A distributed-memory hierarchical solver for general sparse linear systems

•Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general sparse linear systems based on data decomposition.•Implemented a task-based asynchronous scheme by exploiting data dependency in our algorithm....

Full description

Saved in:
Bibliographic Details
Published in:Parallel computing Vol. 74; no. C; pp. 49 - 64
Main Authors: Chen, Chao, Pouransari, Hadi, Rajamanickam, Sivasankaran, Boman, Erik G., Darve, Eric
Format: Journal Article
Language:English
Published: United States Elsevier B.V 01.05.2018
Elsevier
Subjects:
Hierarchical matrix
MATHEMATICS AND COMPUTING
Parallel linear solver
Sparse matrix
Parallel linear solver
Sparse matrix
Hierarchical matrix
ISSN:0167-8191, 1872-7336
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general sparse linear systems based on data decomposition.•Implemented a task-based asynchronous scheme by exploiting data dependency in our algorithm.•Implemented a coloring scheme to extract concurrency in the execution.•Provided benchmarks for various problems and analysis of parallel scalability under different conditions. 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 present various numerical results to demonstrate the versatility and scalability of the parallel algorithm.
Bibliography:AC04-94AL85000; NA0002373-1; AC02-05CH11231; NA-0003525
USDOE Office of Science (SC)
USDOE National Nuclear Security Administration (NNSA)
Stanford Univ., CA (United States)
SAND2017-0977J
ISSN:0167-8191
1872-7336
DOI:10.1016/j.parco.2017.12.004