A Matrix-Free Conjugate Gradient Method for Cluster Computing

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http://hdl.handle.net/11603/39789

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UMBC Mathematics and Statistics Department
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https://orcid.org/0000-0003-1745-2292

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2003-02-01

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journal articles
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Abstract

The conjugate gradient method is applied to a large, sparse, highly structured linear system of equations obtained from a finite difference discretization of the Poisson equation. The matrix-free implementation of the matrix-vector product is shown to be optimal with respect to both memory usage and performance. The parallel implementation of the method can give excellent performance on a cluster of workstations, with the optimal number of processors depending on the quality of the interconnect hardware. This justifies the use of the method as computational kernel for the time-stepping in a system of reaction-diffusion equations.