A distributed-memory hierarchical solver for general sparse linear systems

Journal Article · Wed Dec 20 04:00:00 EST 2017 · Parallel Computing

DOI:https://doi.org/10.1016/j.parco.2017.12.004· OSTI ID:1429626

Chen, Chao ^[1]; Pouransari, Hadi ^[2]; Rajamanickam, Sivasankaran ^[3]; Boman, Erik G. ^[3]; Darve, Eric ^[4]

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1. Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering
2. Stanford Univ., CA (United States). Dept. of Mechanical Engineering
3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
4. Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering and Dept. of Mechanical Engineering

We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); Stanford Univ., CA (United States)
• DOE Contract Number: AC04-94AL85000; AC02-05CH11231; NA0003525
• OSTI ID: 1429626
• Report Number(s): SAND2017--0977J; 650824
• Journal Information: Parallel Computing, Journal Name: Parallel Computing Journal Issue: C Vol. 74; ISSN 0167-8191
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Hierarchical matrix
Parallel linear solver
Sparse matrix