Dune::PDELab::TimeSteppingParameterInterface< R > Class Template Reference

Base parameter class for time stepping scheme parameters. More...

#include <dune/pdelab/instationary/onestepparameter.hh>

Public Member Functions
virtual bool	implicit () const =0
	Return true if method is implicit.
virtual unsigned	s () const =0
	Return number of stages of the method.
virtual R	a (int r, int i) const =0
	Return entries of the A matrix. More...
virtual R	b (int r, int i) const =0
	Return entries of the B matrix. More...
virtual R	d (int r) const =0
	Return entries of the d Vector. More...
virtual std::string	name () const =0
	Return name of the scheme.
virtual	~TimeSteppingParameterInterface ()
	every abstract base class has a virtual destructor

Detailed Description

template<class R>
class Dune::PDELab::TimeSteppingParameterInterface< R >

Base parameter class for time stepping scheme parameters.

The parameters \( a,b \in \mathbb{R}^{s\times s+1} \) and \( d\in \mathbb{R}^d \) implement the generic class of time-stepping methods of Shu and Osher [1]:

\[ \begin{aligned} u_h^{(0)} &= u_h^k\\ \sum_{j=0}^s \left[ a_{ij} m_h\left(u_h^{(j)}, v; t^k + d_j\Delta t^k\right) + b_{ij}\Delta t^k r_h \left( u_h^{(j)},v,t^k+d_j\Delta t^k \right)\right] &= 0 & \forall i=1,\ldots,s \quad \forall v\in V_h(t^{k+1})\\ u_h^{k+1} &= u_h^{(s)} \end{aligned} \]

where \( m_h\) is the temporal residual form (mass operator) and \( r_h \) is the spatial residual form.

This class in particular contains Runge-Kutta and fractional step methods. A more elaborate description can be found in the PDELab tutorials (tutorial03).

[1] Chi W. Shu and Stanley Osher. Efficient implementation of essentially non- oscillatory shock-capturing schemes. J. Comput. Phys., 77:439–471

Template Parameters

R	C++ type of the floating point parameters

Examples

recipe-operator-splitting.cc.

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

• dune/pdelab/instationary/onestepparameter.hh