Parallel Sparse LU Factorization with Partial Pivoting on Distributed Memory Architectures

Gaussian elimination based sparse LU factorization with partial pivoting is important to many scientiic applications, but it is still an open problem to develop a high performance sparse LU code on distributed memory machines. The main diiculty is that partial pivoting operations make structures of L and U factors unpredictable beforehand. This paper presents an approach called S for parallelizing this problem on distributed memory machines. The S approach adopts static symbolic factorization to avoid run-time control overhead, incorporates 2-D L/U supernode partitioning and amalgamation strategies to improve caching performance, and exploits irregular task parallelism embedded in sparse LU using asynchronous computation scheduling. The paper discusses and compares the algorithms using 1-D and 2-D data mapping schemes, and presents experimental studies on Cray-T3D and T3E. The performance results for a set of nonsymmetric benchmark matrices are very encouraging and S has achieved up to 6.878 GFLOPS on 128 T3E nodes.