The parallel solution of sparse linear equations

Abstract

We discuss the solution of large sparse systems using Gaussian elimination on both local and shared memory parallel computers. There is a natural parallelism to Gaussian elimination that has been frequently exploited. We can take advantage of this parallelism in addition to that provided by the sparsity itself. We discuss this latter parallelism in some detail. We discuss an approach that exploits the parallelism due to the sparsity and that can automatically benefit also from the parallelism of Gaussian elimination. This approach, which is applicable to quite general systems, is based on a multifrontal technique. We look at the implementation of the multifrontal approach on shared memory machines and discuss its implementation on a hypercube.