A Grid Solver for Reaction-Convection-Diffusion Operators1

In this paper, we present and analyze the performance of a fast parallel distributed computing time integration procedure for systems of Reaction-Convection-Diffusion equations. Typical applications include large scale computing of air quality models or population models in biology for which the main solver corresponds to a ReactionConvection-Diffusion operator. One starts from a stabilized explicit time stepping scheme analyzed by Dupros et al (Int. Journal for Numerical Methods in Fluids, 2006). The numerical efficiency and the parallel scalability of this algorithm have been demonstrated on homogeneous parallel architectures. We introduce here an additional domain decomposition component to the algorithm to extend the scalability of the method to multi-cluster architectures. The targeted computer architecture is a high latency/low bandwidth network of few parallel systems. This paper provides one of the rare examples of a Partial Differential Equation application that is both numerically efficient and scalable on a wide area network of O(10) parallel systems.