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Title: A distributed-memory hierarchical solver for general sparse linear systems

Abstract

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.

Authors:
ORCiD logo [1];  [2];  [3];  [3]; ORCiD logo [4]
  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
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC); USDOE National Nuclear Security Administration (NNSA); Stanford Univ., CA (United States)
OSTI Identifier:
1429626
Report Number(s):
SAND2017-0977J
Journal ID: ISSN 0167-8191; 650824
DOE Contract Number:  
AC04-94AL85000; NA0002373-1; AC02-05CH11231; NA-0003525
Resource Type:
Journal Article
Journal Name:
Parallel Computing
Additional Journal Information:
Journal Volume: 74; Journal Issue: C; Journal ID: ISSN 0167-8191
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Parallel linear solver; Sparse matrix; Hierarchical matrix

Citation Formats

Chen, Chao, Pouransari, Hadi, Rajamanickam, Sivasankaran, Boman, Erik G., and Darve, Eric. A distributed-memory hierarchical solver for general sparse linear systems. United States: N. p., 2017. Web. doi:10.1016/j.parco.2017.12.004.
Chen, Chao, Pouransari, Hadi, Rajamanickam, Sivasankaran, Boman, Erik G., & Darve, Eric. A distributed-memory hierarchical solver for general sparse linear systems. United States. doi:10.1016/j.parco.2017.12.004.
Chen, Chao, Pouransari, Hadi, Rajamanickam, Sivasankaran, Boman, Erik G., and Darve, Eric. Wed . "A distributed-memory hierarchical solver for general sparse linear systems". United States. doi:10.1016/j.parco.2017.12.004. https://www.osti.gov/servlets/purl/1429626.
@article{osti_1429626,
title = {A distributed-memory hierarchical solver for general sparse linear systems},
author = {Chen, Chao and Pouransari, Hadi and Rajamanickam, Sivasankaran and Boman, Erik G. and Darve, Eric},
abstractNote = {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.},
doi = {10.1016/j.parco.2017.12.004},
journal = {Parallel Computing},
issn = {0167-8191},
number = C,
volume = 74,
place = {United States},
year = {2017},
month = {12}
}