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Add SSP Linear Multistep Methods with Variable Step Size
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Add Strong Stability Preserving Linear Multistep Methods with Variable Step Size.

Stable release, fully barckward compatible.
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@szaghi
szaghi committed Mar 31, 2017
1 parent 518acbe commit 60ac876
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Showing 6 changed files with 407 additions and 76 deletions.
33 changes: 21 additions & 12 deletions papers/announcement/errors_analysis/errors_analysis.sh
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Original file line number Diff line number Diff line change
Expand Up @@ -11,6 +11,7 @@ euler=0
lf=0
lf_raw=0
lmm_ssp=0
lmm_ssp_vss=0
ls_rk=0
tvd_rk=0

Expand All @@ -20,18 +21,19 @@ function print_usage {
echo "script automotion for FOODIE's errors analysis"
echo "Usage: `basename $0` #solver"
echo "Valid solver switches are:"
echo " -ab # => adams-bashforth"
echo " -abm # => adams-bashforth-moulton"
echo " -am # => adams-moulton"
echo " -bdf # => backward differentiation formula"
echo " -emd-rk # => embeded RK"
echo " -euler # => euler"
echo " -lf # => leapfrog"
echo " -lf-raw # => leapfrog raw filtered"
echo " -lmm-ssp # => linear multistep methods SSP"
echo " -ls-rk # => low storage RK"
echo " -tvd-rk # => TVD RK"
echo " -all # => all solvers!"
echo " -ab # => adams-bashforth"
echo " -abm # => adams-bashforth-moulton"
echo " -am # => adams-moulton"
echo " -bdf # => backward differentiation formula"
echo " -emd-rk # => embeded RK"
echo " -euler # => euler"
echo " -lf # => leapfrog"
echo " -lf-raw # => leapfrog raw filtered"
echo " -lmm-ssp # => linear multistep methods SSP"
echo " -lmm-ssp-vss # => linear multistep methods SSP with Variable Step Size"
echo " -ls-rk # => low storage RK"
echo " -tvd-rk # => TVD RK"
echo " -all # => all solvers!"
}

#parsing command line
Expand Down Expand Up @@ -64,6 +66,9 @@ while [ $# -gt 0 ]; do
"-lmm-ssp")
lmm_ssp=1
;;
"-lmm-ssp-vss")
lmm_ssp_vss=1
;;
"-ls-rk")
ls_rk=1
;;
Expand Down Expand Up @@ -149,6 +154,10 @@ fi
if [ $lmm_ssp -eq 1 ] ; then
../tests/oscillation -r -tf 1e6 --solver lmm-ssp --ss 3 5 -Dt 5000.d0 2500.d0 1250.d0 625.d0 320.d0 100.d0 50.d0 10.d0 --errors_analysis > analysis-lmm-ssp.log
fi
if [ $lmm_ssp_vss -eq 1 ] ; then
../tests/oscillation -r -tf 1e6 --solver lmm-ssp-vss --ss 3 5 --order 2 -Dt 5000.d0 2500.d0 1250.d0 625.d0 320.d0 100.d0 --errors_analysis > analysis-lmm-ssp-vss.log
../tests/oscillation -r -tf 1e6 --solver lmm-ssp-vss --ss 3 5 --order 3 -Dt 5000.d0 2500.d0 1250.d0 625.d0 320.d0 100.d0 --errors_analysis > analysis-lmm-ssp-vss.log
fi
if [ $ls_rk -eq 1 ] ; then
../tests/oscillation -r -tf 1e6 --solver ls-runge-kutta --ss 1 -Dt 5000.d0 2500.d0 1250.d0 625.d0 320.d0 100.d0 --errors_analysis #> analysis-leapfrog.log
../tests/oscillation -r -tf 1e6 --solver ls-runge-kutta --ss 5 7 -Dt 5000.d0 2500.d0 1250.d0 625.d0 320.d0 100.d0 --errors_analysis #> analysis-leapfrog.log
Expand Down
17 changes: 16 additions & 1 deletion src/lib/foodie.f90
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Original file line number Diff line number Diff line change
Expand Up @@ -72,6 +72,7 @@ module foodie
use foodie_integrator_euler_explicit, only : integrator_euler_explicit
use foodie_integrator_leapfrog, only : integrator_leapfrog
use foodie_integrator_lmm_ssp, only : integrator_lmm_ssp
use foodie_integrator_lmm_ssp_vss, only : integrator_lmm_ssp_vss
use foodie_integrator_runge_kutta_emd, only : integrator_runge_kutta_emd
use foodie_integrator_runge_kutta_low_storage, only : integrator_runge_kutta_ls
use foodie_integrator_runge_kutta_tvd, only : integrator_runge_kutta_tvd
Expand All @@ -87,13 +88,14 @@ module foodie
public :: integrator_euler_explicit
public :: integrator_leapfrog
public :: integrator_lmm_ssp
public :: integrator_lmm_ssp_vss
public :: integrator_runge_kutta_emd
public :: integrator_runge_kutta_ls
public :: foodie_integrator
public :: integrator_runge_kutta_tvd

contains
function foodie_integrator(scheme, steps, stages, tolerance, nu, alpha) result(integrator)
function foodie_integrator(scheme, steps, stages, order, tolerance, nu, alpha) result(integrator)
!< Return a concrete instance of [[integrator]] given a scheme selection.
!<
!< This is the FOODIE integrators factory.
Expand All @@ -102,6 +104,7 @@ function foodie_integrator(scheme, steps, stages, tolerance, nu, alpha) result(i
character(*), intent(in) :: scheme !< Selected integrator given.
integer(I_P), intent(in), optional :: steps !< Number of time steps used in multi-step schemes.
integer(I_P), intent(in), optional :: stages !< Number of Runge-Kutta stages used in multi-stage schemes.
integer(I_P), intent(in), optional :: order !< Order of accuracy.
real(R_P), intent(in), optional :: tolerance !< Tolerance on the local truncation error.
real(R_P), intent(in), optional :: nu !< Williams-Robert-Asselin filter coefficient.
real(R_P), intent(in), optional :: alpha !< Robert-Asselin filter coefficient.
Expand Down Expand Up @@ -176,6 +179,18 @@ function foodie_integrator(scheme, steps, stages, tolerance, nu, alpha) result(i
error_message='missing steps number for initializing integrator!', &
is_severe=.true.)
endif
case('lmm_ssp_vss')
allocate(integrator_lmm_ssp_vss :: integrator)
if ((.not.present(steps)).or.(.not.present(order))) then
call integrator%trigger_error(error=ERROR_MISSING_STEPS_NUMBER, &
error_message='missing steps number for initializing integrator!', &
is_severe=.true.)
else
select type(integrator)
type is(integrator_lmm_ssp_vss)
call integrator%init(steps=steps, order=order)
endselect
endif
case('runge_kutta_emd')
allocate(integrator_runge_kutta_emd :: integrator)
if (present(stages)) then
Expand Down
2 changes: 2 additions & 0 deletions src/lib/foodie_error_codes.f90
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Original file line number Diff line number Diff line change
Expand Up @@ -11,9 +11,11 @@ module foodie_error_codes
public :: ERROR_BAD_STEPS_NUMBER
public :: ERROR_MISSING_STAGES_NUMBER
public :: ERROR_BAD_STAGES_NUMBER
public :: ERROR_INTEGRATOR_INIT_FAIL

integer(I_P), parameter :: ERROR_MISSING_STEPS_NUMBER = 1 !< Error missing steps number (for FOODIE factory).
integer(I_P), parameter :: ERROR_BAD_STEPS_NUMBER = 2 !< Error bad (unsupported) steps number.
integer(I_P), parameter :: ERROR_MISSING_STAGES_NUMBER = 3 !< Error missing stages number (for FOODIE factory).
integer(I_P), parameter :: ERROR_BAD_STAGES_NUMBER = 4 !< Error bad (unsupported) stages number.
integer(I_P), parameter :: ERROR_INTEGRATOR_INIT_FAIL = 5 !< Error integrator initialization failed.
endmodule foodie_error_codes
60 changes: 31 additions & 29 deletions src/lib/foodie_integrator_lmm_ssp.f90
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Original file line number Diff line number Diff line change
Expand Up @@ -115,39 +115,39 @@ subroutine init(self, steps)
if (self%is_supported(steps)) then
call self%destroy
self%steps = steps
allocate(self%a(1:steps)) ; self%a = 0.0_R_P
allocate(self%b(1:steps)) ; self%b = 0.0_R_P
allocate(self%a(1:steps)) ; self%a = 0._R_P
allocate(self%b(1:steps)) ; self%b = 0._R_P
select case(steps)
case(3) ! LMM-SSP(3,2)
self%a(1) = 1.0_R_P/4.0_R_P
self%a(2) = 0.0_R_P
self%a(3) = 3.0_R_P/4.0_R_P
self%a(1) = 1._R_P/4._R_P
self%a(2) = 0._R_P
self%a(3) = 3._R_P/4._R_P

self%b(1) = 0.0_R_P
self%b(2) = 0.0_R_P
self%b(3) = 3.0_R_P/2.0_R_P
self%b(1) = 0._R_P
self%b(2) = 0._R_P
self%b(3) = 3._R_P/2._R_P
case(4) ! LMM-SSP(4,3)
self%a(1) = 11.0_R_P/27.0_R_P
self%a(2) = 0.0_R_P
self%a(3) = 0.0_R_P
self%a(4) = 16.0_R_P/27.0_R_P

self%b(1) = 12.0_R_P/27.0_R_P
self%b(2) = 0.0_R_P
self%b(3) = 0.0_R_P
self%b(4) = 16.0_R_P/9.0_R_P
self%a(1) = 11._R_P/27._R_P
self%a(2) = 0._R_P
self%a(3) = 0._R_P
self%a(4) = 16._R_P/27._R_P

self%b(1) = 12._R_P/27._R_P
self%b(2) = 0._R_P
self%b(3) = 0._R_P
self%b(4) = 16._R_P/9._R_P
case(5) ! LMM-SSP(5,3)
self%a(1) = 7.0_R_P/32.0_R_P
self%a(2) = 0.0_R_P
self%a(3) = 0.0_R_P
self%a(4) = 0.0_R_P
self%a(5) = 25.0_R_P/32.0_R_P

self%b(1) = 5.0_R_P/16.0_R_P
self%b(2) = 0.0_R_P
self%b(3) = 0.0_R_P
self%b(4) = 0.0_R_P
self%b(5) = 25.0_R_P/16.0_R_P
self%a(1) = 7._R_P/32._R_P
self%a(2) = 0._R_P
self%a(3) = 0._R_P
self%a(4) = 0._R_P
self%a(5) = 25._R_P/32._R_P

self%b(1) = 5._R_P/16._R_P
self%b(2) = 0._R_P
self%b(3) = 0._R_P
self%b(4) = 0._R_P
self%b(5) = 25._R_P/16._R_P
endselect
else
call self%trigger_error(error=ERROR_BAD_STEPS_NUMBER, &
Expand All @@ -170,7 +170,9 @@ subroutine integrate(self, U, previous, Dt, t, autoupdate)
autoupdate_ = .true. ; if (present(autoupdate)) autoupdate_ = autoupdate
U = U * 0._R_P
do s=1, self%steps
U = U + previous(s) * self%a(s) + previous(s)%t(t=t(s)) * (Dt * self%b(s))
if (self%a(s) /= 0._R_P) U = U + previous(s) * self%a(s)
if (self%b(s) /= 0._R_P) U = U + previous(s)%t(t=t(s)) * (Dt * self%b(s))
! U = U + previous(s) * self%a(s) + previous(s)%t(t=t(s)) * (Dt * self%b(s))
enddo
if (autoupdate_) call self%update_previous(U=U, previous=previous)
endsubroutine integrate
Expand Down
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