Ecient Mesh Partitioning for Parallel P.d.e. Solvers on Distributed Memory Machines Extended Version of the Paper Which Appears in the Proceedings of the Sixth Siam Conference on Parallel Processing for Scientic Computing

When solving a partial dierential equation on a MIMD distributed memory computer there arises the problem of distributing the mesh so that the communication requirement of the numerical solver is minimised subject to a load balancing constraint. In this paper we introduce a new algorithm for this partitioning problem for unstructured meshes and study its properties, along with those of other common strategies. In particular we consider the eects of dierent partitions on a parallel nite element solver and analyse the trade-o which exists between obtaining very good partitions at a high computational cost and obtaining poorer partitions but far more cheaply.