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DAMASK_EICMD
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restructured algorithm, initialization now not longer within increments, lot of small improvements/polishing 

makefile now calls compiler with lot of warning flags
This commit is contained in:
Martin Diehl 2012-02-10 11:59:59 +00:00
parent 37ac7bf1b4
commit 1cc2315954
3 changed files with 516 additions and 387 deletions
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code/DAMASK_spectral.f90
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@ -49,7 +49,7 @@ program DAMASK_spectral
use math
use kdtree2_module
use CPFEM, only: CPFEM_general, CPFEM_initAll
use FEsolving, only: restartWrite, restartReadInc
use FEsolving, only: restartWrite, restartInc
use numerics, only: err_div_tol, err_stress_tolrel, rotation_tol, itmax, &
memory_efficient, update_gamma, &
simplified_algorithm, divergence_correction, &
@ -115,13 +115,23 @@ program DAMASK_spectral
! stress, stiffness and compliance average etc.
real(pReal), dimension(3,3) :: pstress, pstress_av, &
defgradAim = math_I3, defgradAimOld = math_I3,&
mask_stress, mask_defgrad, fDot, &
mask_stress, mask_defgrad, deltaF, &
pstress_av_lab, defgradAim_lab, defgrad_av_lab ! quantities rotated to other coordinate system
real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current = 0.0_pReal, s_prev, c_prev ! stiffness and compliance
real(pReal), dimension(3,3,3,3) :: dPdF, c0_reference, c_current = 0.0_pReal, s_prev, c_prev,& ! stiffness and compliance
s0_reference
real(pReal), dimension(6) :: cstress ! cauchy stress
real(pReal), dimension(6,6) :: dsde ! small strain stiffness
real(pReal), dimension(9,9) :: s_prev99, c_prev99 ! compliance and stiffness in matrix notation
real(pReal), dimension(6,6) :: dsde, c0_66, s0_66 ! small strain stiffness
real(pReal), dimension(9,9) :: s_prev99, c_prev99, c0_99, s0_99 ! compliance and stiffness in matrix notation
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
real(pReal), dimension(6,6) :: mask_inversion = reshape([&
1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,&
1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,&
1.0_pReal, 1.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal,&
0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal, 0.0_pReal,&
0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal, 0.0_pReal,&
0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 0.0_pReal, 1.0_pReal],&
[ 6_pInt, 6_pInt])
real(pReal), dimension(3,3,3,3) :: temp_3333 = 0.0_pReal
integer(pInt) :: size_reduced = 0.0_pReal ! number of stress BCs
!--------------------------------------------------------------------------------------------------
@ -129,8 +139,8 @@ program DAMASK_spectral
type(C_PTR) :: tensorField, tau ! fields in real an fourier space
real(pReal), dimension(:,:,:,:,:), pointer :: tensorField_real ! fields in real space (pointer)
real(pReal), dimension(:,:,:,:,:), pointer :: tau_real
complex(pReal), dimension(:,:,:,:,:), pointer :: tensorField_complex ! fields in fourier space (pointer)
complex(pReal), dimension(:,:,:,:,:), pointer :: tau_complex
complex(pReal), dimension(:,:,:,:,:), pointer :: tensorField_fourier ! fields in fourier space (pointer)
complex(pReal), dimension(:,:,:,:,:), pointer :: tau_fourier
real(pReal), dimension(:,:,:,:,:), allocatable :: defgrad, defgradold
real(pReal), dimension(:,:,:,:), allocatable :: coordinates
real(pReal), dimension(:,:,:), allocatable :: temperature
@ -145,7 +155,7 @@ program DAMASK_spectral
!--------------------------------------------------------------------------------------------------
! loop variables, convergence etc.
real(pReal) :: time = 0.0_pReal, time0 = 0.0_pReal, timeinc ! elapsed time, begin of interval, time interval
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
@ -153,8 +163,8 @@ program DAMASK_spectral
real(pReal), dimension(3,3) :: temp33_Real
integer(pInt) :: i, j, k, l, m, n, p, errorID
integer(pInt) :: N_Loadcases, loadcase, inc, iter, ielem, CPFEM_mode, &
ierr, notConvergedCounter = 0_pInt, totalIncsCounter = 0_pInt,&
writtenRestart = 0_pInt
ierr, totalIncsCounter = 0_pInt,&
notConvergedCounter = 0_pInt, convergedCounter = 0_pInt
logical :: errmatinv
real(pReal) :: defgradDet, correctionFactor
@ -164,25 +174,24 @@ program DAMASK_spectral
!--------------------------------------------------------------------------------------------------
!variables for additional output due to general debugging
real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew
real(pReal) :: defgradDetMax, defgradDetMin, maxCorrectionSym, maxCorrectionSkew, max_diag, max_offdiag
!--------------------------------------------------------------------------------------------------
! variables for additional output of divergence calculations
type(C_PTR) :: divergence, plan_divergence
real(pReal), dimension(:,:,:,:), pointer :: divergence_real
complex(pReal), dimension(:,:,:,:), pointer :: divergence_complex
complex(pReal), dimension(:,:,:,:), pointer :: divergence_fourier
real(pReal), dimension(:,:,:,:), allocatable :: divergence_postProc
real(pReal) :: p_hat_avg, p_real_avg,&
err_div_RMS, err_real_div_RMS,&
real(pReal) :: pstress_av_L2, err_div_RMS, err_real_div_RMS,&
err_div_max, err_real_div_max,&
max_div_error
!--------------------------------------------------------------------------------------------------
! variables for debugging fft using a scalar field
type(C_PTR) :: scalarField_realPointer, scalarField_complexPointer,&
type(C_PTR) :: scalarField_realC, scalarField_fourierC,&
plan_scalarField_forth, plan_scalarField_back
real(pReal), dimension(:,:,:), pointer :: scalarField_real
complex(pReal), dimension(:,:,:), pointer :: scalarField_complex
complex(pReal), dimension(:,:,:), pointer :: scalarField_real
complex(pReal), dimension(:,:,:), pointer :: scalarField_fourier
integer(pInt) :: row, column
!##################################################################################################
@ -250,7 +259,7 @@ program DAMASK_spectral
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)%maskDeformation = transpose(reshape(temp_maskVector,[ 3,3]))
bc(loadcase)%deformation = math_plain9to33(temp_valueVector)
case('p','pk1','piolakirchhoff','stress')
temp_valueVector = 0.0_pReal
@ -260,7 +269,7 @@ program DAMASK_spectral
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)%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)
@ -359,7 +368,7 @@ program DAMASK_spectral
! sanity checks of geometry parameters
if (.not.(gotDimension .and. gotHomogenization .and. gotResolution))&
call IO_error(error_ID = 45_pInt)
if (any(geomdim<=0.0_pReal)) stop
if (any(geomdim<=0.0_pReal)) call IO_error(error_ID = 102_pInt)
if(mod(res(1),2_pInt)/=0_pInt .or.&
mod(res(2),2_pInt)/=0_pInt .or.&
(mod(res(3),2_pInt)/=0_pInt .and. res(3)/= 1_pInt))&
@ -411,9 +420,9 @@ program DAMASK_spectral
print '(a)','deformation gradient rate:'
endif
write (*,'(3(3(f12.7,1x)/))',advance='no') merge(math_transpose33(bc(loadcase)%deformation),&
reshape(spread(DAMASK_NaN,1,9),(/3,3/)),transpose(bc(loadcase)%maskDeformation))
reshape(spread(DAMASK_NaN,1,9),[ 3,3]),transpose(bc(loadcase)%maskDeformation))
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' stress / GPa:',&
1e-9*merge(math_transpose33(bc(loadcase)%stress),reshape(spread(DAMASK_NaN,1,9),(/3,3/))&
1e-9*merge(math_transpose33(bc(loadcase)%stress),reshape(spread(DAMASK_NaN,1,9),[ 3,3])&
,transpose(bc(loadcase)%maskStress))
if (any(bc(loadcase)%rotation /= math_I3)) &
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') ' rotation of loadframe:',&
@ -426,10 +435,10 @@ program DAMASK_spectral
if (any(bc(loadcase)%maskStress .eqv. bc(loadcase)%maskDeformation)) errorID = 31 ! exclusive or masking only
if (any(bc(loadcase)%maskStress .and. transpose(bc(loadcase)%maskStress) .and. &
reshape((/.false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false./),(/3,3/)))) &
reshape([ .false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false.],[ 3,3]))) &
errorID = 38_pInt ! no rotation is allowed by stress BC
if (any(abs(math_mul33x33(bc(loadcase)%rotation,math_transpose33(bc(loadcase)%rotation))&
-math_I3) > reshape(spread(rotation_tol,1,9),(/3,3/)))&
-math_I3) > reshape(spread(rotation_tol,1,9),[ 3,3]))&
.or. abs(math_det33(bc(loadcase)%rotation)) > 1.0_pReal + rotation_tol)&
errorID = 46_pInt ! given rotation matrix contains strain
if (bc(loadcase)%time < 0.0_pReal) errorID = 34_pInt ! negative time increment
@ -446,56 +455,9 @@ program DAMASK_spectral
debugFFTW = iand(debug_spectral,debug_spectralFFTW) > 0_pInt
!##################################################################################################
! Loop over loadcases defined in the loadcase file
! initialization
!##################################################################################################
do loadcase = 1_pInt, N_Loadcases
time0 = time ! loadcase start time
if (bc(loadcase)%followFormerTrajectory) then ! continue to guess along former trajectory where applicable
guessmode = 1.0_pReal
else
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
endif
!--------------------------------------------------------------------------------------------------
! arrays for mixed boundary conditions
mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
size_reduced = count(bc(loadcase)%maskStressVector)
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
fDot = bc(loadcase)%deformation ! only valid for given fDot. will be overwritten later in case L is given
!##################################################################################################
! loop oper incs defined in input file for current loadcase
!##################################################################################################
do inc = 1_pInt, bc(loadcase)%incs
!--------------------------------------------------------------------------------------------------
! forwarding time
if (bc(loadcase)%logscale == 1_pInt) then ! logarithmic scale
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
totalIncsCounter = totalIncsCounter + 1_pInt
!##################################################################################################
! initialization start after forwarding to restart step
!##################################################################################################
if(totalIncsCounter == restartReadInc+1_pInt) then ! Initialize values
guessmode = 0.0_pReal ! no old values
allocate (defgrad ( res(1), res(2),res(3),3,3)); defgrad = 0.0_pReal
allocate (defgradold ( res(1), res(2),res(3),3,3)); defgradold = 0.0_pReal
allocate (coordinates( res(1), res(2),res(3),3)); coordinates = 0.0_pReal
@ -503,83 +465,32 @@ program DAMASK_spectral
allocate (xi (3,res1_red,res(2),res(3))); xi = 0.0_pReal
tensorField = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T)) ! allocate continous data using a C function, C_SIZE_T is of type integer(8)
call c_f_pointer(tensorField, tensorField_real, [ res(1)+2_pInt,res(2),res(3),3,3]) ! place a pointer for the real representation
call c_f_pointer(tensorField, tensorField_complex, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
call c_f_pointer(tensorField, tensorField_fourier, [ res1_red, res(2),res(3),3,3]) ! place a pointer for the complex representation
!--------------------------------------------------------------------------------------------------
! 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=102) ! check for correct precision in C
#ifdef _OPENMP
if(DAMASK_NumThreadsInt > 0_pInt) then
ierr = fftw_init_threads()
if (ierr == 0_pInt) call IO_error(error_ID = 104_pInt)
call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
endif
#endif
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! creating plans
plan_stress = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),9,& ! dimensions , length in each dimension in reversed order
tensorField_real,(/res(3),res(2) ,res(1)+2_pInt/),& ! input data , physical length in each dimension in reversed order
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
tensorField_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
plan_correction =fftw_plan_many_dft_c2r(3,(/res(3),res(2) ,res(1)/),9,&
tensorField_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,&
tensorField_real,(/res(3),res(2) ,res(1)+2_pInt/),&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
!--------------------------------------------------------------------------------------------------
! depending on (debug) options, allocate more memory and create additional plans
if (.not. simplified_algorithm) then
print*, 'using polarization field based algorithm'
tau = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T))
call c_f_pointer(tau, tau_real, [ res(1)+2_pInt,res(2),res(3),3,3])
call c_f_pointer(tau, tau_complex, [ res1_red, res(2),res(3),3,3])
plan_tau = fftw_plan_many_dft_r2c(3,(/res(3),res(2) ,res(1)/),9,&
tau_real,(/res(3),res(2) ,res(1)+2_pInt/),&
1, res(3)*res(2)*(res(1)+2_pInt),&
tau_complex,(/res(3),res(2) ,res1_red/),&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
endif
if (debugDivergence) then
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
call c_f_pointer(divergence, divergence_complex, [ res1_red, res(2),res(3),3])
allocate (divergence_postProc(res(1),res(2),res(3),3)); divergence_postProc= 0.0_pReal
plan_divergence = fftw_plan_many_dft_c2r(3,(/res(3),res(2) ,res(1)/),3,&
divergence_complex,(/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_realPointer = fftw_alloc_complex(int(res(1) *res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
scalarField_complexPointer = fftw_alloc_complex(int(res1_red*res(2)*res(3),C_SIZE_T))
call c_f_pointer(scalarField_realPointer, scalarField_real, [res(1), res(2),res(3)])
call c_f_pointer(scalarField_complexPointer, scalarField_complex, [res1_red,res(2),res(3)])
plan_scalarField_forth = fftw_plan_dft_r2c_3d(res(3),res(2),res(1),& !reversed order
scalarField_real,scalarField_complex,fftw_planner_flag)
plan_scalarField_back = fftw_plan_dft_c2r_3d(res(3),res(2),res(1),& !reversed order
scalarField_complex,scalarField_real,fftw_planner_flag)
endif
if (debugGeneral) print '(a)' , 'FFTW initialized'
!--------------------------------------------------------------------------------------------------
! calculate initial deformation
if (restartReadInc==0_pInt) then ! not restarting, no deformation at the beginning
! init fields to no deformation
ielem = 0_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
ielem = ielem + 1_pInt
defgrad(i,j,k,1:3,1:3) = math_I3
defgradold(i,j,k,1:3,1:3) = math_I3
coordinates(i,j,k,1:3) = geomdim/real(res, pReal)*[i,j,k] - geomdim/real(2_pInt*res,pReal)
call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c_current = c_current + dPdF
enddo; enddo; enddo
else ! using old values from file
c0_reference = c_current * wgt ! linear reference material stiffness
c0_66 = math_Mandel3333to66(c0_reference)
call math_invert(6_pInt, c0_66, s0_66, i, errmatinv) ! invert in mandel notation
if(errmatinv) call IO_error(error_ID=800_pInt)
s0_reference = math_Mandel66to3333(s0_66)
!--------------------------------------------------------------------------------------------------
! possible restore deformation gradient from saved state
if (restartInc > 1_pInt) then ! using old values from file
if (debugRestart) print '(a,i6,a)' , 'Reading values of increment ',&
restartReadInc ,' from file'
restartInc - 1_pInt,' from file'
if (IO_read_jobBinaryFile(777,'convergedSpectralDefgrad',&
trim(getSolverJobName()),size(defgrad))) then
read (777,rec=1) defgrad
@ -592,22 +503,10 @@ program DAMASK_spectral
enddo; enddo; enddo
defgradAim = defgradAim * wgt
defgradAimOld = defgradAim
guessmode=0.0_pInt
endif
call deformed_fft(res,geomdim,defgradAimOld,1.0_pReal,defgrad,coordinates) ! calculate current coordinates
ielem = 0_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
ielem = ielem + 1_pInt
call CPFEM_general(2_pInt,coordinates(i,j,k,1:3),math_I3,math_I3,temperature(i,j,k),&
0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
c_current = c_current + dPdF
enddo; enddo; enddo
c0_reference = c_current * wgt ! linear reference material stiffness
!--------------------------------------------------------------------------------------------------
! calculation of discrete angular frequencies, ordered as in FFTW (wrap around) and remove the given highest frequencies
if (debugGeneral) print '(a)' , 'first call to CPFEM_general finished'
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)
@ -619,12 +518,6 @@ program DAMASK_spectral
xi(1:3,i,j,k) = real(k_s, pReal)/geomdim
enddo; enddo; enddo
xi(1,res1_red-cutting_freq(1):res1_red , 1:res(2) , 1:res(3)) = 0.0_pReal
xi(2,1:res1_red, res(2)/2_pInt+1_pInt-cutting_freq(2):res(2)/2_pInt+1_pInt+cutting_freq(2),&
1:res(3)) = 0.0_pReal
xi(3,1:res1_red, 1:res(2) ,&
res(3)/2_pInt+1_pInt-cutting_freq(3):res(3)/2_pInt+1_pInt+cutting_freq(3)) = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! calculate the gamma operator
if(memory_efficient) then ! allocate just single fourth order tensor
@ -633,34 +526,98 @@ program DAMASK_spectral
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3)); gamma_hat = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
if (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)
do m = 1_pInt ,3_pInt; do p = 1_pInt,3_pInt
xiDyad(m,p) = xi(m, i,j,k)*xi(p, i,j,k)
enddo; enddo
temp33_Real = math_inv33(math_mul3333xx33(c0_reference, xiDyad))
! do l = 1_pInt,3_pInt
! do n = 1_pInt,3_pInt
! temp33_Real(l,n) = sum(c0_reference(l,1:3,n,1:3)*xiDyad(1:3,1:3))
! enddo; enddo
temp33_Real= math_mul3333xx33(c0_reference,xiDyad)
temp33_Real = math_inv33(temp33_Real)
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
! if (k==res(3)/2 .or. k==res(3)/2+2 .or.&
! j==res(2)/2 .or. j==res(2)/2+2 .or.&
! i==res(1)/2 .or. i==res(1)/2+2) &
! gamma_hat(1,1,1,1:3,1:3,1:3,1:3) = s0_reference
do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt; do p=1_pInt,3_pInt
gamma_hat(i,j,k, l,m,n,p) = - 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
gamma_hat(i,j,k, l,m,n,p) = 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
(xiDyad(m,p)+xiDyad(p,m))
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! empirical factor for making divergence resolution and dimension indpendent
divergence_correction =.false.
if (divergence_correction) then
if (res(3) == 1_pInt) then
correctionFactor = minval(geomdim(1:2))*wgt**(-1.0_pReal/4.0_pReal) ! 2D case, ToDo: correct?
else
correctionFactor = minval(geomdim(1:3))*wgt**(-1.0_pReal/4.0_pReal) ! multiplying by minimum dimension to get rid of dimension dependency and phenomenologigal factor wgt**(-1/4) to get rid of resolution dependency
! general initialization of fftw (see manual on fftw.org for more details)
if (pReal /= C_DOUBLE .or. pInt /= C_INT) call IO_error(error_ID=108_pInt) ! check for correct precision in C
#ifdef _OPENMP
if(DAMASK_NumThreadsInt > 0_pInt) then
ierr = fftw_init_threads()
if (ierr == 0_pInt) call IO_error(error_ID = 109_pInt)
call fftw_plan_with_nthreads(DAMASK_NumThreadsInt)
endif
else
#endif
call fftw_set_timelimit(fftw_timelimit) ! set timelimit for plan creation
!--------------------------------------------------------------------------------------------------
! creating plans
plan_stress = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,& ! dimensions , length in each dimension in reversed order
tensorField_real,[ res(3),res(2) ,res(1)+2_pInt],& ! input data , physical length in each dimension in reversed order
1, res(3)*res(2)*(res(1)+2_pInt),& ! striding , product of physical lenght in the 3 dimensions
tensorField_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
plan_correction =fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],9,&
tensorField_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,&
tensorField_real,[ res(3),res(2) ,res(1)+2_pInt],&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
!--------------------------------------------------------------------------------------------------
! depending on (debug) options, allocate more memory and create additional plans
if (.not. simplified_algorithm) then
print*, 'using polarization field based algorithm'
tau = fftw_alloc_complex(int(res1_red*res(2)*res(3)*9_pInt,C_SIZE_T))
call c_f_pointer(tau, tau_real, [ res(1)+2_pInt,res(2),res(3),3,3])
call c_f_pointer(tau, tau_fourier, [ res1_red, res(2),res(3),3,3])
plan_tau = fftw_plan_many_dft_r2c(3,[ res(3),res(2) ,res(1)],9,&
tau_real,[ res(3),res(2) ,res(1)+2_pInt],&
1, res(3)*res(2)*(res(1)+2_pInt),&
tau_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,fftw_planner_flag)
endif
if (debugDivergence) then
divergence = fftw_alloc_complex(int(res1_red*res(2)*res(3)*3_pInt,C_SIZE_T))
call c_f_pointer(divergence, divergence_real, [ res(1)+2_pInt,res(2),res(3),3])
call c_f_pointer(divergence, divergence_fourier, [ res1_red, res(2),res(3),3])
allocate (divergence_postProc(res(1),res(2),res(3),3)); divergence_postProc= 0.0_pReal
plan_divergence = fftw_plan_many_dft_c2r(3,[ res(3),res(2) ,res(1)],3,&
divergence_fourier,[ res(3),res(2) ,res1_red],&
1, res(3)*res(2)* res1_red,&
divergence_real,[ res(3),res(2) ,res(1)+2_pInt],&
1, res(3)*res(2)*(res(1)+2_pInt),fftw_planner_flag)
endif
if (debugFFTW) then
scalarField_realC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T)) ! do not do an inplace transform
scalarField_fourierC = fftw_alloc_complex(int(res(1)*res(2)*res(3),C_SIZE_T))
call c_f_pointer(scalarField_realC, scalarField_real, [res(1),res(2),res(3)])
call c_f_pointer(scalarField_fourierC, scalarField_fourier, [res(1),res(2),res(3)])
plan_scalarField_forth = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
scalarField_real,scalarField_fourier,-1,fftw_planner_flag)
plan_scalarField_back = fftw_plan_dft_3d(res(3),res(2),res(1),& !reversed order
scalarField_fourier,scalarField_real,+1,fftw_planner_flag)
endif
if (debugGeneral) print '(a)' , 'FFTW initialized'
!--------------------------------------------------------------------------------------------------
! do not correct divergence criterion (usefull to kill dimension and resolution dependenc)
correctionFactor = 1.0_pReal
endif
!--------------------------------------------------------------------------------------------------
! write header of output file
@ -676,55 +633,87 @@ program DAMASK_spectral
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
bc(1)%incs = bc(1)%incs + 1_pInt ! additional for zero deformation
write(538) 'increments', bc(1:N_Loadcases)%incs ! one entry per loadcase
bc(1)%incs = bc(1)%incs - 1_pInt
write(538) 'startingIncrement', restartReadInc ! start with writing out the previous inc
write(538) 'startingIncrement', restartInc - 1_pInt ! start with writing out the previous inc
write(538) 'eoh' ! end of header
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! initial (non-deformed or read-in) results
if (debugGeneral) print '(a)' , 'Header of result file written out'
!##################################################################################################
! Loop over loadcases defined in the loadcase file
!##################################################################################################
do loadcase = 1_pInt, N_Loadcases
time0 = time ! loadcase start time
if (bc(loadcase)%followFormerTrajectory .and. &
(restartInc < totalIncsCounter .or. &
restartInc > totalIncsCounter+bc(loadcase)%incs) ) then ! continue to guess along former trajectory where applicable
guessmode = 1.0_pReal
else
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first inc
endif
if(totalIncsCounter > restartReadInc) then ! Do calculations (otherwise just forwarding)
if(bc(loadcase)%restartFrequency>0_pInt) &
restartWrite = ( mod(inc - 1_pInt,bc(loadcase)%restartFrequency)==0_pInt) ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
if (bc(loadcase)%velGradApplied) & ! calculate fDot from given L and current F
fDot = math_mul33x33(bc(loadcase)%deformation, defgradAim)
!--------------------------------------------------------------------------------------------------
! arrays for mixed boundary conditions
mask_defgrad = merge(ones,zeroes,bc(loadcase)%maskDeformation)
mask_stress = merge(ones,zeroes,bc(loadcase)%maskStress)
size_reduced = count(bc(loadcase)%maskStressVector)
allocate (c_reduced(size_reduced,size_reduced)); c_reduced = 0.0_pReal
allocate (s_reduced(size_reduced,size_reduced)); s_reduced = 0.0_pReal
!##################################################################################################
! loop oper incs defined in input file for current loadcase
!##################################################################################################
do inc = 1_pInt, bc(loadcase)%incs
totalIncsCounter = totalIncsCounter + 1_pInt
if(totalIncsCounter >= restartInc) then ! do calculations (otherwise just forwarding)
!--------------------------------------------------------------------------------------------------
! forwarding time
timeinc_old = timeinc
if (bc(loadcase)%logscale == 0_pInt) then ! linear scale
timeinc = bc(loadcase)%time/bc(loadcase)%incs ! only valid for given linear time scale. will be overwritten later in case loglinear scale is used
else
if (loadcase == 1_pInt) then ! 1st loadcase of logarithmic scale
if (inc == 1_pInt) then ! 1st inc of 1st loadcase of logarithmic scale
timeinc = bc(1)%time*(2.0_pReal**real( 1_pInt-bc(1)%incs ,pReal)) ! assume 1st inc is equal to 2nd
else ! not-1st inc of 1st loadcase of logarithmic scale
timeinc = bc(1)%time*(2.0_pReal**real(inc-1_pInt-bc(1)%incs ,pReal))
endif
else ! not-1st loadcase of logarithmic scale
timeinc = time0 *( (1.0_pReal + bc(loadcase)%time/time0 )**(real( inc,pReal)/&
real(bc(loadcase)%incs ,pReal))&
-(1.0_pReal + bc(loadcase)%time/time0 )**(real( (inc-1_pInt),pReal)/&
real(bc(loadcase)%incs ,pReal)) )
endif
endif
time = time + timeinc
if (bc(loadcase)%velGradApplied) then ! calculate deltaF from given L and current F
deltaF = timeinc * mask_defgrad * math_mul33x33(bc(loadcase)%deformation, defgradAim)
else ! deltaF = fDot *timeinc where applicable
deltaF = timeinc * mask_defgrad * bc(loadcase)%deformation
endif
!--------------------------------------------------------------------------------------------------
! winding forward of deformation aim in loadcase system
temp33_Real = defgradAim
defgradAim = defgradAim &
+ guessmode * mask_stress * (defgradAim - defgradAimOld) &
+ mask_defgrad * fDot * timeinc
+ guessmode * mask_stress * (defgradAim - defgradAimOld)*timeinc/timeinc_old &
+ deltaF
defgradAimOld = temp33_Real
!--------------------------------------------------------------------------------------------------
! update local deformation gradient
if (any(bc(loadcase)%rotation/=math_I3)) then ! lab and loadcase coordinate system are NOT the same
deltaF = math_rotate_backward33(deltaF,bc(loadcase)%rotation)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc(loadcase)%velGradApplied) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc(loadcase)%deformation,&
math_rotate_forward33(defgradold(i,j,k,1:3,1:3),bc(loadcase)%rotation))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ math_rotate_backward33((1.0_pReal-guessmode) * mask_defgrad * fDot,&
bc(loadcase)%rotation) *timeinc ! apply the prescribed value where deformation is given if not guessing
*timeinc/timeinc_old &
+ (1.0_pReal-guessmode) * deltaF ! if not guessing, use prescribed average deformation where applicable
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
else ! one coordinate system for lab and loadcase, save some multiplications
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = defgrad(i,j,k,1:3,1:3)
if (bc(loadcase)%velGradApplied) & ! use velocity gradient to calculate new deformation gradient (if not guessing)
fDot = math_mul33x33(bc(loadcase)%deformation,defgradold(i,j,k,1:3,1:3))
defgrad(i,j,k,1:3,1:3) = defgrad(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (defgrad(i,j,k,1:3,1:3) - defgradold(i,j,k,1:3,1:3))& ! guessing...
+ (1.0_pReal-guessmode) * mask_defgrad * fDot * timeinc ! apply the prescribed value where deformation is given if not guessing
defgradold(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! calculate reduced compliance
@ -742,7 +731,7 @@ program DAMASK_spectral
c_reduced(k,j) = c_prev99(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(error_ID=799)
if(errmatinv) call IO_error(error_ID=800_pInt)
s_prev99 = 0.0_pReal ! build full compliance
k = 0_pInt
do n = 1_pInt,9_pInt
@ -761,14 +750,6 @@ program DAMASK_spectral
! report begin of new increment
print '(a)', '##################################################################'
print '(A,I5.5,A,es12.6)', 'Increment ', totalIncsCounter, ' Time ',time
if (restartWrite ) then
print '(A)', 'writing converged results of previous increment for restart'
if(IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(defgrad))) then ! writing deformation gradient field to file
write (777,rec=1) defgrad
close (777)
endif
writtenRestart=totalIncsCounter-1_pInt
endif
guessmode = 1.0_pReal ! keep guessing along former trajectory during same loadcase
CPFEM_mode = 1_pInt ! winding forward
@ -827,7 +808,6 @@ program DAMASK_spectral
!--------------------------------------------------------------------------------------------------
! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
scalarField_real = 0.0_pReal
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
@ -843,7 +823,7 @@ program DAMASK_spectral
= tensorField_real(i,j,k,1:3,1:3) &
- math_mul3333xx33(c0_reference,defgrad(i,j,k,1:3,1:3))
enddo; enddo; enddo
call fftw_execute_dft_r2c(plan_tau,tau_real,tau_complex)
call fftw_execute_dft_r2c(plan_tau,tau_real,tau_fourier)
endif
!--------------------------------------------------------------------------------------------------
@ -854,12 +834,37 @@ program DAMASK_spectral
!--------------------------------------------------------------------------------------------------
! doing the FT because it simplifies calculation of average stress in real space also
call fftw_execute_dft_r2c(plan_stress,tensorField_real,tensorField_complex)
pstress_av_lab = real(tensorField_complex(1,1,1,1:3,1:3),pReal)*wgt
call fftw_execute_dft_r2c(plan_stress,tensorField_real,tensorField_fourier)
pstress_av_lab = real(tensorField_fourier(1,1,1,1:3,1:3),pReal)*wgt
pstress_av = math_rotate_forward33(pstress_av_lab,bc(loadcase)%rotation)
write (*,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa:',&
math_transpose33(pstress_av)/1.e6
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
call fftw_execute_dft(plan_scalarField_forth,scalarField_real,scalarField_fourier)
print '(a,i1,1x,i1)', 'checking FT results of compontent ', row, column
print '(a,2(es10.4,1x))', 'max FT relative error ',&
maxval( real((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
tensorField_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_fourier(1:res1_red,1:res(2),1:res(3)))), &
maxval(aimag((scalarField_fourier(1:res1_red,1:res(2),1:res(3))-&
tensorField_fourier(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
! removing highest frequencies
tensorField_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
tensorField_fourier (1:res1_red, res(2)/2_pInt+1_pInt,1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
if(res(3)>1_pInt) &
tensorField_fourier (1:res1_red,1:res(2), res(3)/2_pInt+1_pInt,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(size_reduced > 0_pInt) then ! calculate stress BC if applied
@ -884,61 +889,50 @@ program DAMASK_spectral
print '(a)', ''
print '(a)', '... calculating equilibrium with spectral method .................'
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
call fftw_execute_dft_r2c(plan_scalarField_forth,scalarField_real,scalarField_complex)
print '(a,i1,1x,i1)', 'checking FT results of compontent ', row, column
print '(a,2(es10.4,1x))', 'max FT relative error ',&
maxval( real((scalarField_complex(1:res1_red,1:res(2),1:res(3))-&
tensorField_complex(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_complex(1:res1_red,1:res(2),1:res(3)))), &
maxval(aimag((scalarField_complex(1:res1_red,1:res(2),1:res(3))-&
tensorField_complex(1:res1_red,1:res(2),1:res(3),row,column))/&
scalarField_complex(1:res1_red,1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
p_hat_avg = sqrt(maxval (math_eigenvalues33(math_mul33x33(real(tensorField_complex(1,1,1,1:3,1:3)),& ! L_2 norm of average stress (freq 0,0,0) in fourier space,
math_transpose33(real(tensorField_complex(1,1,1,1:3,1:3))))))) ! ignore imaginary part as it is always zero for real only input
pstress_av_L2 = sqrt(maxval (math_eigenvalues33(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress
math_transpose33(pstress_av_lab)))))
err_div_RMS = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2)
do i = 2_pInt, res1_red -1_pInt ! Has somewhere a conj. complex counterpart. Therefore count it twice.
err_div_RMS = err_div_RMS &
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_complex(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
+ 2.0_pReal*(sum (real(math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(tensorField_complex(i,j,k,1:3,1:3),&
+sum(aimag(math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*two_pi_img)**2.0_pReal))
enddo
err_div_RMS = err_div_RMS & ! Those two layers do not have a conjugate complex counterpart
+ sum(real(math_mul33x3_complex(tensorField_complex(1 ,j,k,1:3,1:3),&
err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ sum(real(math_mul33x3_complex(tensorField_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(tensorField_complex(1 ,j,k,1:3,1:3),&
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*two_pi_img)**2.0_pReal)&
+ sum(real(math_mul33x3_complex(tensorField_complex(res1_red,j,k,1:3,1:3),&
+ sum(real(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(tensorField_complex(res1_red,j,k,1:3,1:3),&
+ sum(aimag(math_mul33x3_complex(tensorField_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*two_pi_img)**2.0_pReal)
enddo; enddo
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
! if(err_div_RMS/p_hat_avg/sqrt(wgt) * correctionFactor>err_div&
! .and. iter >2_pInt&
! .and.err_stress > err_stress_tol) iter = itmax
err_div = err_div_RMS/p_hat_avg/sqrt(wgt) * correctionFactor ! criterion to stop iterations
if(err_div_RMS/pstress_av_L2*sqrt(wgt) * correctionFactor>err_div&
.and.iter >2_pInt&
.and.err_stress < err_stress_tol) then
print*, 'Increasing divergence, stopping iterations'
iter = itmax
endif
err_div = err_div_RMS/pstress_av_L2*sqrt(wgt) * correctionFactor ! criterion to stop iterations
!--------------------------------------------------------------------------------------------------
! calculate additional divergence criteria and report
if(debugDivergence) then ! calculate divergence again
err_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
temp3_Complex = math_mul33x3_complex(tensorField_complex(i,j,k,1:3,1:3),&
temp3_Complex = math_mul33x3_complex(tensorField_fourier(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*two_pi_img
err_div_max = max(err_div_max,sqrt(sum(abs(temp3_Complex)**2.0_pReal)))
divergence_complex(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_execute_dft_c2r(plan_divergence,divergence_complex,divergence_real)
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real)
divergence_real = divergence_real*wgt
err_real_div_RMS = 0.0_pReal
err_real_div_max = 0.0_pReal
@ -949,8 +943,6 @@ program DAMASK_spectral
err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of L_2 norm of div(stress) in real space
err_real_div_max = max(err_real_div_max, sqrt(sum(divergence_real(i,j,k,1:3)**2.0_pReal))) ! maximum of L two norm of div(stress) in real space
enddo; enddo; enddo
p_real_avg = sqrt(maxval (math_eigenvalues33(math_mul33x33(pstress_av_lab,& ! L_2 norm of average stress in real space,
math_transpose33(pstress_av_lab)))))
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
err_div_max = err_div_max*sqrt(wgt)
@ -960,69 +952,100 @@ program DAMASK_spectral
print '(a,es10.4)', 'error divergence Real max = ',err_real_div_max
print '(a,es10.4)', 'divergence RMS FT/real = ',err_div_RMS/err_real_div_RMS
print '(a,es10.4)', 'divergence max FT/real = ',err_div_max/err_real_div_max
print '(a,es10.4)', 'avg stress FT/real = ',p_hat_avg*wgt/p_real_avg
print '(a,es10.4)', 'max deviat. from postProc = ',max_div_error
endif
print '(a,es10.4,a,f6.2)', 'error divergence = ',err_div, ', rel. error = ', err_div/err_div_tol
!--------------------------------------------------------------------------------------------------
! divergence is calculated from FT(stress), depending on algorithm use field for spectral method
if (.not. simplified_algorithm) tensorField_complex = tau_complex
if (.not. simplified_algorithm) tensorField_fourier = tau_fourier
max_diag = tiny(1.0_pReal)
max_offdiag = tiny(1.0_pReal)
!--------------------------------------------------------------------------------------------------
! to the actual spectral method calculation (mechanical equilibrium)
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
if (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)
do m = 1_pInt ,3_pInt; do p = 1_pInt,3_pInt
xiDyad(m,p) = xi(m, i,j,k)*xi(p, i,j,k)
enddo; enddo
temp33_Real = math_inv33(math_mul3333xx33(c0_reference, xiDyad))
! do l = 1_pInt,3_pInt
! do n = 1_pInt,3_pInt
! temp33_Real(l,n) = sum(c0_reference(l,1:3,n,1:3)*xiDyad)
! enddo; enddo
temp33_Real= math_mul3333xx33(c0_reference,xiDyad)
! max_diag = max(max_diag,maxval( math_mul33x33(temp33_Real,math_inv33(temp33_Real)),&
! reshape([ .false.,.true.,.true.,.true.,.false.,.true.,.true.,.true.,.false.],[ 3,3])))
! max_offdiag = max(max_offdiag,maxval( math_mul33x33(temp33_Real,math_inv33(temp33_Real)),&
! reshape([ .true.,.false.,.false.,.false.,.true.,.false.,.false.,.false.,.true.],[ 3,3])))
! temp33_Real = math_inv33(temp33_Real)
else
xiDyad = 0.0_pReal
temp33_Real = 0.0_pReal
endif
do l=1_pInt,3_pInt; do m=1_pInt,3_pInt; do n=1_pInt,3_pInt; do p=1_pInt,3_pInt
gamma_hat(1,1,1, l,m,n,p) = - 0.25_pReal*(temp33_Real(l,n)+temp33_Real(n,l))*&
gamma_hat(1,1,1, l,m,n,p) = 0.25*(temp33_Real(l,n)+temp33_Real(n,l)) *&
(xiDyad(m,p)+xiDyad(p,m))
enddo; enddo; enddo; enddo
! if (k==res(3)/2 .or. k==res(3)/2+2 .or.&
! j==res(2)/2 .or. j==res(2)/2+2 .or.&
! i==res(1)/2 .or. i==res(1)/2+2) then
! print*,'gamma_hat', gamma_hat(1,1,1,1:3,1:3,1:3,1:3)
! print*, 's0', s0_reference
! pause
! endif
do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
temp33_Complex(m,n) = sum(gamma_hat(1,1,1, m,n, 1:3,1:3) * tensorField_complex(i,j,k,1:3,1:3))
temp33_Complex(m,n) = sum(gamma_hat(1,1,1, m,n, 1:3,1:3) * tensorField_fourier(i,j,k,1:3,1:3))
enddo; enddo
tensorField_complex(i,j,k,1:3,1:3) = temp33_Complex
tensorField_fourier(i,j,k,1:3,1:3) = temp33_Complex
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
do m = 1_pInt,3_pInt; do n = 1_pInt,3_pInt
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) * tensorField_complex(i,j,k,1:3,1:3))
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) * tensorField_fourier(i,j,k,1:3,1:3))
enddo; enddo
tensorField_complex(i,j,k,1:3,1:3) = temp33_Complex
tensorField_fourier(i,j,k,1:3,1:3) = temp33_Complex
enddo; enddo; enddo
endif
tensorField_complex(1,1,1,1:3,1:3) = (defgradAim_lab - defgrad_av_lab)& ! assign average deformation gradient change to zero frequency (real part)
tensorField_fourier(1,1,1,1:3,1:3) = (defgrad_av_lab -defgradAim_lab)& ! assign (negative) average deformation gradient change to zero frequency (real part)
* real(Npoints,pReal)
if (.not. simplified_algorithm) tensorField_complex(1,1,1,1:3,1:3) = & ! assign deformation aim to zero frequency (real part)
if (.not. simplified_algorithm) tensorField_fourier(1,1,1,1:3,1:3) = & ! assign deformation aim to zero frequency (real part)
defgradAim_lab * real(Npoints,pReal)
! print*, 'max off diagonal', max_offdiag
! print*, 'max diagonal', max_diag
!--------------------------------------------------------------------------------------------------
! 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_complex(i,j,k) = tensorField_complex(i,j,k,row,column)
scalarField_fourier(i,j,k) = tensorField_fourier(i,j,k,row,column)
enddo; enddo; enddo
do i = 0_pInt, res(1)/2_pInt-2_pInt !unpack fft data for conj complex symmetric part. can be directly used in calculation of cstress_field
m = 1_pInt
do k = 1_pInt, res(3)
n = 1_pInt
do j = 1_pInt, res(2)
scalarField_fourier(res(1)-i,j,k) = conjg(scalarField_fourier(2+i,n,m))
if(n == 1_pInt) n = res(2) + 1_pInt
n = n-1_pInt
enddo
if(m == 1_pInt) m = res(3) + 1_pInt
m = m -1_pInt
enddo; enddo
endif
!--------------------------------------------------------------------------------------------------
! doing the inverse FT
call fftw_execute_dft_c2r(plan_correction,tensorField_complex,tensorField_real) ! back transform of fluct deformation gradient
call fftw_execute_dft_c2r(plan_correction,tensorField_fourier,tensorField_real) ! back transform of fluct deformation gradient
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 inverse FT results
if (debugFFTW) then
print '(a,i1,1x,i1)', 'checking iFT results of compontent ', row, column
call fftw_execute_dft_c2r(plan_scalarField_back,scalarField_complex,scalarField_real)
call fftw_execute_dft(plan_scalarField_back,scalarField_fourier,scalarField_real)
print '(a,es10.4)', 'max iFT relative error ',&
maxval((scalarField_real(1:res(1),1:res(2),1:res(3))-&
maxval((real(scalarField_real(1:res(1),1:res(2),1:res(3)))-&
tensorField_real(1:res(1),1:res(2),1:res(3),row,column))/&
scalarField_real(1:res(1),1:res(2),1:res(3)))
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
@ -1049,7 +1072,7 @@ program DAMASK_spectral
!--------------------------------------------------------------------------------------------------
! updated deformation gradient
defgrad = defgrad + tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
defgrad = defgrad - tensorField_real(1:res(1),1:res(2),1:res(3),1:3,1:3)*wgt ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
!--------------------------------------------------------------------------------------------------
! updated deformation gradient in case of fluctuation field algorithm
@ -1080,16 +1103,37 @@ program DAMASK_spectral
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' NOT converged'
notConvergedCounter = notConvergedCounter + 1_pInt
else
convergedCounter = convergedCounter + 1_pInt
print '(A,I5.5,A)', 'increment ', totalIncsCounter, ' converged'
endif
if (mod(totalIncsCounter -1_pInt,bc(loadcase)%outputfrequency) == 0_pInt) then ! at output frequency
print '(a)', ''
print '(a)', '... writing results to file ......................................'
write(538) materialpoint_results(1_pInt:materialpoint_sizeResults,1,1_pInt:Npoints) ! write result to file
endif
if( bc(loadcase)%restartFrequency > 0_pInt .and. &
mod(inc - 1_pInt,bc(loadcase)%restartFrequency) == 0_pInt) then ! at frequency of writing restart information set restart parameter for FEsolving (first call to CPFEM_general will write ToDo: true?)
restartWrite = .true.
print '(A)', 'writing converged results for restart'
if(IO_write_jobBinaryFile(777,'convergedSpectralDefgrad',size(defgrad))) then ! writing deformation gradient field to file
write (777,rec=1) defgrad
close (777)
endif
restartInc=totalIncsCounter
endif
if (update_gamma) then
print*, 'update c0_reference '
c0_reference = c_current*wgt
! s0_reference = math_Plain99to3333(s0_99)
!c0_99 = math_Plain3333to99(c0_reference)
! call math_invert(9_pInt, s0_99, c0_99, i, errmatinv) ! invert reduced stiffness
! if(errmatinv) call IO_error(error_ID=800_pInt)
! print*, (c0_reference - math_Plain99to3333(c0_99))/c0_reference
! pause
endif
endif ! end calculation/forwarding
@ -1100,7 +1144,7 @@ program DAMASK_spectral
print '(a)', ''
print '(a)', '##################################################################'
print '(i6.6,a,i6.6,a)', notConvergedCounter, ' out of ', &
totalIncsCounter - restartReadInc, ' increments did not converge!'
notConvergedCounter + convergedCounter, ' increments did not converge!'
close(538)
call fftw_destroy_plan(plan_stress); call fftw_destroy_plan(plan_correction)
if (debugDivergence) call fftw_destroy_plan(plan_divergence)

42
code/FEsolving.f90
View File

@ -21,11 +21,10 @@
!##############################################################
MODULE FEsolving
!##############################################################
use prec, only: pInt,pReal
implicit none
integer(pInt) :: cycleCounter = 0_pInt, theInc = -1_pInt, restartReadInc = 0_pInt
integer(pInt) :: cycleCounter = 0_pInt, theInc = -1_pInt, restartInc = 1_pInt
real(pReal) :: theTime = 0.0_pReal, theDelta = 0.0_pReal
logical :: lastIncConverged = .false.,outdatedByNewInc = .false.,outdatedFFN1 = .false.,terminallyIll = .false.
logical :: symmetricSolver = .false.
@ -46,6 +45,7 @@
!***********************************************************
subroutine FE_init()
use, intrinsic :: iso_fortran_env
use prec, only: pInt
use debug, only: debug_verbosity
use DAMASK_interface
@ -55,7 +55,7 @@
integer(pInt), parameter :: fileunit = 222
integer(pInt), parameter :: maxNchunks = 6
integer(pInt):: i, start = 0_pInt, length=0_pInt
integer(pInt), dimension(1+2*maxNchunks) :: positions
integer(pInt), dimension(1_pInt+2_pInt*maxNchunks) :: positions
character(len=64) tag
character(len=1024) line, commandLine
@ -74,27 +74,29 @@
if(start /= 0_pInt) then ! found something
length = verify(commandLine(start:len(commandLine)),'0123456789',.false.) ! where is first non number after argument?
read(commandLine(start:start+length),'(I12)') restartReadInc ! read argument
restartReadInc = restartReadInc - 1_pInt ! command line argument is inc to compute
restartRead = max(0_pInt,restartReadInc) > 0_pInt
if(restartReadInc < 0_pInt) call IO_warning(warning_ID=34_pInt)
read(commandLine(start:start+length),'(I12)') restartInc ! read argument
restartRead = restartInc > 0_pInt
if(restartInc <= 0_pInt) then
call IO_warning(warning_ID=34_pInt)
restartInc = 1_pInt
endif
endif
else
rewind(fileunit)
do
read (fileunit,'(a1024)',END=100) line
positions = IO_stringPos(line,maxNchunks)
tag = IO_lc(IO_stringValue(line,positions,1)) ! extract key
tag = IO_lc(IO_stringValue(line,positions,1_pInt)) ! extract key
select case(tag)
case ('solver')
read (fileunit,'(a1024)',END=100) line ! next line
positions = IO_stringPos(line,maxNchunks)
symmetricSolver = (IO_intValue(line,positions,2) /= 1_pInt)
symmetricSolver = (IO_intValue(line,positions,2_pInt) /= 1_pInt)
case ('restart')
read (fileunit,'(a1024)',END=100) line ! next line
positions = IO_stringPos(line,maxNchunks)
restartWrite = iand(IO_intValue(line,positions,1),1_pInt) > 0_pInt
restartRead = iand(IO_intValue(line,positions,1),2_pInt) > 0_pInt
restartWrite = iand(IO_intValue(line,positions,1_pInt),1_pInt) > 0_pInt
restartRead = iand(IO_intValue(line,positions,1_pInt),2_pInt) > 0_pInt
case ('*restart')
do i=2,positions(1)
restartWrite = (IO_lc(IO_StringValue(line,positions,i)) == 'write') .or. restartWrite
@ -109,7 +111,7 @@
enddo
endif
else
call IO_error(101, ext_msg=FEmodelGeometry) ! cannot open input file
call IO_error(101_pInt, ext_msg=FEmodelGeometry) ! cannot open input file
endif
100 close(fileunit)
@ -119,27 +121,27 @@
do
read (fileunit,'(a1024)',END=200) line
positions = IO_stringPos(line,maxNchunks)
if ( IO_lc(IO_stringValue(line,positions,1)) == 'restart' .and. &
IO_lc(IO_stringValue(line,positions,2)) == 'file' .and. &
IO_lc(IO_stringValue(line,positions,3)) == 'job' .and. &
IO_lc(IO_stringValue(line,positions,4)) == 'id' ) &
FEmodelGeometry = IO_StringValue(line,positions,6)
if ( IO_lc(IO_stringValue(line,positions,1_pInt)) == 'restart' .and. &
IO_lc(IO_stringValue(line,positions,2_pInt)) == 'file' .and. &
IO_lc(IO_stringValue(line,positions,3_pInt)) == 'job' .and. &
IO_lc(IO_stringValue(line,positions,4_pInt)) == 'id' ) &
FEmodelGeometry = IO_StringValue(line,positions,6_pInt)
enddo
elseif (FEsolver == 'Abaqus' .and. IO_open_inputFile(fileunit,FEmodelGeometry)) then
rewind(fileunit)
do
read (fileunit,'(a1024)',END=200) line
positions = IO_stringPos(line,maxNchunks)
if ( IO_lc(IO_stringValue(line,positions,1))=='*heading') then
if ( IO_lc(IO_stringValue(line,positions,1_pInt))=='*heading') then
read (fileunit,'(a1024)',END=200) line
positions = IO_stringPos(line,maxNchunks)
FEmodelGeometry = IO_StringValue(line,positions,1)
FEmodelGeometry = IO_StringValue(line,positions,1_pInt)
endif
enddo
elseif (FEsolver == 'Spectral') then
!do nothing
else
call IO_error(106) ! cannot open file for old job info
call IO_error(106_pInt) ! cannot open file for old job info
endif
endif

107
code/makefile
View File

@ -33,8 +33,9 @@
# SUFFIX = arbitrary suffix
# STANDARD_CHECK = checking for Fortran 2008, compiler dependend
########################################################################################
# Here are some useful debugging switches. Switch on by uncommenting the #SUFFIX line at the end of this section:
# Here are some useful debugging switches for ifort. Switch on by uncommenting the #SUFFIX line at the end of this section:
# information on http://software.intel.com/en-us/articles/determining-root-cause-of-sigsegv-or-sigbus-errors/
# check if an array index is too small (<1) or too large!
DEBUG1 =-check bounds -g
@ -54,9 +55,12 @@ DEBUG5 =-warn all
#set precision (check for missing _pInt and _pReal)
DEBUG6= -real-size 32 -integer-size 16
#or one of those 16/32/64/128 (= 2,4,8,16 bytes)
#SUFFIX =$(DEBUG1) $(DEBUG2) $(DEBUG3) $(DEBUG4) $(DEBUG5) $(DEBUG6)
# Here are some useful debugging switches for gfortran
# fcheck-bounds: eqv to DEBUG1 of ifort
#SUFFIX =$(DEBUG1) $(DEBUG2) $(DEBUG3)
########################################################################################
#auto values will be set by setup_code.py
@ -70,6 +74,12 @@ COMPILERNAME ?= $(F90)
OPENMP ?= ON
OPTIMIZATION ?= DEFENSIVE
ifeq "$(F90)" "ifort"
ARCHIVE_COMMAND :=xiar
else
ARCHIVE_COMMAND :=ar
endif
ifeq "$(OPTIMIZATION)" "OFF"
OPTI := OFF
MAXOPTI := OFF
@ -126,7 +136,7 @@ ifdef STANDARD_CHECK
STANDARD_CHECK_ifort =$(STANDARD_CHECK)
STANDARD_CHECK_gfortran =$(STANDARD_CHECK)
endif
STANDARD_CHECK_ifort ?= -stand f08
STANDARD_CHECK_ifort ?=-stand f08 -standard-semantics
STANDARD_CHECK_gfortran ?=-std=f2008
@ -138,16 +148,89 @@ OPTIMIZATION_AGGRESSIVE_ifort :=-O3 $(PORTABLE_SWITCH) -ip -static -fp-model
OPTIMIZATION_AGGRESSIVE_gfortran :=-O3 $(PORTABLE_SWITCH) -ffast-math -funroll-loops -ftree-vectorize
COMPILE_OPTIONS_ifort := -fpp -diag-disable 8291,8290,5268
#warning ID 9291,8290:
#warning ID 5268: Extension to standard: The text exceeds right hand column allowed on the line (we have only comments there)
COMPILE_OPTIONS_gfortran := -xf95-cpp-input -ffree-line-length-132 -fno-range-check
COMPILE_OPTIONS_ifort :=-fpp\
-diag-enable sc3\
-diag-disable 8291,8290,5268\
-warn declarations\
-warn general\
-warn usage
#alignments: Determines whether warnings occur for data that is not naturally aligned.
#declarations: Determines whether warnings occur for any undeclared names.
#errors: Determines whether warnings are changed to errors.
#general: Determines whether warning messages and informational messages are issued by the compiler.
#ignore_loc: Determines whether warnings occur when %LOC is stripped from an actual argument.
#interfaces: Determines whether the compiler checks the interfaces of all SUBROUTINEs called and FUNCTIONs invoked in your compilation against an external set of interface blocks.
#stderrors: Determines whether warnings about Fortran standard violations are changed to errors.
#truncated_source: Determines whether warnings occur when source exceeds the maximum column width in fixed-format files.
#uncalled: Determines whether warnings occur when a statement function is never called
#unused: Determines whether warnings occur for declared variables that are never used.
#usage: Determines whether warnings occur for questionable programming practices.
#-fpp: preprocessor
#-diag-disable: disables warnings, where
# warning ID 9291:
# warning ID 8290:
# warning ID 5268: The text exceeds right hand column allowed on the line (we have only comments there)
COMPILE_OPTIONS_gfortran :=-xf95-cpp-input\
-ffree-line-length-132\
-fno-range-check\
-fimplicit-none\
-pedantic\
-Warray-bounds\
-Wunused-parameter\
-Wampersand\
-Wno-tabs\
-Wcharacter-truncation\
-Wintrinsic-shadow\
-Waliasing\
-Wconversion\
-Wsurprising\
-Wunused-value\
-Wunderflow
#-xf95-cpp-input: preprocessor
#-ffree-line-length-132: restrict line length to the standard 132 characters
#-fno-range-check: disables checking if result can be represented by variable. Needs to be set to enable DAMASK_NaN
#-fimplicit-none: assume "implicit-none" even if not present in source
#-pedantic: more strict on standard, enables some of the warnings below
#-Warray-bounds: checks if array reference is out of bounds at compile time. use -fcheck-bounds to also check during runtime
#-Wunused-parameter: find usused variables with "parameter" attribute
#-Wampersand: checks if a character expression is continued proberly by an ampersand at the end of the line and at the beginning of the new line
#-Wno-tabs: do not allow tabs in source
#-Wcharacter-truncation: warn if character expressions (strings) are truncated
#-Wintrinsic-shadow: warn if a user-defined procedure or module procedure has the same name as an intrinsic
#-Waliasing: warn about possible aliasing of dummy arguments. Specifically, it warns if the same actual argument is associated with a dummy argument with "INTENT(IN)" and a dummy argument with "INTENT(OUT)" in a call with an explicit interface.
#-Wconversion: warn about implicit conversions between different type
#-Wsurprising: warn when "suspicious" code constructs are encountered. While technically legal these usually indicate that an error has been made.
#-Wunused-value:
#-Wunderflow: produce a warning when numerical constant expressions are encountered, which yield an UNDERFLOW during compilation
#MORE OPTIONS
# only for gfortran 4.6:
#-Wsuggest-attribute=const
#-Wsuggest-attribute=noreturn
#-Wsuggest-attribute=pure
# too many warnings because we have comments beyond character 132:
#-Wline-truncation
# warnings because of "flush" is not longer in the standard, but still an intrinsic fuction of the compilers:
#-Wintrinsic-std
# warnings because we have many temporary arrays (performance issue?):
#-Warray-temporaries
# -Wimplicit-interface
# -pedantic-errors
# -fmodule-private
COMPILE =$(OPENMP_FLAG_$(F90)) $(COMPILE_OPTIONS_$(F90)) $(STANDARD_CHECK_$(F90)) $(OPTIMIZATION_$(OPTI)_$(F90)) -c
COMPILE_MAXOPTI =$(OPENMP_FLAG_$(F90)) $(COMPILE_OPTIONS_$(F90)) $(STANDARD_CHECK_$(F90)) $(OPTIMIZATION_$(MAXOPTI)_$(F90)) -c
DAMASK_spectral.exe: DAMASK_spectral.o CPFEM.a
$(PREFIX) $(COMPILERNAME) ${OPENMP_FLAG_${F90}} -o DAMASK_spectral.exe DAMASK_spectral.o CPFEM.a \
constitutive.a advanced.a basics.a $(LIB_DIRS) $(LIBRARIES)
@ -158,7 +241,7 @@ DAMASK_spectral.o: DAMASK_spectral.f90 CPFEM.o
CPFEM.a: CPFEM.o
ar rc CPFEM.a homogenization.o homogenization_RGC.o homogenization_isostrain.o crystallite.o CPFEM.o constitutive.o
$(ARCHIVE_COMMAND) rc CPFEM.a homogenization.o homogenization_RGC.o homogenization_isostrain.o crystallite.o CPFEM.o constitutive.o
CPFEM.o: CPFEM.f90 homogenization.o
$(PREFIX) $(COMPILERNAME) $(COMPILE) CPFEM.f90 $(SUFFIX)
@ -178,7 +261,7 @@ crystallite.o: crystallite.f90 constitutive.a
constitutive.a: constitutive.o
ar rc constitutive.a constitutive.o constitutive_titanmod.o constitutive_nonlocal.o constitutive_dislotwin.o constitutive_j2.o constitutive_phenopowerlaw.o basics.a advanced.a
$(ARCHIVE_COMMAND) rc constitutive.a constitutive.o constitutive_titanmod.o constitutive_nonlocal.o constitutive_dislotwin.o constitutive_j2.o constitutive_phenopowerlaw.o basics.a advanced.a
constitutive.o: constitutive.f90 constitutive_titanmod.o constitutive_nonlocal.o constitutive_dislotwin.o constitutive_j2.o constitutive_phenopowerlaw.o
$(PREFIX) $(COMPILERNAME) $(COMPILE) constitutive.f90 $(SUFFIX)
@ -201,7 +284,7 @@ constitutive_phenopowerlaw.o: constitutive_phenopowerlaw.f90 basics.a advanced.a
advanced.a: lattice.o
ar rc advanced.a FEsolving.o mesh.o material.o lattice.o
$(ARCHIVE_COMMAND) rc advanced.a FEsolving.o mesh.o material.o lattice.o
lattice.o: lattice.f90 material.o
$(PREFIX) $(COMPILERNAME) $(COMPILE) lattice.f90 $(SUFFIX)
@ -218,7 +301,7 @@ FEsolving.o: FEsolving.f90 basics.a
basics.a: math.o
ar rc basics.a math.o debug.o numerics.o IO.o DAMASK_spectral_interface.o prec.o
$(ARCHIVE_COMMAND) rc basics.a math.o debug.o numerics.o IO.o DAMASK_spectral_interface.o prec.o
math.o: math.f90 debug.o
$(PREFIX) $(COMPILERNAME) $(COMPILE) math.f90 $(SUFFIX)