Memory Management Issues in Sparse Multifrontal Methods On Multiprocessors

This article addresses the problems of memory man agement in a parallel sparse matrix factorization based on a multifrontal approach. We describe how we have adapted and modified the ideas of Duff and Reid used in a sequential symmetric multifrontal method to de sign an efficient memory management scheme for parallel sparse matrix factorization. With our solution, using the minimum size of the working area to run the multifrontal method on a multiprocessor, we can ex ploit only a part of the parallelism of the method. If we slightly increase the size of the working space, then most of the potential parallelism of the method can be exploited. We have designed a flexible memory man agement scheme which adapts well to a variation in the size of the working area and/or the number of pro cessors. General parallel applications can always be represented in terms of a computational graph, which is effectively the underlying structure of a parallel mul tifrontal method. Therefore, we believe that the tech niques presented here are useful when designing an efficient memory management scheme for a wider range of parallel applications.