A distributed-memory hierarchical solver for general sparse linear systems
[1];
[4]
- Stanford Univ., CA (United States). Inst. for Computational and Mathematical Engineering
- Stanford Univ., CA (United States). Dept. of Mechanical Engineering
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
- 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 Lab. (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; NA0002373-1; AC02-05CH11231; NA-0003525
- OSTI ID:
- 1429626
- Report Number(s):
- SAND2017-0977J; 650824
- Journal Information:
- Parallel Computing, Vol. 74, Issue C; ISSN 0167-8191
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
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