Accessibility navigation


The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

Chandler-Wilde, S. N. and Potthast, R. (2002) The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 458 (2028). pp. 2967-3001. ISSN 1471-2946

Full text not archived in this repository.

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1098/rspa.2002.0999

Abstract/Summary

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:32644
Publisher:Royal Society Publishing

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation