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Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation

✍ Scribed by L. Marin; L. Elliott; P. J. Heggs; D. B. Ingham; D. Lesnic; X. Wen

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
192 KB
Volume
60
Category
Article
ISSN
0029-5981

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✦ Synopsis

Abstract

In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping criteria are developed and the convergence, as well as the stability, of the numerical methods proposed are analysed. The Cauchy problem for the Helmholtz equation can be regularized by various methods, such as the general regularization methods presented in this paper, but more accurate results are obtained by classical methods, such as the singular value decomposition and the Tikhonov regularization methods. Copyright © 2004 John Wiley & Sons, Ltd.

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