2 research outputs found
A combined fractional step domain decomposition method for the numerical integration of parabolic problems
In this paper we develop parallel numerical algorithms to
solve linear time dependent coefficient parabolic problems. Such methods
are obtained by means of two consecutive discretization procedures.
Firstly, we realize a time integration of the original problem using a
Fractional Step Runge Kutta method which provides a family of elliptic
boundary value problems on certain subdomains of the original domain.
Next, we discretize those elliptic problems by means of standard techniques.
Using this framework, the numerical solution is obtained by solving,
at each stage, a set of uncoupled linear systems of low dimension.
Comparing these algorithms with the classical domain decomposition
methods for parabolic problems, we obtain a reduction of computational
cost because of, in this case, no Schwarz iterations are required. We give
an unconditional convergence result for the totally discrete scheme and
we include two numerical examples that show the behaviour of the proposed
method.This research is partially supported by the MCYT research project num. BFM2000-0803 and the research project resolution 134/2002 of Government of Navarra
Error Analysis of Explicit Partitioned Runge-Kutta Schemes for Conservation Laws
An error analysis is presented for explicit partitioned Runge-Kutta methods and multirate methods applied to conservation laws. The interfaces, across which different methods or time steps are used, lead to order reduction of the schemes. Along with cell-based decompositions, also flux-based decompositions are studied. In the latter case mass conservation is guaranteed, but it will be seen that the accuracy may deteriorate