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DAMASK_EICMD
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more modularization….

This commit is contained in:
Pratheek Shanthraj 2012-07-26 13:58:47 +00:00
parent a94b089aaa
commit c341ddd855
3 changed files with 643 additions and 309 deletions
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353
code/DAMASK_spectral_SolverAL.f90
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@ -11,10 +11,28 @@ module DAMASK_spectral_SolverAL
mesh_spectral_getDimension
implicit none
#include <finclude/petsc.h>
#include <finclude/petscvec.h90>
character (len=*), parameter, public :: &
DAMASK_spectral_SolverAL_label = 'AL'
!--------------------------------------------------------------------------------------------------
! PETSc data
SNES snes
KSP ksp
DM da
Vec x,r
PetscErrorCode ierr_psc
PetscMPIInt rank
PetscObject dummy
PetscInt xs,xm,gxs,gxm
PetscInt ys,ym,gys,gym
PetscInt zs,zm,gzs,gzm
character(len=1024) :: PetSc_options = '-snes_type ngmres -snes_ngmres_anderson -snes_monitor -snes_view'
external FormFunctionLocal, SNESConverged_Interactive
!--------------------------------------------------------------------------------------------------
! common pointwise data
real(pReal), dimension(:,:,:,:,:), allocatable :: F, F_lastInc, F_lambda, F_lambda_lastInc, P
@ -27,12 +45,13 @@ module DAMASK_spectral_SolverAL
F_aim = math_I3, &
F_aim_lastInc = math_I3, &
P_av
real(pReal), dimension(3,3,3,3) :: &
C_ref = 0.0_pReal, &
C = 0.0_pReal
!--------------------------------------------------------------------------------------------------
! solution state
integer(pInt) :: iter
real(pReal) :: err_div, err_stress
contains
@ -49,13 +68,14 @@ module DAMASK_spectral_SolverAL
getSolverJobName
implicit none
integer(pInt) :: i,j,k
integer(pInt) :: i, j, k
res = mesh_spectral_getResolution()
geomdim = mesh_spectral_getDimension()
call Utilities_init()
allocate (F ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (F_lambda ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (F_lambda_lastInc(res(1),res(2),res(3),3,3), source = 0.0_pReal)
allocate (P ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (coordinates( res(1), res(2),res(3),3), source = 0.0_pReal)
allocate (temperature( res(1), res(2),res(3)), source = 0.0_pReal)
@ -66,6 +86,8 @@ module DAMASK_spectral_SolverAL
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
F(i,j,k,1:3,1:3) = math_I3
F_lastInc(i,j,k,1:3,1:3) = math_I3
F_lambda(i,j,k,1:3,1:3) = math_I3
F_lambda_lastInc(i,j,k,1:3,1:3) = math_I3
coordinates(i,j,k,1:3) = geomdim/real(res,pReal)*real([i,j,k],pReal) &
- geomdim/real(2_pInt*res,pReal)
enddo; enddo; enddo
@ -80,6 +102,14 @@ module DAMASK_spectral_SolverAL
trim(getSolverJobName()),size(F_lastInc))
read (777,rec=1) F_lastInc
close (777)
call IO_read_jobBinaryFile(777,'convergedSpectralDefgradLambda',&
trim(getSolverJobName()),size(F_lambda))
read (777,rec=1) F
close (777)
call IO_read_jobBinaryFile(777,'convergedSpectralDefgradLambda_lastInc',&
trim(getSolverJobName()),size(F_lambda_lastInc))
read (777,rec=1) F_lastInc
close (777)
call IO_read_jobBinaryFile(777,'F_aim',trim(getSolverJobName()),size(F_aim))
read (777,rec=1) F_aim
close (777)
@ -96,25 +126,51 @@ module DAMASK_spectral_SolverAL
!--------------------------------------------------------------------------------------------------
! reference stiffness
if (restartInc == 1_pInt) then
C_ref = C
call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
write (777,rec=1) C_ref
call IO_write_jobBinaryFile(777,'C_ref',size(C))
write (777,rec=1) C
close(777)
elseif (restartInc > 1_pInt) then
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
read (777,rec=1) C_ref
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C))
read (777,rec=1) C
close (777)
endif
call Utilities_Init(C_ref)
call Utilities_updateGamma(C_ref)
!--------------------------------------------------------------------------------------------------
! PETSc Init
call PetscInitialize(PETSC_NULL_CHARACTER,ierr_psc)
call MPI_Comm_rank(PETSC_COMM_WORLD,rank,ierr_psc)
call SNESCreate(PETSC_COMM_WORLD,snes,ierr_psc)
call DMDACreate3d(PETSC_COMM_WORLD, &
DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE, &
DMDA_STENCIL_BOX,res(1),res(2),res(3),PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE, &
18,1,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,PETSC_NULL_INTEGER,da,ierr_psc)
call DMCreateGlobalVector(da,x,ierr_psc)
call VecDuplicate(x,r,ierr_psc)
call DMDASetLocalFunction(da,FormFunctionLocal,ierr_psc)
call SNESSetDM(snes,da,ierr_psc)
call SNESSetFunction(snes,r,SNESDMDAComputeFunction,da,ierr_psc)
call SNESSetConvergenceTest(snes,SNESConverged_Interactive,dummy,PETSC_NULL_FUNCTION,ierr_psc)
call PetscOptionsInsertString(PetSc_options,ierr_psc)
call SNESSetFromOptions(snes,ierr_psc)
call DMDAGetCorners(da,xs,ys,zs,xm,ym,zm,ierr_psc)
call DMDAGetCorners(da,gxs,gys,gzs,gxm,gym,gzm,ierr_psc)
xs = xs+1; gxs = gxs+1; xm = xm-1; gxm = gxm-1
ys = ys+1; gys = gys+1; ym = ym-1; gym = gym-1
zs = zs+1; gzs = gzs+1; zm = zm-1; gzm = gzm-1
end subroutine AL_init
type(solutionState) function AL_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC,mask_stressVector,velgrad,rotation_BC)
use numerics, only: &
itmax,&
itmin
itmax, &
itmin, &
update_gamma
use IO, only: &
IO_write_JobBinaryFile
@ -144,12 +200,12 @@ type(solutionState) function AL_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC
deltaF_aim, &
F_aim_lab, &
F_aim_lab_lastIter
real(pReal) :: err_div, err_stress
integer(pInt) :: iter
integer(pInt) :: i, j, k
logical :: ForwardData
real(pReal) :: defgradDet
real(pReal) :: defgradDetMax, defgradDetMin
PetscScalar, pointer :: xx_psc(:)
mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3]))
mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3]))
@ -186,16 +242,27 @@ type(solutionState) function AL_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_Real = F(i,j,k,1:3,1:3)
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))*timeinc/timeinc_old& ! guessing...
+ (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
+ guessmode * (F(i,j,k,1:3,1:3) - F_lastInc(i,j,k,1:3,1:3))* &
timeinc/timeinc_old + (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
F_lastInc(i,j,k,1:3,1:3) = temp33_Real
temp33_Real = F_lambda(i,j,k,1:3,1:3)
F_lambda(i,j,k,1:3,1:3) = F_lambda(i,j,k,1:3,1:3) & ! decide if guessing along former trajectory or apply homogeneous addon
+ guessmode * (F_lambda(i,j,k,1:3,1:3) - F_lambda_lastInc(i,j,k,1:3,1:3))* &
timeinc/timeinc_old + (1.0_pReal-guessmode) * deltaF_aim ! if not guessing, use prescribed average deformation where applicable
F_lambda_lastInc(i,j,k,1:3,1:3) = temp33_Real
enddo; enddo; enddo
call deformed_fft(res,geomdim,math_rotate_backward33(F_aim,rotation_BC),& ! calculate current coordinates
1.0_pReal,F_lastInc,coordinates)
iter = 0_pInt
S = S_lastInc(rotation_BC,mask_stressVector,C)
S = Utilities_stressBC(rotation_BC,mask_stressVector,C)
if (update_gamma) call Utilities_updateGamma(C)
call VecGetArrayF90(x,xx_psc,ierr_psc)
call FormInitialGuessLocal(xx_psc)
call VecRestoreArrayF90(x,xx_psc,ierr_psc)
call SNESSolve(snes,PETSC_NULL_OBJECT,x,ierr_psc)
convergenceLoop: do while((iter < itmax .and. (any([err_div ,err_stress] > 1.0_pReal)))&
.or. iter < itmin)
@ -218,21 +285,47 @@ type(solutionState) function AL_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(any(mask_stressVector)) then ! calculate stress BC if applied
err_stress = BCcorrection(mask_stressVector,P_BC,P_av,F_aim,S)
F_aim = F_aim - math_mul3333xx33(S, ((P_av - P_BC)))
err_stress = mask_stress * (P_av - P_BC)))
else
err_stress = 0.0_pReal
endif
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC) ! boundary conditions from load frame into lab (Fourier) frame
!--------------------------------------------------------------------------------------------------
! updated deformation gradient
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = P
err_div = convolution(.True.,F_aim_lab_lastIter - F_aim_lab, C_ref)
call FFT_forward()
err_div = calcDivergence()
call convolution_fourier(F_aim_lab_lastIter - F_aim_lab, C_ref)
call FFT_backward()
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - field_real(i,j,k,1:3,1:3) ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
enddo; enddo; enddo
!--------------------------------------------------------------------------------------------------
! calculate some additional output
if(debugGeneral) then
maxCorrectionSkew = 0.0_pReal
maxCorrectionSym = 0.0_pReal
temp33_Real = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
maxCorrectionSym = max(maxCorrectionSym,&
maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
maxCorrectionSkew = max(maxCorrectionSkew,&
maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
enddo; enddo; enddo
write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
maxCorrectionSym*wgt
write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
maxCorrectionSkew*wgt
write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
maxval(math_symmetric33(temp33_real))/&
maxval(math_skew33(temp33_real))
endif
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
@ -256,8 +349,226 @@ subroutine AL_destroy()
implicit none
call VecDestroy(x,ierr_psc)
call VecDestroy(r,ierr_psc)
call SNESDestroy(snes,ierr_psc)
call DMDestroy(da,ierr_psc)
call PetscFinalize(ierr_psc)
call Utilities_destroy()
end subroutine AL_destroy
! -------------------------------------------------------------------
subroutine FormInitialGuessLocal(xx_psc)
implicit none
#include <finclude/petsc.h>
! Input/output variables:
PetscScalar xx_psc(0:17,gxs:(gxs+gxm),gys:(gys+gym),gxs:(gzs+gzm))
integer(pInt) :: i, j, k
! Compute function over the locally owned part of the grid
do k=gzs,gzs+gzm; do j=gys,gys+gym; do i=gxs,gxs+gxm
xx_psc(0,i,j,k) = F(i,j,k,1,1)
xx_psc(1,i,j,k) = F(i,j,k,1,2)
xx_psc(2,i,j,k) = F(i,j,k,1,3)
xx_psc(3,i,j,k) = F(i,j,k,2,1)
xx_psc(4,i,j,k) = F(i,j,k,2,2)
xx_psc(5,i,j,k) = F(i,j,k,2,3)
xx_psc(6,i,j,k) = F(i,j,k,3,1)
xx_psc(7,i,j,k) = F(i,j,k,3,2)
xx_psc(8,i,j,k) = F(i,j,k,3,3)
xx_psc(9,i,j,k) = F_lambda(i,j,k,1,1)
xx_psc(10,i,j,k) = F_lambda(i,j,k,1,2)
xx_psc(11,i,j,k) = F_lambda(i,j,k,1,3)
xx_psc(12,i,j,k) = F_lambda(i,j,k,2,1)
xx_psc(13,i,j,k) = F_lambda(i,j,k,2,2)
xx_psc(14,i,j,k) = F_lambda(i,j,k,2,3)
xx_psc(15,i,j,k) = F_lambda(i,j,k,3,1)
xx_psc(16,i,j,k) = F_lambda(i,j,k,3,2)
xx_psc(17,i,j,k) = F_lambda(i,j,k,3,3)
enddo; enddo; enddo
return
end subroutine FormInitialGuessLocal
! ---------------------------------------------------------------------
!
! Input Parameter:
! x - local vector data
!
! Output Parameters:
! f - local vector data, f(x)
! ierr - error code
!
! Notes:
! This routine uses standard Fortran-style computations over a 3-dim array.
!
subroutine FormFunctionLocal(in,x_scal,f_scal,dummy,ierr_psc)
use numerics, only: &
itmax, &
itmin
implicit none
#include <finclude/petsc.h>
! Input/output variables:
DMDALocalInfo in(DMDA_LOCAL_INFO_SIZE)
PetscScalar x_scal(0:17,XG_RANGE,YG_RANGE,ZG_RANGE)
PetscScalar f_scal(0:17,X_RANGE,Y_RANGE,Z_RANGE)
real(pReal), dimension (3,3) :: temp
PetscObject dummy
! Compute function over the locally owned part of the grid
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
! report begin of new iteration
write(6,'(a)') ''
write(6,'(a)') '=================================================================='
write(6,'(3(a,i6.6))') ' @ Iter. ',itmin,' < ',iter,' < ',itmax
write(6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'deformation gradient aim =',&
math_transpose33(F_aim)
F_star_av = 0.0
lambda_av = 0.0
do k=gzs,gze; do j=gys,gye; do i=gxs,gxe
F(i,j,k,1,1) = x_scal(0,i,j,k)
F(i,j,k,1,2) = x_scal(1,i,j,k)
F(i,j,k,1,3) = x_scal(2,i,j,k)
F(i,j,k,2,1) = x_scal(3,i,j,k)
F(i,j,k,2,2) = x_scal(4,i,j,k)
F(i,j,k,2,3) = x_scal(5,i,j,k)
F(i,j,k,3,1) = x_scal(6,i,j,k)
F(i,j,k,3,2) = x_scal(7,i,j,k)
F(i,j,k,3,3) = x_scal(8,i,j,k)
F_lambda(i,j,k,1,1) = x_scal(9,i,j,k)
F_lambda(i,j,k,1,2) = x_scal(10,i,j,k)
F_lambda(i,j,k,1,3) = x_scal(11,i,j,k)
F_lambda(i,j,k,2,1) = x_scal(12,i,j,k)
F_lambda(i,j,k,2,2) = x_scal(13,i,j,k)
F_lambda(i,j,k,2,3) = x_scal(14,i,j,k)
F_lambda(i,j,k,3,1) = x_scal(15,i,j,k)
F_lambda(i,j,k,3,2) = x_scal(16,i,j,k)
F_lambda(i,j,k,3,3) = x_scal(17,i,j,k)
F_star_av = F_star_av + F(i,j,k,1:3,1:3)
lambda_av = lambda_av + F_lambda(i,j,k,1:3,1:3)
enddo; enddo; enddo
F_star_av = F_star_av *wgt
lambda_av = math_mul3333xx33(C_inc0,lambda_av*wgt-math_I3)
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
call constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
P,C,P_av,ForwardData,rotation_BC)
ForwardData = .False.
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(any(mask_stressVector)) then ! calculate stress BC if applied
F_aim = F_aim - math_mul3333xx33(S, ((P_av - P_BC)))
err_stress = mask_stress * (P_av - P_BC)))
else
err_stress = 0.0_pReal
endif
F_aim_lab = math_rotate_backward33(F_aim,rotation_BC)
!--------------------------------------------------------------------------------------------------
! doing Fourier transform
field_real = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
field_real(i,j,k,1:3,1:3) = math_mul3333xx33(C_ref,F_lambda(i,j,k,1:3,1:3)-F(i,j,k,1:3,1:3))
enddo; enddo; enddo
call Utilities_forwardFFT()
call Utilities_fourierConvolution(F_aim_lab)
call Utilities_backwardFFT()
err_f = 0.0_pReal
err_f_point = 0.0_pReal
err_p = 0.0_pReal
err_p_point = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
temp33_real = field_real(i,j,k,1:3,1:3) - F(i,j,k,1:3,1:3)
err_f_point = max(err_f_point, maxval(abs(temp33_real)))
err_f = err_f + sum(temp33_real*temp33_real)
temp33_real = F_lambda(i,j,k,1:3,1:3) - &
math_mul3333xx33(S_inc0,P(i,j,k,1:3,1:3)) + math_I3
err_p_point = max(err_p_point, maxval(abs(temp33_real)))
err_p = err_p + sum(temp33_real*temp33_real)
enddo; enddo; enddo
err_f = wgt*sqrt(err_f/sum((F_aim-math_I3)*(F_aim-math_I3)))
err_p = wgt*sqrt(err_p/sum((F_aim-math_I3)*(F_aim-math_I3)))
write(6,'(a,es14.7,es14.7)') 'error stress = ',err_stress/err_stress_tol
write(6,*) ' '
write(6,'(a,es14.7)') 'max abs err F', err_f
write(6,'(a,es14.7)') 'max abs err P', err_p
do k=zs,ze; do j=ys,ye; do i=xs,xe
temp = math_mul3333xx33(S_inc0,P(i,j,k,1:3,1:3)) + math_I3 - F_lambda(i,j,k,1:3,1:3) &
+ F(i,j,k,1:3,1:3) - field_real(i,j,k,1:3,1:3)
f_scal(0,i,j,k) = temp(1,1)
f_scal(1,i,j,k) = temp(1,2)
f_scal(2,i,j,k) = temp(1,3)
f_scal(3,i,j,k) = temp(2,1)
f_scal(4,i,j,k) = temp(2,2)
f_scal(5,i,j,k) = temp(2,3)
f_scal(6,i,j,k) = temp(3,1)
f_scal(7,i,j,k) = temp(3,2)
f_scal(8,i,j,k) = temp(3,3)
f_scal(9,i,j,k) = F(i,j,k,1,1) - field_real(i,j,k,1,1)
f_scal(10,i,j,k) = F(i,j,k,1,2) - field_real(i,j,k,1,2)
f_scal(11,i,j,k) = F(i,j,k,1,3) - field_real(i,j,k,1,3)
f_scal(12,i,j,k) = F(i,j,k,2,1) - field_real(i,j,k,2,1)
f_scal(13,i,j,k) = F(i,j,k,2,2) - field_real(i,j,k,2,2)
f_scal(14,i,j,k) = F(i,j,k,2,3) - field_real(i,j,k,2,3)
f_scal(15,i,j,k) = F(i,j,k,3,1) - field_real(i,j,k,3,1)
f_scal(16,i,j,k) = F(i,j,k,3,2) - field_real(i,j,k,3,2)
f_scal(17,i,j,k) = F(i,j,k,3,3) - field_real(i,j,k,3,3)
enddo; enddo; enddo
return
end subroutine FormFunctionLocal
! ---------------------------------------------------------------------
! User defined convergence check
!
subroutine SNESConverged_Interactive(snes,it,xnorm,snorm,fnorm,reason,dummy,ierr_psc)
implicit none
#include <finclude/petsc.h>
! Input/output variables:
SNES snes
PetscInt it
PetscReal xnorm, snorm, fnorm
SNESConvergedReason reason
PetscObject dummy
PetscErrorCode ierr_psc
err_crit = max(err_stress/err_stress_tol, &
err_f/1e-6, err_p/1e-5)
!fnorm*wgt/sqrt(sum((F_star_av-math_I3)*(F_star_av-math_I3)))/err_div_tol)
if ((err_crit > 1.0_pReal .or. it < itmin) .and. it < itmax) then
reason = 0
else
reason = 1
endif
return
end subroutine SNESConverged_Interactive
end module DAMASK_spectral_SolverAL

98
code/DAMASK_spectral_SolverBasic.f90
View File

@ -12,6 +12,8 @@ module DAMASK_spectral_SolverBasic
implicit none
real(pReal), dimension(3,3) :: temp33_Real
character (len=*), parameter, public :: &
DAMASK_spectral_SolverBasic_label = 'basic'
@ -25,10 +27,9 @@ module DAMASK_spectral_SolverBasic
! stress, stiffness and compliance average etc.
real(pReal), dimension(3,3) :: &
F_aim = math_I3, &
F_aim_lastInc = math_I3, &
P_av
F_aim_lastInc = math_I3
real(pReal), dimension(3,3,3,3) :: &
C_ref = 0.0_pReal, &
C = 0.0_pReal
@ -49,8 +50,7 @@ module DAMASK_spectral_SolverBasic
implicit none
integer(pInt) :: i,j,k
res = mesh_spectral_getResolution()
geomdim = mesh_spectral_getDimension()
call Utilities_Init()
allocate (F ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
allocate (F_lastInc ( res(1), res(2),res(3),3,3), source = 0.0_pReal)
@ -88,31 +88,31 @@ module DAMASK_spectral_SolverBasic
coordinates = 0.0 ! change it later!!!
endif
call constitutiveResponse(coordinates,F,F_lastInc,temperature,0.0_pReal,&
P,C,P_av,.false.,math_I3)
call Utilities_constitutiveResponse(coordinates,F,F_lastInc,temperature,0.0_pReal,&
P,C,temp33_Real,.false.,math_I3)
!--------------------------------------------------------------------------------------------------
! reference stiffness
if (restartInc == 1_pInt) then
C_ref = C
call IO_write_jobBinaryFile(777,'C_ref',size(C_ref))
write (777,rec=1) C_ref
call IO_write_jobBinaryFile(777,'C_ref',size(C))
write (777,rec=1) C
close(777)
elseif (restartInc > 1_pInt) then
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C_ref))
read (777,rec=1) C_ref
call IO_read_jobBinaryFile(777,'C_ref',trim(getSolverJobName()),size(C))
read (777,rec=1) C
close (777)
endif
call Utilities_Init(C_ref)
call Utilities_updateGamma(C)
end subroutine basic_init
type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F_BC,mask_stressVector,velgrad,rotation_BC)
use numerics, only: &
itmax,&
itmin
itmax, &
itmin, &
update_gamma
use IO, only: &
IO_write_JobBinaryFile
@ -141,7 +141,8 @@ type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F
mask_defgrad, &
deltaF_aim, &
F_aim_lab, &
F_aim_lab_lastIter
F_aim_lab_lastIter, &
P_av
real(pReal) :: err_div, err_stress
integer(pInt) :: iter
integer(pInt) :: i, j, k
@ -192,10 +193,10 @@ type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F
1.0_pReal,F_lastInc,coordinates)
iter = 0_pInt
S = S_lastInc(rotation_BC,mask_stressVector,C)
convergenceLoop: do while((iter < itmax .and. (any([err_div ,err_stress] > 1.0_pReal)))&
.or. iter < itmin)
S = Utilities_stressBC(rotation_BC,mask_stressVector,C)
if (update_gamma) call Utilities_updateGamma(C)
convergenceLoop: do while(.not. basic_convergenced(err_div,P_av,err_stress,P_av,iter))
iter = iter + 1_pInt
!--------------------------------------------------------------------------------------------------
@ -209,14 +210,15 @@ type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F
!--------------------------------------------------------------------------------------------------
! evaluate constitutive response
call constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
call Utilities_constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
P,C,P_av,ForwardData,rotation_BC)
ForwardData = .False.
!--------------------------------------------------------------------------------------------------
! stress BC handling
if(any(mask_stressVector)) then ! calculate stress BC if applied
err_stress = BCcorrection(mask_stressVector,P_BC,P_av,F_aim,S)
F_aim = F_aim - math_mul3333xx33(S, ((P_av - P_BC)))
err_stress = mask_stress * (P_av - P_BC)))
else
err_stress = 0.0_pReal
endif
@ -226,11 +228,36 @@ type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F
!--------------------------------------------------------------------------------------------------
! updated deformation gradient
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3) = P
err_div = convolution(.True.,F_aim_lab_lastIter - F_aim_lab, C_ref)
call Utilities_forwardFFT()
err_div = Utilities_divergenceRMS()
call Utilities_fourierConvolution(F_aim_lab_lastIter - F_aim_lab)
call Utilities_backwardFFT()
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
F(i,j,k,1:3,1:3) = F(i,j,k,1:3,1:3) - field_real(i,j,k,1:3,1:3) ! F(x)^(n+1) = F(x)^(n) + correction; *wgt: correcting for missing normalization
enddo; enddo; enddo
!--------------------------------------------------------------------------------------------------
! calculate some additional output
if(debugGeneral) then
maxCorrectionSkew = 0.0_pReal
maxCorrectionSym = 0.0_pReal
temp33_Real = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
maxCorrectionSym = max(maxCorrectionSym,&
maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
maxCorrectionSkew = max(maxCorrectionSkew,&
maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
enddo; enddo; enddo
write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
maxCorrectionSym*wgt
write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
maxCorrectionSkew*wgt
write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
maxval(math_symmetric33(temp33_real))/&
maxval(math_skew33(temp33_real))
endif
!--------------------------------------------------------------------------------------------------
! calculate bounds of det(F) and report
@ -246,10 +273,35 @@ type(solutionState) function basic_solution(guessmode,timeinc,timeinc_old,P_BC,F
write(6,'(a,1x,es11.4)') 'max determinant of deformation =', defgradDetMax
write(6,'(a,1x,es11.4)') 'min determinant of deformation =', defgradDetMin
endif
enddo convergenceLoop
end function basic_solution
logical function basic_convergenced(err_div,P_av,err_stress,P_av,iter)
use numerics, only: &
itmax, &
itmin, &
err_div_tol, &
err_stress_tolrel, &
err_stress_tolabs
implicit none
real(pReal), dimension(3,3) :: P_av
real(pReal) :: err_div, err_stress, field_av_L2
integer(pInt) :: iter
field_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(P_av,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
math_transpose33(P_av)))))
basic_convergenced = (iter < itmax) .and. (iter > itmin) .and. &
(err_div/field_av_L2/err_div_tol < 1.0_pReal) .and. &
(err_stress/min(maxval(abs(P_av))*err_stress_tolrel,err_stress_tolabs) < 1.0_pReal)
end function basic_convergenced
subroutine basic_destroy()
implicit none

501
code/DAMASK_spectral_Utilities.f90
View File

@ -51,6 +51,7 @@ module DAMASK_spectral_Utilities
! variables storing information for spectral method and FFTW
type(C_PTR) :: plan_forward, plan_backward ! plans for fftw
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat ! gamma operator (field) for spectral method
real(pReal), dimension(3,3,3,3) :: C_ref
real(pReal), dimension(:,:,:,:), allocatable :: xi ! wave vector field for divergence and for gamma operator
real(pReal), dimension(:,:,:,:,:), pointer :: field_real
complex(pReal), dimension(:,:,:,:,:), pointer :: field_fourier
@ -87,7 +88,7 @@ module DAMASK_spectral_Utilities
end type solutionState
contains
subroutine Utilities_init(C_ref)
subroutine Utilities_init()
use mesh, only : &
mesh_spectral_getResolution, &
@ -106,17 +107,11 @@ subroutine Utilities_init(C_ref)
debug_spectralDivergence, &
debug_spectralRestart, &
debug_spectralFFTW
use numerics, only: &
memory_efficient
implicit none
real(pReal), dimension(3,3) :: temp33_Real, xiDyad
integer(pInt) :: i, j, k, l, m, n, q, ierr
integer(pInt) :: i, j, k, ierr
integer(pInt), dimension(3) :: k_s
real(pReal), dimension(3,3,3,3) :: &
C_ref
type(C_PTR) :: tensorField ! field in real and fourier space
type(C_PTR) :: scalarField_realC, scalarField_fourierC
@ -225,69 +220,63 @@ subroutine Utilities_init(C_ref)
if(memory_efficient) then ! allocate just single fourth order tensor
allocate (gamma_hat(1,1,1,3,3,3,3), source = 0.0_pReal)
else ! precalculation of gamma_hat field
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source =0.0_pReal)
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
temp33_Real = math_inv33(temp33_Real)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(i,j,k, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
endif
enddo; enddo; enddo
gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
allocate (gamma_hat(res1_red ,res(2),res(3),3,3,3,3), source =0.0_pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
endif
end subroutine Utilities_init
real(pReal) function convolution(calcDivergence,field_aim,C_ref)
subroutine Utilities_updateGamma(C)
use numerics, only: &
memory_efficient, &
err_div_tol
memory_efficient
real(pReal), dimension(3,3) :: xiDyad ! product of wave vectors
real(pReal) :: err_div = 0.0_pReal
real(pReal), dimension(3,3) :: temp33_Real
implicit none
real(pReal), dimension(3,3,3,3) :: C
real(pReal), dimension(3,3) :: temp33_Real, xiDyad
integer(pInt) :: i, j, k, l, m, n, q
real(pReal), dimension(3,3,3,3) :: C_ref
!--------------------------------------------------------------------------------------------------
!variables for additional output due to general debugging
real(pReal) :: maxCorrectionSym, maxCorrectionSkew
logical :: calcDivergence
real(pReal), dimension(3,3) :: field_avg, field_aim
integer(pInt) :: row, column
real(pReal) :: field_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
err_div_max, err_real_div_max
complex(pReal), dimension(3) :: temp3_complex
complex(pReal), dimension(3,3) :: temp33_complex
!--------------------------------------------------------------------------------------------------
! actual spectral method
write(6,'(a)') ''
write(6,'(a)') '... doing convolution .................'
C_ref = C
if(.not. memory_efficient) then
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
temp33_Real = math_inv33(temp33_Real)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(i,j,k, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
endif
enddo; enddo; enddo
gamma_hat(1,1,1, 1:3,1:3,1:3,1:3) = 0.0_pReal ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
endif
end subroutine Utilities_updateGamma
subroutine Utilities_forwardFFT()
implicit none
integer(pInt) :: row, column
!--------------------------------------------------------------------------------------------------
! copy one component of the stress field to to a single FT and check for mismatch
if (debugFFTW) then
row = 3 ! (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 = 3 !(mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
scalarField_real(1:res(1),1:res(2),1:res(3)) =& ! store the selected component
cmplx(field_real(1:res(1),1:res(2),1:res(3),row,column),0.0_pReal,pReal)
endif
!--------------------------------------------------------------------------------------------------
! call function to calculate divergence from math (for post processing) to check results
if (debugDivergence) &
call divergence_fft(res,virt_dim,3_pInt,&
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post) ! padding
field_real(1:res(1),1:res(2),1:res(3),1:3,1:3),divergence_post)
!--------------------------------------------------------------------------------------------------
! doing the FT because it simplifies calculation of average stress in real space also
call fftw_execute_dft_r2c(plan_forward,field_real,field_fourier)
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 FT results
if (debugFFTW) then
@ -302,115 +291,19 @@ real(pReal) function convolution(calcDivergence,field_aim,C_ref)
scalarField_fourier(1:res1_red,1:res(2),1:res(3))))
endif
!--------------------------------------------------------------------------------------------------
! removing highest frequencies
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
field_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) &
field_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)
end subroutine Utilities_forwardFFT
subroutine Utilities_backwardFFT()
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
if(calcDivergence) then
field_avg = real(field_fourier(1,1,1,1:3,1:3),pReal)*wgt
implicit none
field_av_L2 = sqrt(maxval(math_eigenvalues33(math_mul33x33(field_avg,& ! L_2 norm of average stress (http://mathworld.wolfram.com/SpectralNorm.html)
math_transpose33(field_avg)))))
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(field_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
enddo
err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ sum( real(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum( real(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
enddo; enddo
integer(pInt) :: row, column, i, j, k, m, n
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
err_div = err_div_RMS/field_av_L2 ! criterion to stop iterations
!--------------------------------------------------------------------------------------------------
! calculate additional divergence criteria and report
if (debugDivergence) then ! calculate divergence again
err_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
temp3_Complex = math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
xi(1:3,i,j,k))*TWOPIIMG
err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
err_real_div_RMS = 0.0_pReal
err_post_div_RMS = 0.0_pReal
err_real_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
err_post_div_RMS = err_post_div_RMS + sum(divergence_post(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
err_real_div_max = max(err_real_div_max,sum(divergence_real(i,j,k,1:3)**2.0_pReal)) ! max of squared L_2 norm of div(stress) in real space
enddo; enddo; enddo
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
err_real_div_max = sqrt( err_real_div_max) ! max in real space
err_div_max = sqrt( err_div_max) ! max in Fourier space
write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
write(6,'(a,es11.4)') 'error divergence Real max = ',err_real_div_max
endif
write(6,'(a,f6.2,a,es11.4,a)') 'error divergence = ', err_div/err_div_tol,&
' (',err_div,' N/m³)'
end if
!--------------------------------------------------------------------------------------------------
! to the actual spectral method calculation (mechanical equilibrium)
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
temp33_Real = math_inv33(temp33_Real)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(1,1,1, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k,1:3,1:3) = temp33_Complex
endif
enddo; enddo; enddo
else ! use precalculated gamma-operator
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
enddo; enddo; enddo
endif
field_fourier(1,1,1,1:3,1:3) = cmplx(field_aim,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
!--------------------------------------------------------------------------------------------------
! comparing 1 and 3x3 inverse FT results
if (debugFFTW) then
row = 3 ! (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 = 3 !(mod(totalIncsCounter+iter-2_pInt,3_pInt)) + 1_pInt
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res1_red
scalarField_fourier(i,j,k) = field_fourier(i,j,k,row,column)
enddo; enddo; enddo
@ -442,115 +335,192 @@ real(pReal) function convolution(calcDivergence,field_aim,C_ref)
real(scalarField_real(1:res(1),1:res(2),1:res(3))))
endif
end subroutine Utilities_backwardFFT
subroutine Utilities_fourierConvolution(field_aim)
use numerics, only: &
memory_efficient
implicit none
real(pReal), dimension(3,3) :: xiDyad, temp33_Real, field_aim
integer(pInt) :: i, j, k, l, m, n, q
complex(pReal), dimension(3,3) :: temp33_complex
!--------------------------------------------------------------------------------------------------
! calculate some additional output
if(debugGeneral) then
maxCorrectionSkew = 0.0_pReal
maxCorrectionSym = 0.0_pReal
temp33_Real = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
maxCorrectionSym = max(maxCorrectionSym,&
maxval(math_symmetric33(field_real(i,j,k,1:3,1:3))))
maxCorrectionSkew = max(maxCorrectionSkew,&
maxval(math_skew33(field_real(i,j,k,1:3,1:3))))
temp33_Real = temp33_Real + field_real(i,j,k,1:3,1:3)
! actual spectral method
write(6,'(a)') ''
write(6,'(a)') '... doing convolution .................'
!--------------------------------------------------------------------------------------------------
! removing highest frequencies
field_fourier ( res1_red,1:res(2) , 1:res(3) ,1:3,1:3)&
= cmplx(0.0_pReal,0.0_pReal,pReal)
field_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) &
field_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)
!--------------------------------------------------------------------------------------------------
! to the actual spectral method calculation (mechanical equilibrium)
if(memory_efficient) then ! memory saving version, on-the-fly calculation of gamma_hat
do k = 1_pInt, res(3); do j = 1_pInt, res(2) ;do i = 1_pInt, res1_red
if(any([i,j,k] /= 1_pInt)) then ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
xiDyad(l,m) = xi(l, i,j,k)*xi(m, i,j,k)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Real(l,m) = sum(C_ref(l,m,1:3,1:3)*xiDyad)
temp33_Real = math_inv33(temp33_Real)
forall(l=1_pInt:3_pInt, m=1_pInt:3_pInt, n=1_pInt:3_pInt, q=1_pInt:3_pInt)&
gamma_hat(1,1,1, l,m,n,q) = temp33_Real(l,n)*xiDyad(m,q)
forall(l = 1_pInt:3_pInt, m = 1_pInt:3_pInt) &
temp33_Complex(l,m) = sum(gamma_hat(1,1,1, l,m, 1:3,1:3) *&
field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k,1:3,1:3) = temp33_Complex
endif
enddo; enddo; enddo
else ! use precalculated gamma-operator
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt,res1_red
forall( m = 1_pInt:3_pInt, n = 1_pInt:3_pInt) &
temp33_Complex(m,n) = sum(gamma_hat(i,j,k, m,n, 1:3,1:3) *&
field_fourier(i,j,k,1:3,1:3))
field_fourier(i,j,k, 1:3,1:3) = temp33_Complex
enddo; enddo; enddo
write(6,'(a,1x,es11.4)') 'max symmetric correction of deformation =',&
maxCorrectionSym*wgt
write(6,'(a,1x,es11.4)') 'max skew correction of deformation =',&
maxCorrectionSkew*wgt
write(6,'(a,1x,es11.4)') 'max sym/skew of avg correction = ',&
maxval(math_symmetric33(temp33_real))/&
maxval(math_skew33(temp33_real))
endif
field_real = field_real * wgt
convolution = err_div/err_div_tol
field_fourier(1,1,1,1:3,1:3) = cmplx(field_aim,0.0_pReal,pReal) ! singular point at xi=(0.0,0.0,0.0) i.e. i=j=k=1
end function convolution
function S_lastInc(rot_BC,mask_stressVector1,C)
end subroutine Utilities_fourierConvolution
real(pReal), dimension(3,3,3,3) :: S_lastInc
real(pReal), dimension(3,3,3,3), intent(in) :: C
integer(pInt) :: i, j, k, m, n
real(pReal), dimension(3,3), intent(in) :: rot_BC
logical, dimension(9), intent(in) :: mask_stressVector1
real(pReal), dimension(3,3,3,3) :: C_lastInc
real(pReal), dimension(9,9) :: temp99_Real
integer(pInt) :: size_reduced = 0_pInt
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
logical :: errmatinv
size_reduced = count(mask_stressVector1)
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
real(pReal) function Utilities_divergenceRMS()
use numerics, only: err_div_tol
integer(pInt) :: i, j, k, l, m, n, q
!--------------------------------------------------------------------------------------------------
!variables for additional output due to general debugging
real(pReal), dimension(3,3) :: field_avg
real(pReal) :: field_av_L2, err_div_RMS, err_real_div_RMS, err_post_div_RMS,&
err_div_max, err_real_div_max
complex(pReal), dimension(3) :: temp3_complex
!--------------------------------------------------------------------------------------------------
! actual spectral method
write(6,'(a)') ''
write(6,'(a)') '... calculating divergence .................'
C_lastInc = math_rotate_forward3333(C,rot_BC) ! calculate stiffness from former inc
temp99_Real = math_Plain3333to99(C_lastInc)
k = 0_pInt ! build reduced stiffness
do n = 1_pInt,9_pInt
if(mask_stressVector1(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(mask_stressVector1(m)) then
j = j + 1_pInt
c_reduced(k,j) = temp99_Real(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(error_ID=400_pInt)
temp99_Real = 0.0_pReal ! build full compliance
k = 0_pInt
!--------------------------------------------------------------------------------------------------
! calculating RMS divergence criterion in Fourier space
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(field_fourier(i,j,k,1:3,1:3),& ! (sqrt(real(a)**2 + aimag(a)**2))**2 = real(a)**2 + aimag(a)**2. do not take square root and square again
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal)& ! --> sum squared L_2 norm of vector
+sum(aimag(math_mul33x3_complex(field_fourier(i,j,k,1:3,1:3),&
xi(1:3,i,j,k))*TWOPIIMG)**2.0_pReal))
enddo
err_div_RMS = err_div_RMS & ! Those two layers (DC and Nyquist) do not have a conjugate complex counterpart
+ sum( real(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(1 ,j,k,1:3,1:3),&
xi(1:3,1 ,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum( real(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)&
+ sum(aimag(math_mul33x3_complex(field_fourier(res1_red,j,k,1:3,1:3),&
xi(1:3,res1_red,j,k))*TWOPIIMG)**2.0_pReal)
enddo; enddo
err_div_RMS = sqrt(err_div_RMS)*wgt ! RMS in real space calculated with Parsevals theorem from Fourier space
Utilities_divergenceRMS = err_div_RMS ! 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(field_fourier(i,j,k,1:3,1:3)*wgt,& ! weighting P_fourier
xi(1:3,i,j,k))*TWOPIIMG
err_div_max = max(err_div_max,sum(abs(temp3_Complex)**2.0_pReal))
divergence_fourier(i,j,k,1:3) = temp3_Complex ! need divergence NOT squared
enddo; enddo; enddo
call fftw_execute_dft_c2r(plan_divergence,divergence_fourier,divergence_real) ! already weighted
err_real_div_RMS = 0.0_pReal
err_post_div_RMS = 0.0_pReal
err_real_div_max = 0.0_pReal
do k = 1_pInt, res(3); do j = 1_pInt, res(2); do i = 1_pInt, res(1)
err_real_div_RMS = err_real_div_RMS + sum(divergence_real(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
err_post_div_RMS = err_post_div_RMS + sum(divergence_post(i,j,k,1:3)**2.0_pReal) ! avg of squared L_2 norm of div(stress) in real space
err_real_div_max = max(err_real_div_max,sum(divergence_real(i,j,k,1:3)**2.0_pReal)) ! max of squared L_2 norm of div(stress) in real space
enddo; enddo; enddo
err_real_div_RMS = sqrt(wgt*err_real_div_RMS) ! RMS in real space
err_post_div_RMS = sqrt(wgt*err_post_div_RMS) ! RMS in real space
err_real_div_max = sqrt( err_real_div_max) ! max in real space
err_div_max = sqrt( err_div_max) ! max in Fourier space
write(6,'(a,es11.4)') 'error divergence FT RMS = ',err_div_RMS
write(6,'(a,es11.4)') 'error divergence Real RMS = ',err_real_div_RMS
write(6,'(a,es11.4)') 'error divergence post RMS = ',err_post_div_RMS
write(6,'(a,es11.4)') 'error divergence FT max = ',err_div_max
write(6,'(a,es11.4)') 'error divergence Real max = ',err_real_div_max
endif
end function Utilities_divergenceRMS
function Utilities_stressBC(rot_BC,mask_stressVector,C)
real(pReal), dimension(3,3,3,3) :: Utilities_stressBC
real(pReal), dimension(3,3,3,3), intent(in) :: C
integer(pInt) :: i, j, k, m, n
real(pReal), dimension(3,3), intent(in) :: rot_BC
logical, dimension(9), intent(in) :: mask_stressVector
real(pReal), dimension(3,3,3,3) :: C_lastInc
real(pReal), dimension(9,9) :: temp99_Real
integer(pInt) :: size_reduced = 0_pInt
real(pReal), dimension(:,:), allocatable :: s_reduced, c_reduced ! reduced compliance and stiffness (only for stress BC)
logical :: errmatinv
size_reduced = count(mask_stressVector)
allocate (c_reduced(size_reduced,size_reduced), source =0.0_pReal)
allocate (s_reduced(size_reduced,size_reduced), source =0.0_pReal)
C_lastInc = math_rotate_forward3333(C,rot_BC) ! calculate stiffness from former inc
temp99_Real = math_Plain3333to99(C_lastInc)
k = 0_pInt ! build reduced stiffness
do n = 1_pInt,9_pInt
if(mask_stressVector1(n)) then
if(mask_stressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(mask_stressVector1(m)) then
if(mask_stressVector(m)) then
j = j + 1_pInt
temp99_Real(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
S_lastInc = math_Plain99to3333(temp99_Real)
c_reduced(k,j) = temp99_Real(n,m)
endif; enddo; endif; enddo
call math_invert(size_reduced, c_reduced, s_reduced, i, errmatinv) ! invert reduced stiffness
if(errmatinv) call IO_error(error_ID=400_pInt)
temp99_Real = 0.0_pReal ! build full compliance
k = 0_pInt
do n = 1_pInt,9_pInt
if(mask_stressVector(n)) then
k = k + 1_pInt
j = 0_pInt
do m = 1_pInt,9_pInt
if(mask_stressVector(m)) then
j = j + 1_pInt
temp99_Real(n,m) = s_reduced(k,j)
endif; enddo; endif; enddo
Utilities_stressBC = math_Plain99to3333(temp99_Real)
end function S_lastInc
end function Utilities_stressBC
!--------------------------------------------------------------------------------------------------
! calculate reduced compliance
real(pReal) function BCcorrection(mask_stressVector,P_BC,P_av,F_aim,S_lastInc)
use numerics, only: err_stress_tolrel, err_stress_tolabs
logical, dimension(9) :: mask_stressVector
real(pReal) :: err_stress, err_stress_tol
real(pReal), dimension(3,3), parameter :: ones = 1.0_pReal, zeroes = 0.0_pReal
real(pReal), dimension(3,3,3,3) :: S_lastInc
real(pReal), dimension(3,3) :: &
P_BC , &
P_av, &
F_aim, &
mask_stress, &
mask_defgrad
mask_stress = merge(ones,zeroes,reshape(mask_stressVector,[3,3]))
mask_defgrad = merge(zeroes,ones,reshape(mask_stressVector,[3,3]))
!--------------------------------------------------------------------------------------------------
! stress BC handling
! calculate stress BC if applied
err_stress = maxval(abs(mask_stress * (P_av - P_BC))) ! maximum deviaton (tensor norm not applicable)
err_stress_tol = min(maxval(abs(P_av)) * err_stress_tolrel,err_stress_tolabs) ! don't use any tensor norm for the relative criterion because the comparison should be coherent
write(6,'(a)') ''
write(6,'(a)') '... correcting deformation gradient to fulfill BCs ...............'
write(6,'(a,f6.2,a,es11.4,a)') 'error stress = ', err_stress/err_stress_tol, &
' (',err_stress,' Pa)'
F_aim = F_aim - math_mul3333xx33(S_lastInc, ((P_av - P_BC))) ! residual on given stress components
write(6,'(a,1x,es11.4)')'determinant of new deformation = ',math_det33(F_aim)
BCcorrection = err_stress/err_stress_tol
end function BCcorrection
subroutine constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
subroutine Utilities_constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
P,C,P_av,ForwardData,rotation_BC)
use debug, only: &
debug_reset, &
@ -610,23 +580,24 @@ subroutine constitutiveResponse(coordinates,F,F_lastInc,temperature,timeinc,&
write (6,'(a,/,3(3(f12.7,1x)/))',advance='no') 'Piola-Kirchhoff stress / MPa =',&
math_transpose33(P_av)/1.e6_pReal
C = C * wgt
end subroutine constitutiveResponse
end subroutine Utilities_constitutiveResponse
subroutine Utilities_destroy
subroutine Utilities_destroy()
implicit none
if (debugDivergence) then
call fftw_destroy_plan(plan_divergence)
endif
if (debugFFTW) then
call fftw_destroy_plan(plan_scalarField_forth)
call fftw_destroy_plan(plan_scalarField_back)
endif
call fftw_destroy_plan(plan_forward)
call fftw_destroy_plan(plan_backward)
implicit none
if (debugDivergence) then
call fftw_destroy_plan(plan_divergence)
endif
if (debugFFTW) then
call fftw_destroy_plan(plan_scalarField_forth)
call fftw_destroy_plan(plan_scalarField_back)
endif
call fftw_destroy_plan(plan_forward)
call fftw_destroy_plan(plan_backward)
end subroutine Utilities_destroy