corrected divergence calculation. Still some open questions, but improved understanding a lot
This commit is contained in:
Martin Diehl
parent
6dee2616f5
commit
ee401520d7
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@ -122,13 +122,15 @@ program DAMASK_spectral
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! variables storing information for spectral method and FFTW
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real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
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real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
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real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field
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real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
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integer(pInt), dimension(3) :: k_s
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integer*8, dimension(3) :: fftw_plan ! plans for fftw (forward and backward)
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! loop variables, convergence etc.
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real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc ! elapsed time, begin of interval, time interval
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real(pReal) :: guessmode, err_div, err_stress, err_stress_tol, p_hat_avg
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complex(pReal) :: err_div_avg_complex
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complex(pReal), dimension(3) :: divergence_complex
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complex(pReal), parameter :: img = cmplx(0.0_pReal,1.0_pReal)
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real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
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complex(pReal), dimension(3,3) :: temp33_Complex
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@ -139,6 +141,7 @@ program DAMASK_spectral
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logical :: errmatinv, regrid = .false.
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real(pReal) :: defgradDet, defgradDetMax, defgradDetMin
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real(pReal) :: correctionFactor
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integer(pInt), dimension(3) :: cutting_freq
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! --- debugging variables
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real(pReal), dimension(:,:,:,:), allocatable :: divergence
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@ -156,12 +159,10 @@ program DAMASK_spectral
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bc_init%rotation = math_I3 ! assume no rotation
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! --- initializing model size independed parameters
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!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
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if (.not.(command_argument_count()==4 .or. command_argument_count()==6)) &! check for correct number of given arguments
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call IO_error(error_ID=102_pInt)
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!$ call omp_set_num_threads(DAMASK_NumThreadsInt) ! set number of threads for parallel execution set by DAMASK_NUM_THREADS
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call DAMASK_interface_init()
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print '(a)', ''
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print '(a,a)', ' <<<+- DAMASK_spectral init -+>>>'
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print '(a,a)', ' $Id$'
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@ -474,11 +475,12 @@ program DAMASK_spectral
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allocate (defgradold ( res(1),res(2),res(3),3,3)); defgradold = 0.0_pReal
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allocate (coordinates(3,res(1),res(2),res(3))); coordinates = 0.0_pReal
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allocate (temperature( res(1),res(2),res(3))); temperature = bc(1)%temperature ! start out isothermally
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allocate (xi (3,res(1)/2+1,res(2),res(3))); xi =0.0_pReal
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allocate (xi (3,res(1)/2+1,res(2),res(3))); xi =0.0_pReal
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allocate (workfft(res(1)+2,res(2),res(3),3,3)); workfft = 0.0_pReal
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if (debugDivergence) allocate (divergence(res(1)+2,res(2),res(3),3)); divergence = 0.0_pReal
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wgt = 1.0_pReal/real(Npoints, pReal)
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call dfftw_plan_many_dft_r2c(fftw_plan(1),3,(/res(1),res(2),res(3)/),9,&
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workfft,(/res(1) +2_pInt,res(2),res(3)/),1,(res(1) +2_pInt)*res(2)*res(3),&
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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)
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@ -538,24 +540,26 @@ program DAMASK_spectral
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if(j > res(2)/2_pInt + 1_pInt) k_s(2) = k_s(2) - res(2)
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do i = 1, res(1)/2_pInt + 1_pInt
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k_s(1) = i - 1_pInt
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xi(3,i,j,k) = 0.0_pReal ! 2D case
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if(res(3) > 1_pInt) xi(3,i,j,k) = real(k_s(3), pReal)/geomdimension(3) ! 3D case
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xi(2,i,j,k) = real(k_s(2), pReal)/geomdimension(2)
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xi(1,i,j,k) = real(k_s(1), pReal)/geomdimension(1)
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xi(3,i,j,k) = 0.0_pReal ! 2D case
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if(res(3) > 1_pInt) xi(3,i,j,k) = real(k_s(3), pReal)/geomdimension(3) ! 3D case
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xi(2,i,j,k) = real(k_s(2), pReal)/geomdimension(2) ! 2D and 3D case
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xi(1,i,j,k) = real(k_s(1), pReal)/geomdimension(1) ! 2D and 3D case
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enddo; enddo; enddo
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!remove highest frequencies for calculation of divergence (CAREFULL, they will be used for pre calculatet gamma operator!)
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!remove the given highest frequencies for calculation of the gamma operator
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cutting_freq = (/0_pInt,0_pInt,0_pInt/) ! for 0,0,0, just the highest freq. is removed
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do k = 1_pInt ,res(3); do j = 1_pInt ,res(2); do i = 1_pInt,res(1)/2_pInt + 1_pInt
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if(k==res(3)/2_pInt+1_pInt) xi(3,i,j,k)= 0.0_pReal
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if(j==res(2)/2_pInt+1_pInt) xi(2,i,j,k)= 0.0_pReal
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if(i==res(1)/2_pInt+1_pInt) xi(1,i,j,k)= 0.0_pReal
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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
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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
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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
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enddo; enddo; enddo
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if(memory_efficient) then ! allocate just single fourth order tensor
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allocate (gamma_hat(1,1,1,3,3,3,3)); gamma_hat = 0.0_pReal
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else ! precalculation of gamma_hat field
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allocate (gamma_hat(res(1)/2_pInt + 1_pInt ,res(2),res(3),3,3,3,3)); gamma_hat = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)/2_pInt + 1_pInt
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if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then
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do l = 1_pInt ,3_pInt; do m = 1_pInt,3_pInt
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xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
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enddo; enddo
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@ -651,7 +655,7 @@ program DAMASK_spectral
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iter = 0_pInt
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err_div = 2.0_pReal * err_div_tol ! go into loop
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c_prev = math_rotate_forward3x3x3x3(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former step
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c_prev = math_rotate_forward3x3x3x3(c_current*wgt,bc(loadcase)%rotation) ! calculate stiffness from former step
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if(size_reduced > 0_pInt) then ! calculate compliance in case stress BC is applied
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c_prev99 = math_Plain3333to99(c_prev)
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k = 0_pInt ! build reduced stiffness
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@ -731,7 +735,7 @@ program DAMASK_spectral
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cstress,dsde, pstress,dPdF)
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CPFEM_mode = 2_pInt
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workfft(i,j,k,1:3,1:3) = pstress ! build up average P-K stress
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workfft(i,j,k,1:3,1:3) = pstress ! build up average P-K stress
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c_current = c_current + dPdF
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enddo; enddo; enddo
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@ -742,32 +746,60 @@ program DAMASK_spectral
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print '(a)', ''
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print '(a)', '... calculating equilibrium with spectral method ............'
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call dfftw_execute_dft_r2c(fftw_plan(1),workfft,workfft) ! FFT of pstress
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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,
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math_transpose3x3(workfft(1,1,1,1:3,1:3)))))) ! ignore imaginary part as it is always zero for real only input))
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err_div = 0.0_pReal
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err_div_max = 0.0_pReal ! only if if(debugDivergence) == .true. of importace
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call dfftw_execute_dft_r2c(fftw_plan(1),workfft,workfft) ! FFT of pstress
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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,
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math_transpose3x3(workfft(1,1,1,1:3,1:3)))))) ! ignore imaginary part as it is always zero for real only input
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err_div_avg_complex = 0.0_pReal
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err_div_max = 0.0_pReal ! only if debugDivergence == .true. of importance
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divergence = 0.0_pReal ! - '' -
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)/2_pInt+1_pInt
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err_div = err_div + sqrt(sum((& ! avg of L_2 norm of div(stress) in fourier space (Suquet small strain)
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math_mul33x3_complex(workfft(i*2_pInt-1_pInt,j,k,1:3,1:3) + &
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workfft(i*2_pInt ,j,k,1:3,1:3)*img,&
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xi(1:3,i,j,k))&
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)**2.0_pReal))
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if(debugDivergence) &
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err_div_max = max(err_div_max,abs(sqrt(sum((& ! maximum of L two norm of div(stress) in fourier space (Suquet large strain)
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math_mul33x3_complex(workfft(i*2_pInt-1_pInt,j,k,1:3,1:3)+&
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workfft(i*2_pInt ,j,k,1:3,1:3)*img,&
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xi(1:3,i,j,k))&
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)**2.0_pReal))))
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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
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+ workfft(i*2_pInt ,j,k,1:3,1:3)*img,xi(1:3,i,j,k))
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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
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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)
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else ! Has somewhere a conj. complex counterpart. Therefore count it twice.
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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
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endif ! compared to c2c transform results in slight numerical deviations.
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if(debugDivergence) then
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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)
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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
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divergence(i*2_pInt ,j,k,1:3) = real(divergence_complex)*pi*2.0_pReal ! ==> switch order and change sign of img part
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endif
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enddo; enddo; enddo
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err_div = err_div*wgt/p_hat_avg*correctionFactor ! weighting by points and average stress and multiplying with correction factor
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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
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err_div = abs(sqrt (err_div_avg_complex*wgt)) ! weighting by and taking square root. abs(...) because result is a complex number
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err_div = err_div *correctionFactor/p_hat_avg ! weighting by average stress and multiplying with correction factor
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err_div_max = err_div_max*correctionFactor/p_hat_avg ! - '' - only if debugDivergence == .true. of importance
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! calculate additional divergence criteria and report -------------
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if(debugDivergence) then
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call dfftw_execute_dft_c2r(fftw_plan(3),divergence,divergence)
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divergence = divergence * wgt
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err_real_div_avg = 0.0_pReal
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err_real_div_max = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
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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
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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
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enddo; enddo; enddo
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p_real_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space,
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math_transpose3x3(pstress_av_lab)))))
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err_real_div_avg = sqrt(wgt*err_real_div_avg)*correctionFactor/p_hat_avg
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err_real_div_max = err_real_div_max *correctionFactor/p_hat_avg
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print '(a,es10.4,a,f6.2)', 'error divergence FT avg = ',err_div, ', ', err_div/err_div_tol
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print '(a,es10.4)', 'error divergence FT max = ',err_div_max
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print '(a,es10.4)', 'error divergence Real avg = ',err_real_div_avg
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print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max
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else
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print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', ', err_div/err_div_tol
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endif
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! --------------------------
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if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
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do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res(1)/2_pInt+1_pInt
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if (any(xi(:,i,j,k) /= 0.0_pReal)) then
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if (any(xi(1:3,i,j,k) /= 0.0_pReal)) then
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do l = 1_pInt,3_pInt; do m = 1_pInt,3_pInt
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xiDyad(l,m) = xi(l,i,j,k)*xi(m,i,j,k)
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enddo; enddo
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@ -798,53 +830,17 @@ program DAMASK_spectral
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enddo; enddo; enddo
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endif
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! calculate additional divergence criteria and report -------------
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if(debugDivergence) then
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divergence = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)/2_pInt+1_pInt
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! real part at i*2-1, imaginary part at i*2 and multiply by i ==> switch and change sign
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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&
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+ workfft(i*2_pInt ,j,k,1:3,2)*xi(1:3,i,j,k)*pi*2.0_pReal&
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+ workfft(i*2_pInt ,j,k,1:3,3)*xi(1:3,i,j,k)*pi*2.0_pReal
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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&
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- workfft(i*2_pInt-1_pInt,j,k,1:3,2)*xi(1:3,i,j,k)*pi*2.0_pReal&
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- workfft(i*2_pInt-1_pInt,j,k,1:3,3)*xi(1:3,i,j,k)*pi*2.0_pReal
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enddo; enddo; enddo
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divergence = divergence*correctionFactor
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call dfftw_execute_dft_c2r(fftw_plan(3),divergence,divergence)
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divergence = divergence * wgt
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err_real_div_avg = 0.0_pReal
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err_real_div_max = 0.0_pReal
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do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
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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)
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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)
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enddo; enddo; enddo
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p_real_avg = sqrt(maxval (math_eigenvalues3x3(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space,
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math_transpose3x3(pstress_av_lab))))) ! ignore imaginary part as it is always zero for real only input))
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err_real_div_avg = err_real_div_avg*wgt/p_real_avg
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err_real_div_max = err_real_div_max/p_real_avg
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print '(a,es10.4,a,f6.2)', 'error divergence FT avg = ',err_div, ', ', err_div/err_div_tol
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print '(a,es10.4)', 'error divergence FT max = ',err_div_max
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print '(a,es10.4)', 'error divergence Real avg = ',err_real_div_avg
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print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max
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else
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print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', ', err_div/err_div_tol
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endif
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! --------------------------
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workfft(1,1,1,1:3,1:3) = defgrad_av_lab - math_I3 ! assign zero frequency (real part) with average displacement gradient
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workfft(2,1,1,1:3,1:3) = 0.0_pReal ! zero frequency (imaginary part)
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workfft(1,1,1,1:3,1:3) = defgrad_av_lab - math_I3 ! assign zero frequency (real part) with average displacement gradient
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workfft(2,1,1,1:3,1:3) = 0.0_pReal ! zero frequency (imaginary part)
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call dfftw_execute_dft_c2r(fftw_plan(2),workfft,workfft) ! backtransformation of fluct deformation gradient
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call dfftw_execute_dft_c2r(fftw_plan(2),workfft,workfft) ! back transform of fluct deformation gradient
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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
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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
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do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
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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
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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
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enddo; enddo
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! stress boundary condition check -------------
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pstress_av = math_rotate_forward3x3(pstress_av_lab,bc(loadcase)%rotation)
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print '(a,/,3(3(f12.7,x)/)$)', 'Piola-Kirchhoff stress / MPa: ',math_transpose3x3(pstress_av)/1.e6
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@ -865,10 +861,10 @@ program DAMASK_spectral
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! ------------------------------
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! homogeneous correction towards avg deformation gradient -------------
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defgradAim_lab = math_rotate_backward3x3(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
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defgradAim_lab = math_rotate_backward3x3(defgradAim,bc(loadcase)%rotation) ! boundary conditions from load frame into lab (Fourier) frame
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do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
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defgrad(1:res(1),1:res(2),1:res(3),m,n) = &
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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
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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
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enddo; enddo
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! ------------------------------
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||||
|
||||
|
|
|
|||
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Reference in New Issue