An Algebraic Interpretation of Multigrid Methods

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1982 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Numerical Analysis, volume 19, pages 548-560 (issn: 0036-1429, eissn: 1095-7170,

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Authors: McCormick, S. F.;

doi: 10.1137/0719036

An Algebraic Interpretation of Multigrid Methods

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Abstract

The main objective of this paper is to treat the correction cycle of multigrid as a Newton-like method and to analyze it together with relaxation via a natural decomposition of the grid function space. The purpose is to provide a simplified view of multigrid and motivate some general principles for algorithm design.

Keywords

coarse grid correction, Iterative numerical methods for linear systems, Boundary value problems for second-order elliptic equations, relaxation, algebraic interpretation, multigrid methods, correction cycle, Numerical solution of discretized equations for boundary value problems involving PDEs

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