Volume 6, pp. 162-181, 1997.

Wave-ray multigrid method for standing wave equations

A. Brandt and I. Livshits

Abstract

Multigrid methods are known for their high efficiency in the solution of definite elliptic problems. However, difficulties that appear in highly indefinite problems, such as standing wave equations, cause a total loss of efficiency in the standard multigrid solver. The aim of this paper is to isolate these difficulties, analyze them, suggest how to deal with them, and then test the suggestions with numerical experiments. The modified multigrid methods introduced here exhibit the same high convergence rates as usually obtained for definite elliptic problems, for nearly the same cost. They also yield a very efficient treatment of the radiation boundary conditions.

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Key words

Helmholtz equations, multigrid methods, wave-ray approach, radiation boundary conditions.

AMS subject classifications

65N55, 65N06, 65N22, 65B99.

ETNA articles which cite this article

Vol. 6 (1997), pp. 1-34 Achi Brandt: The Gauss Center research in multiscale scientific computation
Vol. 10 (2000), pp. 1-20 Achi Brandt: General highly accurate algebraic coarsening
Vol. 13 (2002), pp. 81-105 Thomas Huckle and Jochen Staudacher: Multigrid preconditioning and Toeplitz matrices

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