Optimization of mesh partitions and impact on parallel CFD

Abstract

Most of the recently proposed parallel computational fluid dynamics (CFD) algorithms stem from the divide and conquer paradigm and involve some form of domain decomposition. When the discretization is highly regular and when the number of desired subdomains is such that a regular mesh decomposition is possible (i.e., box or strip decompositions), finding an appropriate mesh partition is a trivial task. However, the problem becomes more challenging when dealing with unstructured meshes. This chapter explores a two-step procedure for partitioning a given unstructured mesh and attaining a specific objective. The chapter primarily constructs an initial partition using a fast deterministic algorithm. The initial decomposition is refined with a non-deterministic optimization algorithm to reach a specific goal. This method has proven to produce decompositions with close-to-optimal interface sizes and with a relatively low CPU overhead. The chapter concludes that the optimization step provides significantly improved partitions at a reasonable cost.