Sparse Approximate Multifrontal Factorization with Composite Compression Methods

Claus, Lisa; Ghysels, Pieter; Liu, Yang; Nhan, Thái Anh; Thirumalaisamy, Ramakrishnan; Bhalla, Amneet Singh; Li, Sherry

doi:10.1145/3611662

Sparse Approximate Multifrontal Factorization with Composite Compression Methods

Journal Article · Tue Sep 19 00:00:00 EDT 2023 · ACM Transactions on Mathematical Software

DOI:https://doi.org/10.1145/3611662· OSTI ID:2281210

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Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Santa Clara University, CA (United States)
San Diego State University, CA (United States)

This article presents a fast and approximate multifrontal solver for large sparse linear systems. In a recent work by Liu et al., we showed the efficiency of a multifrontal solver leveraging the butterfly algorithm and its hierarchical matrix extension, HODBF (hierarchical off-diagonal butterfly) compression to compress large frontal matrices. The resulting multifrontal solver can attain quasi-linear computation and memory complexity when applied to sparse linear systems arising from spatial discretization of high-frequency wave equations. To further reduce the overall number of operations and especially the factorization memory usage to scale to larger problem sizes, in this article we develop a composite multifrontal solver that employs the HODBF format for large-sized fronts, a reduced-memory version of the nonhierarchical block low-rank format for medium-sized fronts, and a lossy compression format for small-sized fronts. This allows us to solve sparse linear systems of dimension up to 2.7 × larger than before and leads to a memory consumption that is reduced by 70% while ensuring the same execution time. The code is made publicly available in GitHub.

View Accepted Manuscript (DOE)

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Basic Energy Sciences (BES). Scientific User Facilities (SUF)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 2281210

Journal Information:: ACM Transactions on Mathematical Software, Journal Name: ACM Transactions on Mathematical Software Journal Issue: 3 Vol. 49; ISSN 0098-3500

Publisher:: Association for Computing MachineryCopyright Statement

Country of Publication:: United States

Language:: English

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