Exposing Fine-Grained Parallelism in Algebraic Multigrid Methods

Algebraic multigrid methods for large, sparse linear systems are a necessity in many computational simulations, yet parallel algorithms for such solvers are generally decomposed into coarse-grained tasks suitable for distributed computers with traditional processing cores. However, accelerating mult...

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Bibliographic Details
Published in:SIAM journal on scientific computing Vol. 34; no. 4; pp. C123 - C152
Main Authors: Bell, Nathan, Dalton, Steven, Olson, Luke N.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
Subjects:
Aggregates
Algebra
Algorithms
Computation
Computer simulation
Cycles
Explicit knowledge
Exposure
Heuristic
High performance computing
Methods
Multigrid methods
Solvers
Sparsity
ISSN:1064-8275, 1095-7197
Online Access:Get full text
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Summary:Algebraic multigrid methods for large, sparse linear systems are a necessity in many computational simulations, yet parallel algorithms for such solvers are generally decomposed into coarse-grained tasks suitable for distributed computers with traditional processing cores. However, accelerating multigrid methods on massively parallel throughput-oriented processors, such as graphics processing units, demands algorithms with abundant fine-grained parallelism. In this paper, we develop a parallel algebraic multigrid method which exposes substantial fine-grained parallelism in both the construction of the multigrid hierarchy as well as the cycling or solve stage. Our algorithms are expressed in terms of scalable parallel primitives that are efficiently implemented on the GPU. The resulting solver achieves an average speedup of $1.8\times$ in the setup phase and $5.7\times$ in the cycling phase when compared to a representative CPU implementation. [PUBLICATION ABSTRACT]
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ISSN:1064-8275
1095-7197
DOI:10.1137/110838844