Partitioning and mapping for parallel nested dissection on distributed memory architectures

Abstract

In this paper, we consider the parallel implementation of a block Cholesky factorization based on a nested dissection ordering for unstructured problems. We focus on loosely coupled networks of many processors with local memory and message passing mechanism. More precisely, we study a parallel block solver associated with refined partitions from the separator partition; the aim is to find the partition corresponding to the correct granularity leading to a high quality mapping (in terms of load balancing for the processors, of average length for the routing paths, and of average edge contention on the network). Then, we propose a refinement algorithm leading to this good granularity, and we provide some numerical measurements using the mapping tool included in the ADAM environment.