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Title: Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients

Journal Article · · Journal of Computational and Applied Mathematics
ORCiD logo [1];  [2];  [1];  [1]
  1. King Abdullah Univ. of Science and Technology, Thuwal (Saudi Arabia)
  2. American Univ. of Beirut, Beirut (Lebanon)
+ Show Author Affiliations

We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank approximations and the cyclic reduction method. The setup and application phases of the preconditioner achieve log-linear complexity in memory footprint and number of operations, and numerical experiments exhibit good weak and strong scalability at large processor counts in a distributed memory environment. Numerical experiments with linear systems that feature symmetry and nonsymmetry, definiteness and indefiniteness, constant and variable coefficients demonstrate the preconditioner applicability and robustness. Furthermore, it is possible to control the number of iterations via the accuracy threshold of the hierarchical matrix approximations and their arithmetic operations, and the tuning of the admissibility condition parameter. Together, these parameters allow for optimization of the memory requirements and performance of the preconditioner.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1580345
Journal Information:
Journal of Computational and Applied Mathematics, Vol. 344, Issue C; ISSN 0377-0427
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 4 works
Citation information provided by
Web of Science

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Cited By (2)

Distributed-memory lattice H-matrix factorization journal January 2019
Hierarchical algorithms on hierarchical architectures
  • Keyes, D. E.; Ltaief, H.; Turkiyyah, G.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166 https://doi.org/10.1098/rsta.2019.0055
journal January 2020

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Related Subjects

97 MATHEMATICS AND COMPUTING
Preconditioning
Cyclic reduction
Hierarchical matrices