期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 468, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2022.111443
关键词
Compact banded system; Periodic boundary; Parallel cyclic reduction; Distributed memory; Parallel computing
资金
- National Science Foundation [NSF-OAC-2103509, ACI-1548562 [35]]
- Office of Science of the U.S. Department of Energy [DE-AC05-00OR22725 [31]]
- XSEDE resources Bridges and Comet [TG-CCR130001]
In this paper, a scalable algorithm for solving compact banded linear systems on distributed memory architectures is proposed. The algorithm reduces the communication footprint and can be applied to various types of compact banded systems.
A scalable algorithm for solving compact banded linear systems on distributed memory architectures is presented. The proposed method factorizes the original system into two levels of memory hierarchies, and solves it using parallel cyclic reduction on both distributed and shared memory. This method has a lower communication footprint across distributed memory partitions compared to conventional algorithms involving data transposes or re-partitioning. The algorithm developed in this work is generalized to cyclic compact banded systems with flexible data decompositions. For cyclic compact banded systems, the method is a direct solver with a deterministic operation and communication counts depending on the matrix size, its bandwidth, and the partition strategy. The implementation and runtime configuration details are discussed for performance opti-mization. Scalability is demonstrated on the linear solver as well as on a representative fluid mechanics application problem, in which the dominant computational cost is solving the cyclic tridiagonal linear systems of compact numerical schemes on a 3D periodic domain. The algorithm is particularly useful for solving the linear systems arising from the application of compact finite difference operators to a wide range of partial differential equation problems, such as but not limited to the numerical simulations of compressible turbulent flows, aeroacoustics, elastic-plastic wave propagation, and electromagnetics. It alleviates obstacles to their use on modern high performance computing hardware, where memory and computational power are distributed across nodes with multi-threaded processing units. (c) 2022 Elsevier Inc. All rights reserved.
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