Fourier analysis of multigrid-type iterative methods
Experiments indicate that a multigrid-type cycle can be used as an efficient preconditioner in the iterative solution of the discrete problem corresponding to a singularly perturbed elliptic boundary-value problem. Motivated by a report of Goldstein, the author explores the theoretical basis for the efficiency of such a preconditioner when applied to a model problem. The techniques developed are also used to analyze a multigrid V-cycle when used alone as a fast iterative solver. The solution of the one-dimensional indefinite Helmholtz problem using standard multigrid V-cycles is considered. By analyzing various choices of projection, interpolation, smoothers, and coarse-grid operators, a particular combination is found that preserves typical multigrid efficiency even in this indefinite case.
- Research Organization:
- Wisconsin Univ., Madison (USA)
- OSTI ID:
- 6984743
- Country of Publication:
- United States
- Language:
- English
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