76 Parallel Unstructured Mesh

The use of unstructured mesh codes on parallel machines can be one of the most e cient ways to solve large Computational Fluid Dynamics (CFD) and Computational Mechanics (CM) problems. Completely general geometries and complex behaviour can readily be modelled and, in principle, the inherent sparsity of many such problems can be exploited to obtain excellent parallel e ciencies. An important consideration, however, is the problem of distributing the mesh across the memory of the machine at runtime so that the computational load is evenly balanced and the amount of interprocessor communication is minimised. It is well known that this problem is NP complete, so in recent years much attention has been focused on developing suitable heuristics, and some powerful methods, many based on a graph corresponding to the communication requirements of the mesh, have been devised, e.g. [FS93]. Closely related to this graph partitioning problem is the problem of optimising existing mesh partitions and in this paper we discuss the partition optimisation problem and its bearing on the graph partitioning problem. In particular, the algorithms outlined in this paper are designed to address the three problems that arise in partitioning of unstructured nite element and nite volume meshes. Speci cally the: