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crystallite.f90: can now calculate analytic jacobian by setting analyticJaco = 1 in numerics.config 

math.f90: added math_mul3333xx3333…

numerics.f90: to read in analyticJaco and Lp_frac
This commit is contained in:
Pratheek Shanthraj 2012-02-22 20:11:09 +00:00
parent 9a54f3a7ba
commit b9a82156c9
3 changed files with 211 additions and 5 deletions
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184
code/crystallite.f90
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@ -455,7 +455,10 @@ use numerics, only: subStepMinCryst, &
pert_method, &
nCryst, &
numerics_integrator, &
numerics_integrationMode
numerics_integrationMode, &
relevantStrain, &
Lp_frac, &
analyticJaco
use debug, only: debug_verbosity, &
debug_selectiveDebugger, &
debug_e, &
@ -464,12 +467,21 @@ use debug, only: debug_verbosity, &
debug_CrystalliteLoopDistribution
use IO, only: IO_warning
use math, only: math_inv33, &
math_identity2nd, &
math_transpose33, &
math_mul33x33, &
math_mul66x6, &
math_Mandel6to33, &
math_Mandel33to6, &
math_I3
math_I3, &
math_Plain3333to99, &
math_Plain99to3333, &
math_mul99x99, &
math_Mandel66to3333, &
math_mul3333xx33, &
math_invert, &
math_mul3333xx3333, &
math_spectralDecompositionSym33
use FEsolving, only: FEsolving_execElem, &
FEsolving_execIP
use mesh, only: mesh_element, &
@ -485,7 +497,8 @@ use constitutive, only: constitutive_sizeState, &
constitutive_partionedState0, &
constitutive_homogenizedC, &
constitutive_dotState, &
constitutive_dotState_backup
constitutive_dotState_backup, &
constitutive_LpAndItsTangent
implicit none
@ -520,12 +533,57 @@ integer(pInt) NiterationCrystallite, &
g, & ! grain index
k, &
l, &
h, &
o, &
p, &
j, &
perturbation , & ! loop counter for forward,backward perturbation mode
myNgrains, &
mySizeState, &
mySizeDotState
logical, dimension(homogenization_maxNgrains,mesh_maxNips,mesh_NcpElems) :: &
convergenceFlag_backup
! local variables used for calculating analytic Jacobian
real(pReal), dimension(3,3):: Fp_exp1, &
Fp_exp2, &
Fp_inv_current, &
dSdFe_mat1, &
dSdFe_mat2, &
Lp_constitutive, &
Eigvec, &
V_dir, &
phi_mat, &
Fp_rate, &
FDot_temp, &
Rot_mat, &
Fp0, &
Fp_inv_0, &
Lp0, &
Lp_current, &
Fe0
real(pReal), dimension(3,3,3,3) :: C, &
dSdFe, &
dLp_dT, &
Tensor1, &
Tensor2, &
Tensor3, &
Tensor4, &
Tensor5, &
dFedF, &
dSdF
real(pReal), dimension(9,9) :: dLp_dT_constitutive, &
A99, &
A_inv99, &
C99, &
dFedF99, &
dFedF_old99
real(pReal), dimension(3):: Eigval
real(pReal) :: dt, &
fixedpt_error
integer(pInt) :: AnzNegEW, &
fixedpt_iter, &
counter
logical :: error
! --+>> INITIALIZE TO STARTING CONDITION <<+--
@ -719,6 +777,9 @@ enddo
! --+>> STIFFNESS CALCULATION <<+--
if(updateJaco) then ! Jacobian required
if (.not. analyticJaco) then ! Calculate Jacobian using perturbations
numerics_integrationMode = 2_pInt
@ -898,7 +959,124 @@ if(updateJaco) then
crystallite_Tstar_v = Tstar_v_backup
crystallite_P = P_backup
crystallite_converged = convergenceFlag_backup
else ! Calculate Jacobian using analytical expression
! --- CALCULATE ANALYTIC dPdF ---
! !$OMP PARALLEL DO PRIVATE(myNgrains,dt,Fp0,Fp_inv_0,Lp0,Lp_current,Fe0,C,Eigval,Eigvec,Fp_exp1,& ! Does not work with OMP currently
! Fp_exp2,Fp_inv_current,dSdFe_mat1,dSdFe_mat2,Fp_rate,FDot_temp,counter,h,j,o,p,phi_mat,Tensor1,&
! Tensor2,Tensor3,Tensor4,Tensor5,V_dir,dLp_dT_constitutive,dLp_dT,C99,A99,A_inv99,AnzNegEW,error,&
! dFedF99,dFedF,fixedpt_iter,fixedpt_error,dSdF)
do e = FEsolving_execElem(1),FEsolving_execElem(2) ! iterate over elements to be processed
myNgrains = homogenization_Ngrains(mesh_element(3,e))
do i = FEsolving_execIP(1,e),FEsolving_execIP(2,e) ! iterate over IPs of this element to be processed
do g = 1_pInt,myNgrains
dt = crystallite_dt(g,i,e) ! time step size
Fp0 = crystallite_subFp0(1:3,1:3,g,i,e) ! Fp old
Fp_inv_0 = math_inv33(Fp0) ! Fp old^-1
Lp0 = crystallite_subLp0(1:3,1:3,g,i,e) ! Lp old
Lp_current = crystallite_Lp(1:3,1:3,g,i,e) ! Lp current
Fe0 = crystallite_subFe0(1:3,1:3,g,i,e) ! Fe old
C = math_Mandel66to3333(constitutive_homogenizedC(g,i,e))
call math_spectralDecompositionSym33(-(1.0_pReal-Lp_frac)*dt*0.5_pReal*Lp0,Eigval,&
Eigvec,error)
Fp_exp1 = 0.0_pReal
Fp_exp1(1,1) = exp(Eigval(1))
Fp_exp1(2,2) = exp(Eigval(2))
Fp_exp1(3,3) = exp(Eigval(3))
Fp_exp1 = math_mul33x33(math_mul33x33(Eigvec,Fp_exp1),math_transpose33(Eigvec)) ! exp(-(1-Lp_frac)*Lp old*dt/2)
call math_spectralDecompositionSym33(-(Lp_frac)*dt*0.5_pReal*Lp_current,Eigval,Eigvec,error)
Fp_exp2 = 0.0_pReal
Fp_exp2(1,1) = exp(Eigval(1))
Fp_exp2(2,2) = exp(Eigval(2))
Fp_exp2(3,3) = exp(Eigval(3))
Fp_exp2 = math_mul33x33(math_mul33x33(Eigvec,Fp_exp2),math_transpose33(Eigvec)) ! exp(-(Lp_frac)*Lp current*dt/2)
Fp_inv_current = math_mul33x33(math_mul33x33(math_mul33x33(math_mul33x33(Fp_inv_0, &
Fp_exp1),Fp_exp2),Fp_exp2),Fp_exp1) ! Fp current^-1 = Fp old^-1 * exp(-(1-Lp_frac)*Lp old*dt/2) * exp(-(Lp_frac)*Lp current*dt) * exp(-(1-Lp_frac)*Lp old*dt/2)
dSdFe_mat2 = math_mul33x33(math_mul33x33(Fp_exp1,Fp_exp2),Eigvec)
dSdFe_mat1 = math_mul33x33(math_mul33x33(crystallite_subF(1:3,1:3,g,i,e),Fp_inv_0),dSdFe_mat2)
dSdFe_mat2 = math_transpose33(dSdFe_mat2)
Fp_rate = -math_mul33x33(Fp_inv_current,(1.0_pReal-Lp_frac)*Lp0 + Lp_frac*Lp_current)
FDot_temp = crystallite_subF(1:3,1:3,g,i,e) - crystallite_subF0(1:3,1:3,g,i,e)
counter = 0_pInt
phi_mat = 0.0_pReal
do h=1_pInt,3_pInt; do j=1_pInt,3_pInt
if (Eigval(h) == Eigval(j)) then
phi_mat(h,j) = 1.0_pReal
else
phi_mat(h,j) = sinh(Eigval(h) - Eigval(j))/(Eigval(h) - Eigval(j))
endif
if (abs(FDot_temp(h,j)) .lt. relevantStrain) then
counter = counter + 1_pInt
FDot_temp(h,j) = 0.0_pReal
else
FDot_temp(h,j) = dt/FDot_temp(h,j)
endif
enddo; enddo
if (counter .lt. 9_pInt) then
FDot_temp = FDot_temp/(9_pInt - counter)
endif
Tensor1 = 0.0_pReal
Tensor2 = 0.0_pReal
Tensor3 = 0.0_pReal
Tensor4 = 0.0_pReal
Tensor5 = 0.0_pReal
do h=1_pInt,3_pInt; do j=1_pInt,3_pInt
V_dir = 0.0_pReal
V_dir(h,j) = -Lp_frac*dt
V_dir = math_mul33x33(math_mul33x33(math_transpose33(Eigvec),V_dir),Eigvec)
Tensor2(1:3,1:3,h,j) = math_mul33x33(math_mul33x33(dSdFe_mat1,V_dir*phi_mat),dSdFe_mat2)
Tensor1(h,j,1:3,1:3) = Fp_rate(h,j)*FDot_temp !need full-rank Tensor1
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
Tensor1(h,j,o,p) = math_I3(h,o)*Fp_inv_current(p,j) + Tensor1(h,j,o,p) ! dF_im/dF_kl * (Fp current^-1)_mj + d(Fp current^-1)_ij/dt * dt/Fdot_kl
Tensor3(h,j,1:3,1:3) = 0.5_pReal*(math_mul33x33(C(h,j,1:3,1:3),math_transpose33(Fe0))&
+ math_mul33x33(C(h,j,1:3,1:3),math_transpose33(Fe0))) ! dS_ij/dFe_kl
Tensor5(h,j,o,p) = math_I3(h,o)*math_I3(j,p) - math_I3(h,j)*math_I3(o,p)/3.0_pReal ! tensor to strip away volumetric components of Lp added due to numerical error
enddo; enddo; enddo; enddo
call constitutive_LpAndItsTangent(Lp_constitutive, dLp_dT_constitutive, &
crystallite_Tstar_v(1:6,g,i,e), crystallite_Temperature(g,i,e), g, i, e)
dLp_dT = math_Plain99to3333(dLp_dT_constitutive)
Tensor4 = math_mul3333xx3333(math_mul3333xx3333(math_mul3333xx3333(Tensor2,dLp_dT),&
Tensor5),Tensor3) ! applying chain rule to get F_im * dFp^-1_mj/dFe_kl
A99 = math_identity2nd(9_pInt) - math_Plain3333to99(Tensor4)
C99 = math_Plain3333to99(Tensor1) ! [I - F_im * dFp^-1_mj/dFe_op]*dFe_op/dF_kl = dF_im/dF_kl * (Fp current^-1)_mj + d(Fp current^-1)_ij/dt * dt/Fdot_kl
call math_invert(9_pInt,A99, A_inv99, AnzNegEW, error)
dFedF99 = math_mul99x99(A_inv99,C99) ! solve for dFe_ij/dF_kl
dFedF = math_Plain99to3333(dFedF99)
fixedpt_iter = 1_pInt
fixedpt_error = 1.0_pReal
do while ((fixedpt_iter .lt. 10_pInt) .and. (fixedpt_error .gt. 1e-20_pReal)) ! if solution is not accurate, use as estimate for better solution
dFedF_old99 = dFedF99
A99 = math_mul99x99(A_inv99,A99)
C99 = dFedF_old99
call math_invert(9_pInt,A99, A_inv99, AnzNegEW, error)
dFedF99 = math_mul99x99(A_inv99,C99)
fixedpt_error = maxval(abs(dFedF99 - dFedF_old99))
fixedpt_iter = fixedpt_iter + 1_pInt
enddo
dFedF = math_Plain99to3333(dFedF99)
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
dFedF(1:3,1:3,o,p) = math_transpose33(dFedF(1:3,1:3,o,p))
enddo; enddo
dSdF = math_mul3333xx3333(Tensor3,dFedF) ! dS/dF = dS/dFe * dFe/dF
do o=1_pInt,3_pInt; do p=1_pInt,3_pInt
crystallite_dPdF(1:3,1:3,o,p,g,i,e) = math_mul33x33(math_mul33x33(&
crystallite_subF(1:3,1:3,g,i,e),Fp_inv_current),&
math_mul33x33(dSdF(1:3,1:3,o,p),math_transpose33(Fp_inv_current))) ! dP/dF = Fe * dS/dF * Fp^-T
enddo; enddo
! !$OMP CRITICAL (write2out)
if (e == 1_pInt) then
print '(a,/,3(12x,3(e10.3,1x),/))', 'dPdF0 * Del F',math_mul3333xx33(crystallite_dPdF0(1:3,1:3,1:3,1:3,g,i,e), &
(crystallite_subF(1:3,1:3,g,i,e) - crystallite_subF0(1:3,1:3,g,i,e)))
print '(a,/,3(12x,3(e10.3,1x),/))', 'Del P', crystallite_P(1:3,1:3,g,i,e) - math_mul33x33(crystallite_subFe0(1:3,1:3,g,i,e), &
math_mul33x33(math_Mandel6to33(crystallite_subTstar0_v(1:6,g,i,e)), &
math_transpose33(math_inv33(crystallite_subFp0(1:3,1:3,g,i,e)))))
endif
! !$OMP END CRITICAL (write2out)
enddo; enddo; enddo
! !$OMP END PARALLEL DO
endif
endif ! jacobian calculation
endsubroutine

22
code/math.f90
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@ -496,6 +496,28 @@ real(pReal), dimension(4,36), parameter :: math_symOperations = &
endfunction math_mul3333xx33
!**************************************************************************
! matrix multiplication 3333x3333 = 3333 (ijkl *klmn = ijmn)
!**************************************************************************
pure function math_mul3333xx3333(A,B)
implicit none
integer(pInt) :: i,j,k,l
real(pReal), dimension(3,3,3,3), intent(in) :: A
real(pReal), dimension(3,3,3,3), intent(in) :: B
real(pReal), dimension(3,3,3,3) :: math_mul3333xx3333
do i = 1_pInt,3_pInt
do j = 1_pInt,3_pInt
do k = 1_pInt,3_pInt
do l = 1_pInt,3_pInt
math_mul3333xx3333(i,j,k,l) = sum(A(i,j,1:3,1:3)*B(1:3,1:3,k,l))
enddo; enddo; enddo; enddo
endfunction math_mul3333xx3333
!**************************************************************************
! matrix multiplication 33x33 = 33
!**************************************************************************

10
code/numerics.f90
View File

@ -50,7 +50,8 @@ real(pReal) :: relevantStrain = 1.0e-7_pReal, &
rTol_crystalliteTemperature= 1.0e-6_pReal, & ! relative tolerance in crystallite temperature loop
rTol_crystalliteStress = 1.0e-6_pReal, & ! relative tolerance in crystallite stress loop
aTol_crystalliteStress = 1.0e-8_pReal, & ! absolute tolerance in crystallite stress loop, Default 1.0e-8: residuum is in Lp and hence strain is on this order
Lp_frac = 0.5_pReal, & ! fraction of Lp current and Lp previous step to use when integrating Fp from previous step to current
absTol_RGC = 1.0e+4_pReal, & ! absolute tolerance of RGC residuum
relTol_RGC = 1.0e-3_pReal, & ! relative tolerance of RGC residuum
absMax_RGC = 1.0e+10_pReal, & ! absolute maximum of RGC residuum
@ -75,7 +76,8 @@ integer(pInt) :: fftw_planner_flag = -1_pInt, &
logical :: memory_efficient = .true., & ! for fast execution (pre calculation of gamma_hat), Default .true.: do not precalculate
divergence_correction = .false., & ! correct divergence calculation in fourier space, Default .false.: no correction
update_gamma = .false., & ! update gamma operator with current stiffness, Default .false.: use initial stiffness
simplified_algorithm = .true. ! use short algorithm without fluctuation field, Default .true.: use simplified algorithm
simplified_algorithm = .true., & ! use short algorithm without fluctuation field, Default .true.: use simplified algorithm
analyticJaco = .false. ! use analytic Jacobian or perturbation, Default .false.: calculate Jacobian using perturbations
@ -196,6 +198,10 @@ subroutine numerics_init()
numerics_integrator(1) = IO_intValue(line,positions,2_pInt)
case ('integratorstiffness')
numerics_integrator(2) = IO_intValue(line,positions,2_pInt)
case ('lp_frac')
Lp_frac = IO_intValue(line,positions,2_pInt)
case ('analyticjaco')
analyticJaco = IO_intValue(line,positions,2_pInt) > 0_pInt
!* RGC parameters: