On parallel solvers for sparse triangular systems

Abstract

In this paper we describe and compare two different methods for solving general sparse triangular systems in distributed memory multiprocessor architectures. The two methods involve some preprocessing overheads so they are primarily of interest in solving many systems with the same coefficient matrix. Both algorithms start off from the idea of the classical substitution method. The first algorithm we present introduces a concept of data driven flow and makes use of non-blocking communications in order to dynamically extract the inherent parallelism of sparse systems. The second algorithm uses a reordering technique for the unknowns, so the final system can be grouped in variable blocksizes where the rows are independent and can be solved in parallel. This latter technique is called level scheduling because of the way it is represented in the adjacency graph. These methods have been tested in the Fujitsu AP1000 and the Cray T3D and T3E multicomputers. The performance has been analysed using matrices from the Harwell-Boeing collection.