Solving sparse triangular systems on distributed memory multicomputers

The authors describe and compare two different methods for solving 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 presented 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 block sizes 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.