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A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces

Meier, A., Arens, T., Chandler-Wilde, S. N. and Kirsch, A. (2000) A Nyström method for a class of integral equations on the real line with applications to scattering by diffraction gratings and rough surfaces. Journal of Integral Equations and Applications, 12 (3). pp. 281-321. ISSN 1938-2626

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To link to this item DOI: 10.1216/jiea/1020282209

Abstract/Summary

We propose a Nystr¨om/product integration method for a class of second kind integral equations on the real line which arise in problems of two-dimensional scalar and elastic wave scattering by unbounded surfaces. Stability and convergence of the method is established with convergence rates dependent on the smoothness of components of the kernel. The method is applied to the problem of acoustic scattering by a sound soft one-dimensional surface which is the graph of a function f, and superalgebraic convergence is established in the case when f is infinitely smooth. Numerical results are presented illustrating this behavior for the case when f is periodic (the diffraction grating case). The Nystr¨om method for this problem is stable and convergent uniformly with respect to the period of the grating, in contrast to standard integral equation methods for diffraction gratings which fail at a countable set of grating periods.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:32646
Publisher:Rocky Mountain Mathematics Consortium

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