourier space (Suquet large strain) - enddo; enddo; enddo - p_real_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space, - math_transpose3x3(pstress_av_lab))))) ! ignore imaginary part as it is always zero for real only input)) - err_real_div_avg = err_real_div_avg*wgt/p_real_avg - err_real_div_max = err_real_div_max/p_real_avg - - print '(a,es10.4,a,f6.2)', 'error divergence FT avg = ',err_div, ', ', err_div/err_div_tol - print '(a,es10.4)', 'error divergence FT max = ',err_div_max - print '(a,es10.4)', 'error divergence Real avg = ',err_real_div_avg - print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max - else - print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', ', err_div/err_div_tol - endif - ! -------------------------- - - workfft(1,1,1,1:3,1:3) = defgrad_av_lab - math_I3 ! assign zero frequency (real part) with average displacement gradient - workfft(2,1,1,1:3,1:3) = 0.0_pReal ! zero frequency (imaginary part) + workfft(1,1,1,1:3,1:3) = defgrad_av_lab - math_I3 ! assign zero frequency (real part) with average displacement gradient + workfft(2,1,1,1:3,1:3) = 0.0_pReal ! zero frequency (imaginary part) - call dfftw_execute_dft_c2r(fftw_plan(2),workfft,workfft) ! backtransformation of fluct deformation gradient + call dfftw_execute_dft_c2r(fftw_plan(2),workfft,workfft) ! back transform of fluct deformation gradient - defgrad = defgrad + workfft(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 + defgrad = defgrad + workfft(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 do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt - defgrad_av_lab(m,n) = sum(defgrad(1:res(1),1:res(2),1:res(3),m,n))*wgt ! ToDo: check whether this needs recalculation or is equivalent to former defgrad_av + defgrad_av_lab(m,n) = sum(defgrad(1:res(1),1:res(2),1:res(3),m,n))*wgt ! ToDo: check whether this needs recalculation or is equivalent to former defgrad_av enddo; enddo - ! stress boundary condition check ------------- pstress_av = math_rotate_forward3x3(pstress_av_lab,bc(loadcase)%rotation) print '(a,/,3(3(f12.7,x)/)$)', 'Piola-Kirchhoff stress / MPa: ',math_transpose3x3(pstress_av)/1.e6 @@ -865,10 +861,10 @@ program DAMASK_spectral ! ------------------------------ ! homogeneous correction towards avg deformation gradient ------------- - defgradAim_lab = math_rotate_backward3x3(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame + defgradAim_lab = math_rotate_backward3x3(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt defgrad(1:res(1),1:res(2),1:res(3),m,n) = & - defgrad(1:res(1),1:res(2),1:res(3),m,n) + (defgradAim_lab(m,n) - defgrad_av_lab(m,n)) ! anticipated target minus current state + defgrad(1:res(1),1:res(2),1:res(3),m,n) + (defgradAim_lab(m,n) - defgrad_av_lab(m,n)) ! anticipated target minus current state enddo; enddo ! ------------------------------