Chapter 1 Performance evaluation of the parallel multifrontal method in a distributed memory environment

We study, using analytic models and simulation, the performance of the multifrontal methods on distributed memory architectures. We focus on a particular strategy for partitioning, clustering, and mapping of task nodes to processors in order to minimize the overall parallel execution time and minimize communication costs. The performance model has been used to obtain estimates for the speedups of various engineering and scientific problems, on several distributed architectures. 1 Problem Statement There have been various efforts directed at solving large sparse systems using direct solvers on distributed memory architectures (see [3] for a survey). One of the difficulties involved in the distributed implementation of some direct solvers, such as the multifrontal method [2], is that the irregular sparse structure of the matrices makes it difficult to partition and map the sparse matrix to a distributed architecture in a way that minimizes communication costs and minimizes the total exe..