Parallel sparse LU factorization on different message passing platforms

Abstract

Several message passing-based parallel solvers have been developed for general (non-symmetric) sparse LU factorization with partial pivoting. Existing solvers were mostly deployed and evaluated on parallel computing platforms with high message passing performance (e.g., 1– 10 μ s in message latency and 100–1000 Mbytes/s in message throughput) while little attention has been paid on slower platforms. This paper investigates techniques that are specifically beneficial for LU factorization on platforms with slow message passing. In the context of the S + distributed memory solver, we find that significant reduction in the application message passing overhead can be attained at the cost of extra computation and slightly weakened numerical stability. In particular, we propose batch pivoting to make pivot selections in groups through speculative factorization, and thus substantially decrease the inter-processor synchronization granularity. We experimented on three different message passing platforms with different communication speeds. While the proposed techniques provide no performance benefit and even slightly weaken numerical stability on an IBM Regatta multiprocessor with fast message passing, they improve the performance of our test matrices by 15–460% on an Ethernet-connected 16-node PC cluster. Given the different tradeoffs of communication-reduction techniques on different message passing platforms, we also propose a sampling-based runtime application adaptation approach that automatically determines whether these techniques should be employed for a given platform and input matrix.