Performance of a fully parallel sparse solver

The performance of a fully parallel direct solver for large sparse symmetric positive definite systems of linear equations is demonstrated. The solver is designed for distributed-memory message-passing parallel computer systems, particularly massively parallel machines. All phases of the computation, including symbolic processing as well as numeric factorization and triangular solution, are performed in parallel. A parallel Cartesian nested dissection algorithm is used to compute a fill-reducing ordering for the matrix and an appropriate partitioning of the problem across the processors. The separator tree resulting from nested dissection is used to identify and exploit large-grain parallelism in the remaining steps of the computation. The parallel performance of the solver is reported for a series of test problems on the Thinking Machines CM-5. The parallel efficiency and scalability of the solver, as well as the relative importance of the various phases of the computation, are investigated empirically