DUNE PDELab (git)
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
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.
The documentation for this class was generated from the following file:
- dune/pdelab/instationary/onestepparameter.hh