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Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems. II

Howard C. Elman and Gene H. Golub
Mathematics of Computation
Vol. 56, No. 193 (Jan., 1991), pp. 215-242
DOI: 10.2307/2008538
Stable URL: http://www.jstor.org/stable/2008538
Page Count: 28
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Iterative Methods for Cyclically Reduced Non-Self-Adjoint Linear Systems. II
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Abstract

We perform an analytic and experimental study of line iterative methods for solving linear systems arising from finite difference discretizations of non-self-adjoint elliptic partial differential equations on two-dimensional domains. The methods consist of performing one step of cyclic reduction, followed by solution of the resulting reduced system by line relaxation. We augment previous analyses of one-line methods, and we derive a new convergence analysis for two-line methods, showing that both classes of methods are highly effective for solving the convection-diffusion equation. In addition, we compare the experimental performance of several variants of these methods, and we show that the methods can be implemented efficiently on parallel architectures.

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