Parallel Sparse Orthogonal Factorization on Distributed-Memory Multiprocessors

Abstract

In this paper, we propose a new parallel multifrontal algorithm for the orthogonal factorization of large sparse matrices on distributed-memory multiprocessors. We explore the use of block partitioning schemes in parallel sparse orthogonal factorization. Our block-oriented parallel algorithm for sparse orthogonal factorization achieves high performance by incurring strictly less communication overhead than the conventional nonblock algorithm, maintaining relatively balanced load distribution among processors, and accelerating the parallel numerical kernel via increased cache utilization. We analyze the performance of our parallel algorithm and present its arithmetic and communication complexities for regular grid problems. We report the experimental results of an implementation of our parallel algorithm on an Intel iPSC/860 machine. Through our theoretical analysis and experimental results, we demonstrate that our new block-oriented algorithm outperforms the conventional nonblock algorithm impressively.