dune-pdelab 2.7-git
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Public Types | Public Member Functions | List of all members
Dune::PDELab::TimeSteppingParameterInterface< R > Class Template Referenceabstract

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

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

Inheritance diagram for Dune::PDELab::TimeSteppingParameterInterface< R >:
Inheritance graph

Public Types

typedef R RealType
 

Public Member Functions

virtual bool implicit () const =0
 Return true if method is implicit. More...
 
virtual unsigned s () const =0
 Return number of stages of the method. More...
 
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. More...
 
virtual ~TimeSteppingParameterInterface ()
 every abstract base class has a virtual destructor More...
 

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
RC++ type of the floating point parameters
Examples
recipe-operator-splitting.cc.

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