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Mathematics of Computation

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Iterative methods for cyclically reduced nonselfadjoint linear systems. II

Authors: Howard C. Elman and Gene H. Golub
Journal: Math. Comp. 56 (1991), 215-242
MSC: Primary 65F10; Secondary 65N22
MathSciNet review: 1052093
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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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Keywords: Linear systems, reduced system, iterative methods, convection-diffusion, non-self-adjoint
Article copyright: © Copyright 1991 American Mathematical Society

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