foodie_integrator_lmm_ssp Module

  1. foodie_integrator_lmm_ssp.f90
  2. foodie_integrator_lmm_ssp
module~~foodie_integrator_lmm_ssp~~UsesGraph module~foodie_integrator_lmm_ssp foodie_integrator_lmm_ssp module~foodie_integrator_object foodie_integrator_object module~foodie_integrator_object->module~foodie_integrator_lmm_ssp module~foodie_integrator_multistep_object foodie_integrator_multistep_object module~foodie_integrator_object->module~foodie_integrator_multistep_object module~foodie_integrator_multistep_object->module~foodie_integrator_lmm_ssp penf penf penf->module~foodie_integrator_lmm_ssp penf->module~foodie_integrator_object penf->module~foodie_integrator_multistep_object module~foodie_error_codes foodie_error_codes penf->module~foodie_error_codes module~foodie_integrand_object foodie_integrand_object penf->module~foodie_integrand_object module~foodie_error_codes->module~foodie_integrator_lmm_ssp module~foodie_integrand_object->module~foodie_integrator_lmm_ssp module~foodie_integrand_object->module~foodie_integrator_multistep_object iso_fortran_env iso_fortran_env iso_fortran_env->module~foodie_integrator_object iso_fortran_env->module~foodie_integrator_multistep_object
Help

FOODIE integrator: provide an explicit class of Linear Multi-step Methods (LLM) with Strong Stability Preserving property, from 2nd to 3rd order accurate.

Considering the following ODE system:

$$ U_t = R(t,U) $$

where \(U_t = \frac{dU}{dt}\), U is the vector of state variables being a function of the time-like independent variable t, R is the (vectorial) residual function, the LMM-SSP class scheme implemented is:

$$ U^{n+N_s} = \sum_{s=1}^{N_s}{\left[a_s U^{n+s-1} + \Delta t b_s \cdot R(t^{n+s-1}, U^{n+s-1}) \right]} $$

where \(N_s\) is the number of previous steps considered.

The schemes are explicit. The coefficients a,b define the actual scheme, that is selected accordingly to the number of steps used. Currently, the schemes provided have steps number in [3, 5]. The formal order of accuracy varies consistently in [2nd, 3rd] order.

Bibliography

[1] Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations, S. Gottlieb, D. Ketcheson, C.W. Shu, 2011, 978-981-4289-26-9, doi:10.1142/7498, World Scientific Publishing Co. Pte. Ltd.

Used By

module~~foodie_integrator_lmm_ssp~~UsedByGraph module~foodie_integrator_lmm_ssp foodie_integrator_lmm_ssp module~foodie foodie module~foodie_integrator_lmm_ssp->module~foodie program~integrate_burgers integrate_burgers module~foodie->program~integrate_burgers program~integrate_lorenz integrate_lorenz module~foodie->program~integrate_lorenz module~type_euler_1d type_euler_1D module~foodie->module~type_euler_1d module~foodie_test_integrand_tester_object foodie_test_integrand_tester_object module~foodie->module~foodie_test_integrand_tester_object module~foodie_test_lcce_test foodie_test_lcce_test module~foodie->module~foodie_test_lcce_test module~type_euler_1d_openmp type_euler_1D_openmp module~foodie->module~type_euler_1d_openmp program~integrate_euler_1d_caf~2 integrate_euler_1D_caf module~foodie->program~integrate_euler_1d_caf~2 module~foodie_test_oscillation_test foodie_test_oscillation_test module~foodie->module~foodie_test_oscillation_test program~integrate_euler_1d integrate_euler_1D module~foodie->program~integrate_euler_1d module~foodie_test_object foodie_test_object module~foodie->module~foodie_test_object module~foodie_test_integrand_oscillation foodie_test_integrand_oscillation module~foodie->module~foodie_test_integrand_oscillation module~foodie_test_integrand_lcce foodie_test_integrand_lcce module~foodie->module~foodie_test_integrand_lcce module~type_euler_1d_caf type_euler_1D_caf module~foodie->module~type_euler_1d_caf module~type_burgers type_burgers module~foodie->module~type_burgers module~foodie_test_integrand_ladvection foodie_test_integrand_ladvection module~foodie->module~foodie_test_integrand_ladvection program~integrate_euler_1d_openmp integrate_euler_1D_openmp module~foodie->program~integrate_euler_1d_openmp module~type_lorenz type_lorenz module~foodie->module~type_lorenz module~type_euler_1d->program~integrate_euler_1d module~foodie_test_integrand_tester_object->module~foodie_test_object module~foodie_test_integrand_tester_object->module~foodie_test_integrand_oscillation module~foodie_test_integrand_tester_object->module~foodie_test_integrand_lcce module~foodie_test_integrand_tester_object->module~foodie_test_integrand_ladvection program~foodie_test_lcce foodie_test_lcce module~foodie_test_lcce_test->program~foodie_test_lcce module~type_euler_1d_openmp->program~integrate_euler_1d_openmp program~foodie_test_oscillation foodie_test_oscillation module~foodie_test_oscillation_test->program~foodie_test_oscillation program~foodie_tester foodie_tester module~foodie_test_object->program~foodie_tester module~foodie_test_integrand_oscillation->module~foodie_test_oscillation_test module~foodie_test_integrand_oscillation->module~foodie_test_object module~foodie_test_integrand_lcce->module~foodie_test_lcce_test module~foodie_test_integrand_lcce->module~foodie_test_object module~type_euler_1d_caf->program~integrate_euler_1d_caf~2 module~type_burgers->program~integrate_burgers module~foodie_test_integrand_ladvection->module~foodie_test_object module~type_lorenz->program~integrate_lorenz
Help

Variables

Derived Types

Functions

Subroutines


Variables

TypeVisibility AttributesNameInitial
character(len=99), private, parameter:: class_name_ ='lmm_ssp'

Name of the class of schemes.
logical, private, parameter:: has_fast_mode_ =.true.

Flag to check if integrator provides fast mode integrate.
character(len=99), private, parameter:: supported_schemes_(1:3) =[trim(class_name_)//'_steps_3_order_2', trim(class_name_)//'_steps_4_order_3', trim(class_name_)//'_steps_5_order_3']

List of supported schemes.

Derived Types

type, public, extends(integrator_multistep_object) :: integrator_lmm_ssp

FOODIE integrator: provide an explicit class of Linear Multi-step Methods (LLM) with Strong Stability Preserving property, from 2nd to 3rd order accurate.

Components

TypeVisibility AttributesNameInitial
real(kind=R_P), public, allocatable:: Dt(:)

Previous time steps.
real(kind=R_P), private, allocatable:: a(:)

a coefficients.
logical, public :: autoupdate

Perform cyclic autoupdate of previous time steps buffers.
real(kind=R_P), private, allocatable:: b(:)

b coefficients.
class(integrand_object), public, allocatable:: buffer

Buffer used for fast integration.
character(len=:), public, allocatable:: description_

Informative description of the integrator.
integer(kind=I_P), public :: error =0

Error status code.
character(len=:), public, allocatable:: error_message

Error message, hopefully meaningful.
integer(kind=I_P), public :: iterations

Implicit iterations.
class(integrand_object), public, allocatable:: previous(:)

Previous steps.
integer(kind=I_P), public :: registers

Number of registers used for steps.
integer(kind=I_P), public :: steps

Number of time steps.
real(kind=R_P), public, allocatable:: t(:)

Previous times.

Type-Bound Procedures

procedure, public, pass(self) :: allocate_integrand_members

Allocate integrand members.

procedure, public, pass(lhs) :: assign_abstract

Assign ony members of abstract integrator_object type.

procedure, public, pass(lhs) :: assign_multistep

Assign members of integrator_multistep_object and parents.

generic, public :: assignment(=) => integr_assign_integr

Overload =.

procedure, public, pass(self) :: check_error

Check for error occurrencies.

procedure, public, pass(self) :: class_name

Return the class name of schemes.

procedure, public, pass(self) :: description

Return informative integrator description.

procedure, public, pass(self) :: destroy

Destroy the integrator.

procedure, public, pass(self) :: destroy_abstract

Destroy only members of abstract integrator_object type.

procedure, public, pass(self) :: destroy_multistep

Destroy the integrator.

procedure, public, pass(self) :: has_fast_mode

Return .true. if the integrator class has fast mode integrate.

procedure, public, pass(self) :: initialize

Initialize (create) the integrator.

procedure, public, pass(lhs) :: integr_assign_integr

Operator =.

procedure, public, pass(self) :: integrate

Integrate integrand field.

procedure, public, pass(self) :: integrate_fast

Integrate integrand field, fast mode.

procedure, public, pass(self) :: is_multistage

Return .true. for multistage integrator.

procedure, public, pass(self) :: is_multistep

Return .true. for multistep integrator.

procedure, public, pass(self) :: is_supported

Return .true. if the integrator class support the given scheme.

procedure, public, pass(self) :: stages_number

Return number of stages used.

procedure, public, pass(self) :: steps_number

Return number of steps used.

procedure, public, pass(self) :: supported_schemes

Return the list of supported schemes.

procedure, public, pass(self) :: trigger_error

Trigger an error.

procedure, public, nopass :: update_previous

Cyclic update previous time steps.

Functions

private pure function class_name(self)

Return the class name of schemes.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(in) :: self

Integrator.

Return Value character(len=99)

Class name.

private elemental function has_fast_mode(self)

Return .true. if the integrator class has fast mode integrate.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(in) :: self

Integrator.

Return Value logical

Inquire result.

private elemental function is_supported(self, scheme)

Return .true. if the integrator class support the given scheme.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(in) :: self

Integrator.
character(len=*), intent(in) :: scheme

Selected scheme.

Return Value logical

Inquire result.

private pure function supported_schemes(self) result(schemes)

Return the list of supported schemes.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(in) :: self

Integrator.

Return Value character(len=99), allocatable, (:)

Queried scheme.


Subroutines

private elemental subroutine destroy(self)

Destroy the integrator.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(inout) :: self

Integrator.

private subroutine initialize(self, scheme, autoupdate, U, stop_on_fail)

Create the actual LMM-SSP integrator: initialize the a,b coefficients.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(inout) :: self

Integrator.
character(len=*), intent(in) :: scheme

Selected scheme.
logical, intent(in), optional :: autoupdate

Enable cyclic autoupdate of previous time steps.
class(integrand_object), intent(in), optional :: U

Integrand molding prototype.
logical, intent(in), optional :: stop_on_fail

Stop execution if initialization fail.

private subroutine integr_assign_integr(lhs, rhs)

Operator =.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(inout) :: lhs

Left hand side.
class(integrator_object), intent(in) :: rhs

Right hand side.

private subroutine integrate(self, U, Dt, t)

Integrate field with LMM-SSP class scheme.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(inout) :: self

Integrator.
class(integrand_object), intent(inout) :: U

Field to be integrated.
real(kind=R_P), intent(in) :: Dt

Time step.
real(kind=R_P), intent(in) :: t

Time.

private subroutine integrate_fast(self, U, Dt, t)

Integrate field with LMM-SSP class scheme, fast mode.

Arguments

Type IntentOptional AttributesName
class(integrator_lmm_ssp), intent(inout) :: self

Integrator.
class(integrand_object), intent(inout) :: U

Field to be integrated.
real(kind=R_P), intent(in) :: Dt

Time step.
real(kind=R_P), intent(in) :: t

Time.

All Modules