dg::mat::ConvertsToFunctionalButcherTableau< real_type > Struct Template Reference

Convert identifiers to their corresponding dg::mat::FunctionalButcherTableau. More...

Public Types
using	value_type = real_type

Public Member Functions
	ConvertsToFunctionalButcherTableau (FunctionalButcherTableau< real_type > tableau)
	ConvertsToFunctionalButcherTableau (enum tableau_identifier id)
	Create FunctionalButcherTableau from dg::mat::func_tableau_identifier.
	ConvertsToFunctionalButcherTableau (std::string name)
	Create FunctionalButcherTableau from its name (very useful)
	ConvertsToFunctionalButcherTableau (const char *name)
	Create FunctionalButcherTableau from its name (very useful)
	operator FunctionalButcherTableau< real_type > () const

Detailed Description

template<class real_type>
struct dg::mat::ConvertsToFunctionalButcherTableau< real_type >

Convert identifiers to their corresponding dg::mat::FunctionalButcherTableau.

This is a helper class to simplify the interfaces of our timestepper functions and classes. The sole purpose is to implicitly convert either a FunctionalButcherTableau or one of the following identifiers to an instance of a FunctionalButcherTableau.

We follow the naming convention of the ARKode library https://sundials.readthedocs.io/en/latest/arkode/Butcher_link.html (They also provide nice stability plots for their methods) as NAME-S-P-Q or NAME-S-Q, where

• NAME is the author or name of the method
• S is the number of stages in the method
• P is the global order of the embedding
• Q is the global order of the method

Name	Identifier	Description
Euler	dg::mat::EXPLICIT_EULER_1_1	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Midpoint-2-2	dg::mat::MIDPOINT_2_2	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Runge-Kutta-4-4	dg::mat::CLASSIC_4_4	Cox and Matthews, J. Comput. Phys., 176 (2002)
Hochbruck-3-3-4	dg::mat::HOCHBRUCK_3_3_4	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010) (The exprb43 method)

Note

In exponential Rosenbrock type schemes it is assumed that \( A\) (the matrix) is the Jacobian of the system. If it is not, then the order conditions are different and the order and embedded orders are not what is indicated in our names.

Parameters

real_type

The type of the coefficients in the FunctionalButcherTableau

Member Typedef Documentation

value_type

template<class real_type >

using dg::mat::ConvertsToFunctionalButcherTableau< real_type >::value_type = real_type

Constructor & Destructor Documentation

ConvertsToFunctionalButcherTableau() [1/4]

template<class real_type >

dg::mat::ConvertsToFunctionalButcherTableau< real_type >::ConvertsToFunctionalButcherTableau ( FunctionalButcherTableau< real_type > tableau )

inline

Of course a FunctionalButcherTableau converts to a FunctionalButcherTableau Useful if you constructed your very own coefficients

ConvertsToFunctionalButcherTableau() [2/4]

template<class real_type >

dg::mat::ConvertsToFunctionalButcherTableau< real_type >::ConvertsToFunctionalButcherTableau ( enum tableau_identifier id )

inline

Create FunctionalButcherTableau from dg::mat::func_tableau_identifier.

The use of this constructor might be a bit awkward because you'll have to write all caps.

Parameters

id	the identifier, for example dg::mat::RUNGE_KUTTA_4_4

ConvertsToFunctionalButcherTableau() [3/4]

template<class real_type >

dg::mat::ConvertsToFunctionalButcherTableau< real_type >::ConvertsToFunctionalButcherTableau ( std::string name )

inline

Create FunctionalButcherTableau from its name (very useful)

Note

In some of the links in the Description below you might want to use the search function of your browser to find the indicated method

Explicit methods

We follow the naming convention of the ARKode library https://sundials.readthedocs.io/en/latest/arkode/Butcher_link.html (They also provide nice stability plots for their methods) as NAME-S-P-Q or NAME-S-Q, where

• NAME is the author or name of the method
• S is the number of stages in the method
• P is the global order of the embedding
• Q is the global order of the method

Name	Identifier	Description
Euler	dg::mat::EXPLICIT_EULER_1_1	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Midpoint-2-2	dg::mat::MIDPOINT_2_2	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Runge-Kutta-4-4	dg::mat::CLASSIC_4_4	Cox and Matthews, J. Comput. Phys., 176 (2002)
Hochbruck-3-3-4	dg::mat::HOCHBRUCK_3_3_4	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010) (The exprb43 method)

Note

In exponential Rosenbrock type schemes it is assumed that \( A\) (the matrix) is the Jacobian of the system. If it is not, then the order conditions are different and the order and embedded orders are not what is indicated in our names.

Parameters

name	The name of the tableau as stated in the Name column above, as a string, for example "Euler"

ConvertsToFunctionalButcherTableau() [4/4]

template<class real_type >

dg::mat::ConvertsToFunctionalButcherTableau< real_type >::ConvertsToFunctionalButcherTableau ( const char * name )

inline

Create FunctionalButcherTableau from its name (very useful)

Note

In some of the links in the Description below you might want to use the search function of your browser to find the indicated method

Explicit methods

We follow the naming convention of the ARKode library https://sundials.readthedocs.io/en/latest/arkode/Butcher_link.html (They also provide nice stability plots for their methods) as NAME-S-P-Q or NAME-S-Q, where

• NAME is the author or name of the method
• S is the number of stages in the method
• P is the global order of the embedding
• Q is the global order of the method

Name	Identifier	Description
Euler	dg::mat::EXPLICIT_EULER_1_1	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Midpoint-2-2	dg::mat::MIDPOINT_2_2	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010)
Runge-Kutta-4-4	dg::mat::CLASSIC_4_4	Cox and Matthews, J. Comput. Phys., 176 (2002)
Hochbruck-3-3-4	dg::mat::HOCHBRUCK_3_3_4	Hochbruck and Ostermann, Exponential Integrators, Acta Numerica (2010) (The exprb43 method)

Note

In exponential Rosenbrock type schemes it is assumed that \( A\) (the matrix) is the Jacobian of the system. If it is not, then the order conditions are different and the order and embedded orders are not what is indicated in our names.

Parameters

name	The name of the tableau as stated in the Name column above, as a string, for example "Euler"

Member Function Documentation

operator FunctionalButcherTableau< real_type >()

template<class real_type >

dg::mat::ConvertsToFunctionalButcherTableau< real_type >::operator FunctionalButcherTableau< real_type > ( ) const

inline

Convert to FunctionalButcherTableau

which means an object can be directly assigned to a FunctionalButcherTableau

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The documentation for this struct was generated from the following file:

• tableau.h