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Merge branch 'unified-RK4-RKCK45' into 'development' 

Unified RK4 RKCK45

See merge request damask/DAMASK!161
This commit is contained in:
Franz Roters 2020-04-24 16:32:13 +02:00
parent 05fd943cf4 49963b9f04
commit c6d58954fb
1 changed files with 71 additions and 168 deletions
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195
src/crystallite.f90
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@ -1301,9 +1301,9 @@ subroutine integrateStateAdaptiveEuler(todo)
end subroutine integrateStateAdaptiveEuler
!--------------------------------------------------------------------------------------------------
!> @brief integrate stress, state with 4th order explicit Runge Kutta method
!--------------------------------------------------------------------------------------------------
!---------------------------------------------------------------------------------------------------
!> @brief Integrate state (including stress integration) with the classic Runge Kutta method
!---------------------------------------------------------------------------------------------------
subroutine integrateStateRK4(todo)
logical, dimension(:,:,:), intent(in) :: todo
@ -1312,157 +1312,59 @@ subroutine integrateStateRK4(todo)
A = reshape([&
0.5_pReal, 0.0_pReal, 0.0_pReal, &
0.0_pReal, 0.5_pReal, 0.0_pReal, &
0.0_pReal, 0.0_pReal, 1.0_pReal], &
[3,3])
0.0_pReal, 0.0_pReal, 1.0_pReal],&
shape(A))
real(pReal), dimension(3), parameter :: &
CC = [0.5_pReal, 0.5_pReal, 1.0_pReal] ! factor giving the fraction of the original timestep used for Runge Kutta Integration
C = [0.5_pReal, 0.5_pReal, 1.0_pReal]
real(pReal), dimension(4), parameter :: &
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal] ! weight of slope used for Runge Kutta integration (final weight divided by 6)
B = [1.0_pReal/6.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/3.0_pReal, 1.0_pReal/6.0_pReal]
integer :: &
e, & ! element index in element loop
i, & ! integration point index in ip loop
g, & ! grain index in grain loop
stage, & ! stage index in integration stage loop
n, &
p, &
c, &
s, &
sizeDotState
logical :: &
nonlocalBroken, broken
real(pReal), dimension(constitutive_source_maxSizeDotState,4,maxval(phase_Nsources)) :: source_RK4dotState
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,4) :: plastic_RK4dotState
nonlocalBroken = .false.
!$OMP PARALLEL DO PRIVATE(sizeDotState,p,c,source_RK4dotState,plastic_RK4dotState,broken)
do e = FEsolving_execElem(1),FEsolving_execElem(2)
do i = FEsolving_execIP(1),FEsolving_execIP(2)
do g = 1,homogenization_Ngrains(material_homogenizationAt(e))
broken = .false.
p = material_phaseAt(g,e)
if(todo(g,i,e) .and. .not. (nonlocalBroken .and. plasticState(p)%nonlocal)) then
c = material_phaseMemberAt(g,i,e)
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
crystallite_partionedF0, &
crystallite_Fi(1:3,1:3,g,i,e), &
crystallite_partionedFp0, &
crystallite_subdt(g,i,e), g,i,e,p,c)
if(broken) cycle
do stage = 1,3
sizeDotState = plasticState(p)%sizeDotState
plastic_RK4dotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RK4dotState(1:sizeDotState,1)
do s = 1, phase_Nsources(p)
sizeDotState = sourceState(p)%p(s)%sizeDotState
source_RK4dotState(1:sizeDotState,stage,s) = sourceState(p)%p(s)%dotState(:,c)
sourceState(p)%p(s)%dotState(:,c) = A(1,stage) * source_RK4dotState(1:sizeDotState,1,s)
enddo
do n = 2, stage
sizeDotState = plasticState(p)%sizeDotState
plasticState(p)%dotState(:,c) = plasticState(p)%dotState(:,c) &
+ A(n,stage) * plastic_RK4dotState(1:sizeDotState,n)
do s = 1, phase_Nsources(p)
sizeDotState = sourceState(p)%p(s)%sizeDotState
sourceState(p)%p(s)%dotState(:,c) = sourceState(p)%p(s)%dotState(:,c) &
+ A(n,stage) * source_RK4dotState(1:sizeDotState,n,s)
enddo
enddo
sizeDotState = plasticState(p)%sizeDotState
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
+ plasticState(p)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
do s = 1, phase_Nsources(p)
sizeDotState = sourceState(p)%p(s)%sizeDotState
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
enddo
broken = integrateStress(g,i,e,CC(stage))
if(broken) exit
broken = constitutive_collectDotState(crystallite_S(1:3,1:3,g,i,e), &
crystallite_partionedF0, &
crystallite_Fi(1:3,1:3,g,i,e), &
crystallite_partionedFp0, &
crystallite_subdt(g,i,e)*CC(stage), g,i,e,p,c)
if(broken) exit
enddo
if(broken) cycle
sizeDotState = plasticState(p)%sizeDotState
plastic_RK4dotState(1:sizeDotState,4) = plasticState (p)%dotState(:,c)
plasticState(p)%dotState(:,c) = matmul(plastic_RK4dotState(1:sizeDotState,1:4),B)
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
+ plasticState(p)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
do s = 1, phase_Nsources(p)
sizeDotState = sourceState(p)%p(s)%sizeDotState
source_RK4dotState(1:sizeDotState,4,s) = sourceState(p)%p(s)%dotState(:,c)
sourceState(p)%p(s)%dotState(:,c) = matmul(source_RK4dotState(1:sizeDotState,1:4,s),B)
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
enddo
broken = constitutive_deltaState(crystallite_S(1:3,1:3,g,i,e), &
crystallite_Fe(1:3,1:3,g,i,e), &
crystallite_Fi(1:3,1:3,g,i,e),g,i,e,p,c)
if(broken) cycle
broken = integrateStress(g,i,e)
crystallite_converged(g,i,e) = .not. broken
endif
if(broken .and. plasticState(p)%nonlocal) nonlocalBroken = .true.
enddo; enddo; enddo
!$OMP END PARALLEL DO
if (nonlocalBroken) call nonlocalConvergenceCheck
call integrateStateRK(todo,A,B,C)
end subroutine integrateStateRK4
!--------------------------------------------------------------------------------------------------
!> @brief integrate stress, state with 5th order Runge-Kutta Cash-Karp method with
!> adaptive step size (use 5th order solution to advance = "local extrapolation")
!--------------------------------------------------------------------------------------------------
!---------------------------------------------------------------------------------------------------
!> @brief Integrate state (including stress integration) with the Cash-Carp method
!---------------------------------------------------------------------------------------------------
subroutine integrateStateRKCK45(todo)
logical, dimension(:,:,:), intent(in) :: todo
real(pReal), dimension(5,5), parameter :: &
A = reshape([&
.2_pReal, .075_pReal, .3_pReal, -11.0_pReal/54.0_pReal, 1631.0_pReal/55296.0_pReal, &
.0_pReal, .225_pReal, -.9_pReal, 2.5_pReal, 175.0_pReal/512.0_pReal, &
.0_pReal, .0_pReal, 1.2_pReal, -70.0_pReal/27.0_pReal, 575.0_pReal/13824.0_pReal, &
.0_pReal, .0_pReal, .0_pReal, 35.0_pReal/27.0_pReal, 44275.0_pReal/110592.0_pReal, &
.0_pReal, .0_pReal, .0_pReal, .0_pReal, 253.0_pReal/4096.0_pReal], &
[5,5], order=[2,1]) !< coefficients in Butcher tableau (used for preliminary integration in stages 2 to 6)
1._pReal/5._pReal, .0_pReal, .0_pReal, .0_pReal, .0_pReal, &
3._pReal/40._pReal, 9._pReal/40._pReal, .0_pReal, .0_pReal, .0_pReal, &
3_pReal/10._pReal, -9._pReal/10._pReal, 6._pReal/5._pReal, .0_pReal, .0_pReal, &
-11._pReal/54._pReal, 5._pReal/2._pReal, -70.0_pReal/27.0_pReal, 35.0_pReal/27.0_pReal, .0_pReal, &
1631._pReal/55296._pReal,175._pReal/512._pReal,575._pReal/13824._pReal,44275._pReal/110592._pReal,253._pReal/4096._pReal],&
shape(A))
real(pReal), dimension(5), parameter :: &
C = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal]
real(pReal), dimension(6), parameter :: &
B = &
[37.0_pReal/378.0_pReal, .0_pReal, 250.0_pReal/621.0_pReal, &
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], & !< coefficients in Butcher tableau (used for final integration and error estimate)
125.0_pReal/594.0_pReal, .0_pReal, 512.0_pReal/1771.0_pReal], &
DB = B - &
[2825.0_pReal/27648.0_pReal, .0_pReal, 18575.0_pReal/48384.0_pReal,&
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 0.25_pReal] !< coefficients in Butcher tableau (used for final integration and error estimate)
13525.0_pReal/55296.0_pReal, 277.0_pReal/14336.0_pReal, 1._pReal/4._pReal]
real(pReal), dimension(5), parameter :: &
CC = [0.2_pReal, 0.3_pReal, 0.6_pReal, 1.0_pReal, 0.875_pReal] !< coefficients in Butcher tableau (fractions of original time step in stages 2 to 6)
call integrateStateRK(todo,A,B,C,DB)
end subroutine integrateStateRKCK45
!--------------------------------------------------------------------------------------------------
!> @brief Integrate state (including stress integration) with an explicit Runge-Kutta method or an
!! embedded explicit Runge-Kutta method
!--------------------------------------------------------------------------------------------------
subroutine integrateStateRK(todo,A,B,CC,DB)
logical, dimension(:,:,:), intent(in) :: todo
real(pReal), dimension(:,:), intent(in) :: A
real(pReal), dimension(:), intent(in) :: B, CC
real(pReal), dimension(:), intent(in), optional :: DB
integer :: &
e, & ! element index in element loop
@ -1476,8 +1378,8 @@ subroutine integrateStateRKCK45(todo)
sizeDotState
logical :: &
nonlocalBroken, broken
real(pReal), dimension(constitutive_source_maxSizeDotState,6,maxval(phase_Nsources)) :: source_RKdotState
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,6) :: plastic_RKdotState
real(pReal), dimension(constitutive_source_maxSizeDotState,size(B),maxval(phase_Nsources)) :: source_RKdotState
real(pReal), dimension(constitutive_plasticity_maxSizeDotState,size(B)) :: plastic_RKdotState
nonlocalBroken = .false.
!$OMP PARALLEL DO PRIVATE(sizeDotState,p,c,plastic_RKdotState,source_RKdotState,broken)
@ -1497,7 +1399,7 @@ subroutine integrateStateRKCK45(todo)
crystallite_subdt(g,i,e), g,i,e,p,c)
if(broken) cycle
do stage = 1,5
do stage = 1,size(A,1)
sizeDotState = plasticState(p)%sizeDotState
plastic_RKdotState(1:sizeDotState,stage) = plasticState(p)%dotState(:,c)
plasticState(p)%dotState(:,c) = A(1,stage) * plastic_RKdotState(1:sizeDotState,1)
@ -1544,12 +1446,13 @@ subroutine integrateStateRKCK45(todo)
sizeDotState = plasticState(p)%sizeDotState
plastic_RKdotState(1:sizeDotState,6) = plasticState (p)%dotState(:,c)
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:6),B)
plastic_RKdotState(1:sizeDotState,size(B)) = plasticState (p)%dotState(:,c)
plasticState(p)%dotState(:,c) = matmul(plastic_RKdotState(1:sizeDotState,1:size(B)),B)
plasticState(p)%state(1:sizeDotState,c) = plasticState(p)%subState0(1:sizeDotState,c) &
+ plasticState(p)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:6),DB) &
if(present(DB)) &
broken = .not. converged( matmul(plastic_RKdotState(1:sizeDotState,1:size(DB)),DB) &
* crystallite_subdt(g,i,e), &
plasticState(p)%state(1:sizeDotState,c), &
plasticState(p)%atol(1:sizeDotState))
@ -1557,13 +1460,13 @@ subroutine integrateStateRKCK45(todo)
do s = 1, phase_Nsources(p)
sizeDotState = sourceState(p)%p(s)%sizeDotState
source_RKdotState(1:sizeDotState,6,s) = sourceState(p)%p(s)%dotState(:,c)
sourceState(p)%p(s)%dotState(:,c) = matmul(source_RKdotState(1:sizeDotState,1:6,s),B)
source_RKdotState(1:sizeDotState,size(B),s) = sourceState(p)%p(s)%dotState(:,c)
sourceState(p)%p(s)%dotState(:,c) = matmul(source_RKdotState(1:sizeDotState,1:size(B),s),B)
sourceState(p)%p(s)%state(1:sizeDotState,c) = sourceState(p)%p(s)%subState0(1:sizeDotState,c) &
+ sourceState(p)%p(s)%dotState (1:sizeDotState,c) &
* crystallite_subdt(g,i,e)
broken = broken .and. .not. &
converged(matmul(source_RKdotState(1:sizeDotState,1:6,s),DB) &
if(present(DB)) &
broken = broken .or. .not. converged(matmul(source_RKdotState(1:sizeDotState,1:size(DB),s),DB) &
* crystallite_subdt(g,i,e), &
sourceState(p)%p(s)%state(1:sizeDotState,c), &
sourceState(p)%p(s)%atol(1:sizeDotState))
@ -1585,7 +1488,7 @@ subroutine integrateStateRKCK45(todo)
if(nonlocalBroken) call nonlocalConvergenceCheck
end subroutine integrateStateRKCK45
end subroutine integrateStateRK
!--------------------------------------------------------------------------------------------------