On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

A. Meier; S. N. Chandler‐Wilde

doi:10.1002/mma.210

journal article Feb 08, 2001

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

A. Meier S. N. Chandler‐Wilde

Mathematical Methods in the Applied Sciences Vol. 24 No. 4 pp. 209-232 · Wiley

View at Publisher Save 10.1002/mma.210

Abstract

AbstractWe consider the Dirichlet and Robin boundary value problems for the Helmholtz equation in a non‐locally perturbed half‐plane, modelling time harmonic acoustic scattering of an incident field by, respectively, sound‐soft and impedance infinite rough surfaces.Recently proposed novel boundary integral equation formulations of these problems are discussed. It is usual in practical computations to truncate the infinite rough surface, solving a boundary integral equation on a finite section of the boundary, of length 2A, say. In the case of surfaces of small amplitude and slope we prove the stability and convergence as A→∞ of this approximation procedure. For surfaces of arbitrarily large amplitude and/or surface slope we prove stability and convergence of a modified finite section procedure in which the truncated boundary is ‘flattened’ in finite neighbourhoods of its two endpoints. Copyright © 2001 John Wiley & Sons, Ltd.

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Details

Published: Feb 08, 2001
Vol/Issue: 24(4)
Pages: 209-232
License: View

Authors

Cite This Article

A. Meier, S. N. Chandler‐Wilde (2001). On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering. Mathematical Methods in the Applied Sciences, 24(4), 209-232. https://doi.org/10.1002/mma.210

On the stability and convergence of the finite section method for integral equation formulations of rough surface scattering

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