4 research outputs found
Embedded pairs of fractional step Runge-Kutta methods and improved domain decomposition techniques for parabolic problems
In this paper we design and apply new embedded pairs of Frac-
tional Step Runge-Kutta methods to the e±cient solution of multidimensional
parabolic problems. These time integrators are combined with a suitable split-
ting of the elliptic operator subordinated to a decomposition of the spatial
domain and a standard spatial discretization. With this technique we ob-
tain parallel algorithms which have the main advantages of classical domain
decomposition methods and, besides, avoid iterative processes like Schwarz
iterations, typical of them. The use of these embedded methods permits a
fast variable step time integration process.This research is partially supported by the MEC research project num. MTM2004-05221
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