Parallelization of Implicit-Explicit Runge-Kutta Methods for Cluster of PCs

Abstract

Several physical phenomena of great importance in science and engineering are described by large partly stiff differential systems where the stiff terms can be easily separated from the remaining terms. Implicit-Explicit Runge-Kutta (IMEXRK) methods have proven to be useful solving these systems efficiently. However, the application of these methods still requires a large computational effort and their parallel implementation constitutes a suitable way to achieve acceptable response times. In this paper, a technique to parallelize and implement efficiently IMEXRK methods on PC clusters is proposed. This technique has been used to parallelize a particular IMEXRK method and an efficient parallel implementation of the resultant scheme has been derived in a structured manner by following a component-based approach. Several numerical experiments which have been performed on a cluster of dual PCs reveal the good speedup and the satisfactory scalability of the parallel solver obtained.