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DAMASK_EICMD
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added functions math_mul33x3_complex math_Plain99to3333 to math.f90. 

mpie_spectral.f90 uses both functions
math_Plain99to3333 is used for inversion of c0
math_mul33x3_complex is used for equilibrium check in fourier space
also did some cleaning up on mpie_spectral.f90
This commit is contained in:
Martin Diehl 2010-09-22 12:04:43 +00:00
parent 80618c9814
commit 6ea8623f65
2 changed files with 140 additions and 117 deletions
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34
code/math.f90
View File

@ -509,6 +509,24 @@ real(pReal), dimension(4,36), parameter :: math_symOperations = &
endfunction
!**************************************************************************
! matrix multiplication complex(33) x real(3) = complex(3)
!**************************************************************************
pure function math_mul33x3_complex(A,B)
use prec, only: pReal, pInt
implicit none
integer(pInt) i
complex(pReal), dimension(3,3), intent(in) :: A
real(pReal), dimension(3), intent(in) :: B
complex(pReal), dimension(3) :: math_mul33x3_complex
forall (i=1:3) math_mul33x3_complex(i) = A(i,1)*B(1) + A(i,2)*B(2) + A(i,3)*B(3)
return
endfunction
!**************************************************************************
! matrix multiplication 66x6 = 6
@ -1165,7 +1183,23 @@ pure function math_transpose3x3(A)
endfunction
!********************************************************************
! plain matrix 9x9 into 3x3x3x3 tensor
!********************************************************************
pure function math_Plain99to3333(m99)
use prec, only: pReal,pInt
implicit none
real(pReal), dimension(9,9), intent(in) :: m99
real(pReal), dimension(3,3,3,3) :: math_Plain99to3333
integer(pInt) i,j
forall (i=1:9,j=1:9) math_Plain99to3333(mapPlain(1,i),mapPlain(2,i),&
mapPlain(1,j),mapPlain(2,j)) = m99(i,j)
return
endfunction
!********************************************************************
! convert symmetric 3x3x3x3 tensor into Mandel matrix 6x6

159
code/mpie_spectral.f90
View File

@ -33,60 +33,59 @@ program mpie_spectral
implicit none
include 'fftw3.f' !header file for fftw3 (declaring variables). Library file is also needed
!variables to read in from loadcase and mesh file
! variables to read from loadcase and mesh file
real(pReal), dimension(9) :: valuevector ! stores information temporarily from loadcase file
integer(pInt), parameter :: maxNchunksInput = 24 ! 4 identifiers, 18 values for the matrices and 2 scalars
integer(pInt), dimension (1+maxNchunksInput*2) :: posInput
integer(pInt), parameter :: maxNchunksMesh = 7 ! 4 identifiers, 3 values
integer(pInt), dimension (1+2*maxNchunksMesh) :: posMesh
integer(pInt) unit, N_l, N_s, N_t, N_n ! numbers of identifiers
character(len=1024) path, line
logical gotResolution,gotDimension,gotHomogenization
logical, dimension(9) :: bc_maskvector
character(len=1024) path, line
! variables storing information from loadcase file
integer(pInt) N_Loadcases, steps
integer(pInt), dimension(:), allocatable :: bc_steps ! number of steps
real(pReal) timeinc
real(pReal), dimension (:,:,:), allocatable :: bc_velocityGrad, &
bc_stress ! velocity gradient and stress BC
real(pReal), dimension(:), allocatable :: bc_timeIncrement ! length of increment
integer(pInt) N_Loadcases, steps
integer(pInt), dimension(:), allocatable :: bc_steps ! number of steps
logical, dimension(:,:,:,:), allocatable :: bc_mask ! mask of boundary conditions
! variables storing information from mesh file
integer(pInt) homog, prodnn
real(pReal) wgt
integer(pInt), dimension(3) :: resolution
real(pReal), dimension(3) :: meshdimension
integer(pInt) homog, prodnn
integer(pInt), dimension(3) :: resolution
! stress etc.
real(pReal), dimension(3,3) :: pstress, defgradmacro, pstress_av, defgrad_av, temp33_Real
real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0
real(pReal), dimension(6) :: cstress ! cauchy stress in Mandel notation (not needed)
real(pReal), dimension(3,3) :: pstress ! Piola-Kirchhoff stress in Matrix notation
real(pReal), dimension(3,3,3,3) :: dPdF, c0, s0 ! ??, reference stiffnes, compliance
real(pReal), dimension(6,6) :: dsde, s066
real(pReal), dimension(3,3) :: defgradmacro
real(pReal), dimension(3,3) :: pstress_av, defgrad_av, temp33_Real
real(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field, defgrad, defgradold
real(pReal), dimension(6,6) :: dsde
real(pReal), dimension(9,9) :: s099
real(pReal), dimension(:,:,:), allocatable :: ddefgrad
real(pReal), dimension(:,:,:,:,:), allocatable :: pstress_field, defgrad, defgradold
! variables storing information for spectral method
complex(pReal), dimension(:,:,:,:,:), allocatable :: workfft
complex(pReal), dimension(3,3) :: temp33_Complex
real(pReal), dimension(:,:,:,:,:,:,:), allocatable :: gamma_hat
real(pReal), dimension(:,:,:,:,:), allocatable :: xknormdyad
real(pReal), dimension(:,:,:,:,:), allocatable :: xinormdyad
real(pReal), dimension(:,:,:,:), allocatable :: xi
integer(pInt), dimension(3) :: k_s
integer*8, dimension(2,3,3) :: plan_fft
! convergency etc.
logical errmatinv
integer(pInt) itmax, ierr
real(pReal) error, err_div, sigma0
integer(pInt) itmax, ierr
logical errmatinv
! loop variables etc.
real(pReal) guessmode ! flip-flop to guess defgrad fluctuation field evolution
integer(pInt) i, j, k, l, m, n, p
integer(pInt) loadcase, ielem, iter, calcmode
real(pReal) guessmode ! flip-flop to guess defgrad fluctuation field evolution
real(pReal) temperature ! not used, but needed
@ -115,7 +114,7 @@ program mpie_spectral
gotResolution =.false.; gotDimension =.false.; gotHomogenization = .false.
if (IargC() < 2) call IO_error(102) ! check for correct number of arguments given
if (IargC() /= 2) call IO_error(102) ! check for correct number of given arguments
! Reading the loadcase file and assign variables
path = getLoadcaseName()
@ -251,7 +250,7 @@ program mpie_spectral
allocate (workfft(resolution(1)/2+1,resolution(2),resolution(3),3,3)); workfft = 0.0_pReal
allocate (gamma_hat(resolution(1)/2+1,resolution(2),resolution(3),3,3,3,3)); gamma_hat = 0.0_pReal
allocate (xknormdyad(resolution(1)/2+1,resolution(2),resolution(3),3,3)); xknormdyad = 0.0_pReal
allocate (xinormdyad(resolution(1)/2+1,resolution(2),resolution(3),3,3)); xinormdyad = 0.0_pReal
allocate (xi(resolution(1)/2+1,resolution(2),resolution(3),3)); xi = 0.0_pReal
allocate (pstress_field(resolution(1),resolution(2),resolution(3),3,3)); pstress_field = 0.0_pReal
allocate (displacement(resolution(1),resolution(2),resolution(3),3)); displacement = 0.0_pReal
@ -259,6 +258,7 @@ program mpie_spectral
allocate (defgradold(resolution(1),resolution(2),resolution(3),3,3)); defgradold = 0.0_pReal
allocate (ddefgrad(resolution(1),resolution(2),resolution(3))); ddefgrad = 0.0_pReal
! Initialization of fftw (see manual on fftw.org for more details)
call dfftw_init_threads(ierr)
call dfftw_plan_with_nthreads(4)
do m = 1,3; do n = 1,3
@ -272,6 +272,7 @@ program mpie_spectral
wgt = 1_pReal/real(prodnn, pReal)
defgradmacro = math_I3
! Initialization of CPFEM_general (= constitutive law) and of deformation gradient field
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
defgradold(i,j,k,:,:) = math_I3 !no deformation at the beginning
@ -280,7 +281,7 @@ program mpie_spectral
call CPFEM_general(2,math_I3,math_I3,temperature,0.0_pReal,ielem,1_pInt,cstress,dsde,pstress,dPdF)
enddo; enddo; enddo
!calculation of xknormdyad (needed to calculate gamma_hat) and xi (waves, needed for proof of equilibrium)
!calculation of xinormdyad (needed to calculate gamma_hat) and xi (waves, needed for proof of equilibrium)
do k = 1, resolution(3)
k_s(3) = k-1
if(k > resolution(3)/2+1) k_s(3) = k_s(3)-resolution(3)
@ -289,14 +290,14 @@ program mpie_spectral
if(j > resolution(2)/2+1) k_s(2) = k_s(2)-resolution(2)
do i = 1, resolution(1)/2+1
k_s(1) = i-1
xi(i,j,k,3) = .0_pReal
xi(i,j,k,3) = 0.0_pReal
if(resolution(3) > 1) xi(i,j,k,3) = real(k_s(3), pReal)/meshdimension(3)
xi(i,j,k,2) = real(k_s(2), pReal)/meshdimension(2)
xi(i,j,k,1) = real(k_s(1), pReal)/meshdimension(1)
if (any(xi(i,j,k,:) /= .0_pReal)) then
if (any(xi(i,j,k,:) /= 0.0_pReal)) then
do l = 1,3; do m = 1,3
xknormdyad(i,j,k, l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2)
xinormdyad(i,j,k, l,m) = xi(i,j,k, l)*xi(i,j,k, m)/sum(xi(i,j,k,:)**2)
enddo; enddo
endif
@ -312,23 +313,23 @@ program mpie_spectral
!*************************************************************
timeinc = bc_timeIncrement(loadcase)/bc_steps(loadcase)
guessmode = 0.0_pReal ! change of load case
guessmode = 0.0_pReal ! change of load case, homogeneous guess for the first step
!*************************************************************
! loop oper steps defined in input file for current loadcase
do steps = 1, bc_steps(loadcase)
!*************************************************************
defgradmacro = defgradmacro&
+ math_mul33x33(bc_velocityGrad(:,:,loadcase), defgradmacro)*timeinc !update macroscopic displacement gradient (stores the desired BCs of defgrad)
defgradmacro = defgradmacro& ! update macroscopic displacement gradient (BC of defgrad)
+ math_mul33x33(bc_velocityGrad(:,:,loadcase), defgradmacro)*timeinc
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
temp33_Real = defgrad(i,j,k,:,:)
defgrad(i,j,k,:,:) = defgrad(i,j,k,:,:)&
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))& ! old fluctuations as guess for new step
+ (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,k,:,:))*timeinc ! no fluctuations for new loadcase
defgrad(i,j,k,:,:) = defgrad(i,j,k,:,:)& ! old fluctuations as guess for new step, no fluctuations for new loadcase
+ guessmode * (defgrad(i,j,k,:,:) - defgradold(i,j,k,:,:))&
+ (1.0_pReal-guessmode) * math_mul33x33(bc_velocityGrad(:,:,loadcase),defgradold(i,j,k,:,:))*timeinc
defgradold(i,j,k,:,:) = temp33_Real
enddo; enddo; enddo
guessmode = 1_pReal ! keep guessing along former trajectory
guessmode = 1_pReal ! keep guessing along former trajectory during same loadcase
calcmode = 1_pInt
iter = 0_pInt
err_div= 2_pInt * error
@ -339,9 +340,10 @@ program mpie_spectral
iter = iter + 1
print '(A,I5.5,tr2,A,I5.5)', ' Step = ',steps,'Iteration = ',iter
!*************************************************************
err_div = .0_pReal; sigma0 = .0_pReal
pstress_av = .0_pReal; defgrad_av=.0_pReal
err_div = 0.0_pReal; sigma0 = 0.0_pReal
pstress_av = 0.0_pReal; defgrad_av = 0.0_pReal
! Calculate stress field for current deformation gradient using CPFEM_general
print *, 'Update Stress Field'
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
@ -351,7 +353,7 @@ program mpie_spectral
cstress,dsde, pstress, dPdF)
enddo; enddo; enddo
c0 = .0_pReal
c0 = 0.0_pReal
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
@ -364,34 +366,35 @@ program mpie_spectral
pstress_field(i,j,k,:,:) = pstress
pstress_av = pstress_av + pstress ! average stress
enddo; enddo; enddo
pstress_av = pstress_av*wgt ! do the weighting of average stress
if(iter==1) then !update gamma_hat with new reference stiffness
call math_invert(6,math_mandel3333to66(c0),s066,i,errmatinv) !i is just a dummy variable
! Update gamma_hat with new reference stiffness and calculate new average compliance (for stress BC)
if(iter==1) then
call math_invert(9, math_plain3333to99(c0),s099,i, errmatinv)
if(errmatinv) call IO_error(45,ext_msg = "problem in c0 inversion") ! todo: change number and add message to io.f90 (and remove No. 48)
s0 = math_mandel66to3333(s066)*real(prodnn, pReal)
s0 = math_plain99to3333(s099) * real(prodnn, pReal)
c0 = c0 * wgt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
temp33_Real = .0_pReal
temp33_Real = 0.0_pReal
do l = 1,3; do m = 1,3; do n = 1,3; do p = 1,3
temp33_Real(l,m) = temp33_Real(l,m)+c0(l,n,m,p)*xknormdyad(i,j,k, n,p)
temp33_Real(l,m) = temp33_Real(l,m) + c0(l,n,m,p) * xinormdyad(i,j,k, n,p)
enddo; enddo; enddo; enddo
temp33_Real = math_inv3x3(temp33_Real)
do l=1,3; do m=1,3; do n=1,3; do p=1,3
gamma_hat(i,j,k, l,m,n,p) = -temp33_Real(l,n)*xknormdyad(i,j,k, m,p)
gamma_hat(i,j,k, l,m,n,p) = - temp33_Real(l,n) * xinormdyad(i,j,k, m,p)
enddo; enddo; enddo; enddo
enddo; enddo; enddo
endif
! Using the spectral method to calculate the change of deformation gradient, check divergence of stress field in fourier space
print *, 'Update Deformation Gradient Field'
do m = 1,3; do n = 1,3
call dfftw_execute_dft_r2c(plan_fft(1,m,n), pstress_field(:,:,:,m,n),workfft(:,:,:,m,n))
if(n == 3) sigma0 = max(sigma0, sum(abs(real(workfft(1,1,1,m,:))))) ! L infinity Norm of stress tensor in Fourier space
if(n == 3) sigma0 = max(sigma0, sum(abs(real(workfft(1,1,1,m,:))))) ! L infinity Norm of stress tensor
enddo; enddo
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)/2+1
err_div = err_div + (maxval(abs(math_mul33x3c(workfft(i,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress tensor) in Fourier space
err_div = err_div + (maxval(abs(math_mul33x3_complex(workfft(i,j,k,:,:),xi(i,j,k,:))))) ! L infinity Norm of div(stress)
temp33_Complex = .0_pReal
do m = 1,3; do n = 1,3
temp33_Complex(m,n) = sum(gamma_hat(i,j,k,m,n,:,:) * workfft(i,j,k,:,:))
@ -399,7 +402,7 @@ program mpie_spectral
workfft(i,j,k,:,:) = temp33_Complex(:,:)
enddo; enddo; enddo
err_div = err_div/(real(prodnn/resolution(1)*(resolution(1)/2+1)))/sigma0 !calculate error (divergence of stress field)
err_div = err_div/(real(prodnn/resolution(1)*(resolution(1)/2+1)))/sigma0 !weighting of error
do m = 1,3; do n = 1,3
call dfftw_execute_dft_c2r(plan_fft(2,m,n), workfft(:,:,:,m,n),ddefgrad(:,:,:))
@ -422,7 +425,7 @@ program mpie_spectral
enddo; enddo
print '(2(a,E8.2))', ' Error = ',err_div,' Criteria = ', error
print '(A)', '----------------------------------'
print '(A)', '---------------------------------------'
enddo ! end looping when convergency is achieved
@ -436,9 +439,9 @@ program mpie_spectral
print '(A,3(E10.4,tr2))', ' ', pstress_av(3,:)
print '(A)', '************************************************************'
!gsmh output
temp33_Real(1,:) = 0.0_pReal
temp33_Real(1,3) = -1.0_pReal
! Postprocessing (gsmh output)
temp33_Real(1,:) = 0.0_pReal; temp33_Real(1,3) = -(real(resolution(3))/meshdimension(3)) ! start just below origin
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
if((j==1).and.(i==1)) then
temp33_Real(1,:) = temp33_Real(1,:) + math_mul33x3(defgrad(i,j,k,:,:),(/0.0_pReal,0.0_pReal,(real(resolution(3))/meshdimension(3))/))
@ -456,59 +459,45 @@ program mpie_spectral
endif
endif
enddo; enddo; enddo
write(nriter, *) iter
write(nrstep, *) steps
nrstep = 'stress'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'
open(589,file = nrstep)
write(589, '(A, /, A, /, A, /, A, /, I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
write(nriter, *) iter; write(nrstep, *) steps
open(589,file = 'stress' //trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh')
open(588,file = 'disgrad'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh')
write(589, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
write(588, '(4(A, /), I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(I10,tr2,E12.6,tr2,E12.6,tr2,E12.6)'), ielem, displacement(i,j,k,:) !real(i), real(j), real(k)
write(589, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:)
write(588, '(I10, 3(tr2, E12.6))'), ielem, displacement(i,j,k,:)
enddo; enddo; enddo
write(589, '(A, /, A, /, I10)'), '$EndNodes', '$Elements', prodnn
write(589, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn
write(588, '(2(A, /), I10)'), '$EndNodes', '$Elements', prodnn
do i = 1, prodnn
write(589, '(I10, A, I10)'), i, ' 15 2 1 2', i
write(588, '(I10, A, I10)'), i, ' 15 2 1 2', i
enddo
write(589, '(A)'), '$EndElements'
write(589, '(A, /, A, /, A, /, A, /, A, /, A, /, A, /, A, /, I10)'), '$NodeData', '1',&
'"'//trim(adjustl(nrstep))//'"', '1','0.0', '3', '0', '9', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(i10,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,&
tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2)'), ielem, pstress_field(i,j,k,:,:)
enddo; enddo; enddo
write(nriter, *) iter
write(nrstep, *) steps
write(589, *), '$EndNodeData'
close(589)
nrstep = 'defgrad'//trim(adjustl(nrstep))//'-'//trim(adjustl(nriter))//'_cpfem.msh'
open(589,file = nrstep)
write(589, '(A, /, A, /, A, /, A, /, I10)'), '$MeshFormat', '2.1 0 8', '$EndMeshFormat', '$Nodes', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(I10,tr2,E12.6,tr2,E12.6,tr2,E12.6)'), ielem, displacement(i,j,k,:) !real(i), real(j), real(k)
enddo; enddo; enddo
write(589, '(A, /, A, /, I10)'), '$EndNodes', '$Elements', prodnn
do i = 1, prodnn
write(589, '(I10, A, I10)'), i, ' 15 2 1 2', i
enddo
write(589, '(A)'), '$EndElements'
write(589, '(A, /, A, /, A, /, A, /, A, /, A, /, A, /, A, /, I10)'), '$NodeData', '1',&
'"'//trim(adjustl(nrstep))//'"', '1','0.0', '3', '0', '9', prodnn
write(588, '(A)'), '$EndElements'
write(589, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('stress'//trim(adjustl(nrstep))//&
'-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn
write(588, '(8(A, /), I10)'), '$NodeData', '1','"'//trim(adjustl('disgrad'//trim(adjustl(nrstep))//&
'-'//trim(adjustl(nriter))//'_cpfem.msh'))//'"','1','0.0', '3', '0', '9', prodnn
ielem = 0_pInt
do k = 1, resolution(3); do j = 1, resolution(2); do i = 1, resolution(1)
ielem = ielem + 1
write(589, '(i10,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2,E12.6,&
tr2,E12.6,tr2,E12.6,tr2,E12.6,tr2)'), ielem, defgrad(i,j,k,:,:) - math_I3
write(589, '(i10, 9(tr2, E12.6))'), ielem, pstress_field(i,j,k,:,:)
write(588, '(i10, 9(tr2, E12.6))'), ielem, defgrad(i,j,k,:,:) - math_I3
enddo; enddo; enddo
write(589, *), '$EndNodeData'
close(589)
!end gmsh
write(588, *), '$EndNodeData'
close(589); close(588)
enddo ! end looping over steps in current loadcase
enddo ! end looping over loadcases