foodie_integrator_euler_explicit

FOODIE integrator: provide explicit Euler scheme, it being 1st 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 Forward Explicit Euler scheme implemented is:

$$ U^{n+1} = U^n +\Delta t R(t, U^n) $$

Note

The value of $\Delta t$ must be provided, it not being computed by the integrator.

Used By

Help

Variables

class_name_ has_fast_mode_ supported_schemes_

Derived Types

integrator_euler_explicit

Functions

class_name has_fast_mode is_supported supported_schemes

Subroutines

destroy initialize integr_assign_integr integrate integrate_fast

Variables

Type	Visibility	Attributes		Name		Initial
character(len=99),	private,	parameter	::	class_name_	=	'euler_explicit'	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_(1:1)	=	[trim(class_name_)]	List of supported schemes.

Derived Types

type, public, extends(integrator_multistage_object) :: integrator_euler_explicit

FOODIE integrator: provide explicit Euler scheme, it being 1st order accurate.

Components

Type	Visibility	Attributes		Name		Initial
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		::	registers			Number of registers used for stages.
class(integrand_object),	public,	allocatable	::	stage(:)			Stages.
integer(kind=I_P),	public		::	stages			Number of stages.

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_multistage	Assign members of integrator_multistage_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_multistage	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.

Functions

private pure function class_name(self)

Return the class name of schemes.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	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	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	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	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	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	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	intent(in)			::	self	Integrator.

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

Queried scheme.

Subroutines

private elemental subroutine destroy(self)

Destroy the integrator.

Arguments

Type	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	intent(inout)			::	self	Integrator.

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

Create the actual RK integrator: initialize the Butcher' table coefficients.

Arguments

Type	Intent	Optional		Name
class(integrator_euler_explicit),	intent(inout)		::	self	Integrator.
character(len=*),	intent(in)		::	scheme	Selected scheme.
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	Intent	Optional	Attributes		Name
class(integrator_euler_explicit),	intent(inout)			::	lhs	Left hand side.
class(integrator_object),	intent(in)			::	rhs	Right hand side.

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

Integrate field with explicit Euler scheme, 1st order.

Arguments

Type	Intent	Optional		Name
class(integrator_euler_explicit),	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.
real(kind=R_P),	intent(out),	optional	::	new_Dt	New adapted time step.

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

Integrate field with explicit Euler scheme, 1st order, fast mode.

Arguments

Type	Intent	Optional		Name
class(integrator_euler_explicit),	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.
real(kind=R_P),	intent(out),	optional	::	new_Dt	New adapted time step.

foodie_integrator_euler_explicit Module

Uses:

Note

Used By

Variables

Derived Types

type, public, extends(integrator_multistage_object) :: integrator_euler_explicit

Components

Type-Bound Procedures

Functions

private pure function class_name(self)

Arguments

Return Value character(len=99)

private elemental function has_fast_mode(self)

Arguments

Return Value logical

private elemental function is_supported(self, scheme)

Arguments

Return Value logical

private pure function supported_schemes(self) result(schemes)

Arguments

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

Subroutines

private elemental subroutine destroy(self)

Arguments

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

Arguments

private subroutine integr_assign_integr(lhs, rhs)

Arguments

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

Arguments

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

Arguments