Parallel sparse LU factorization on different message passing platforms

Abstract

Several message passing-based parallel solvers have been developed for general (nonsymmetric) 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 µs in message latency and 100-1000 Mbytes/sec 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 interprocessor 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.

A new parallel direct solver for 2D frequency-domain modeling

“…This verifies the accuracy of BBCR solver. Secondly, the speed-up ratios of BBCR solver and MUMPS solver are compared in Fig 3. On the one hand, we can see that the MUMPS shows a poor speed up performance, which is consistent with relative research (Shen K, 2006). And it seems that the limit speed-up ratio of MUMPS for this problem is less than 2.…”

“…It can not only simulate multi-shot seismic data efficiently , but also reduce the memory requirement and computing time. However, the speed-up performance of traditional parallel sparse LU solvers, such as MUMPS (Amestoy et al, 2006;MUMPS Team 2015) and superLU, are quite poor (Shen K, 2006). Therefore, new parallel direct solver is required to get better speed-up performance.…”

A Massively Parallel Algorithm for the Approximate Calculation of Inverse p-th Roots of Large Sparse Matrices

“…For example, Van der Stappen et al [32] present an algorithm for parallel calculation of the LU decomposition on a mesh network of transputers where each processor holds a part of the matrix. Shen [31] evaluates techniques for LU decomposition distributed over nodes that are connected via slow message passing. Dongarra et al [9] demonstrate an optimized implementation of matrix inversion on a single multicore node, focusing on the minimization of synchronization between the different processing cores.…”