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This paper is concerned with the direct and inverse acoustic orelectromagnetic scattering problems by a locally perturbed, perfectlyreflecting, infinite plane (which is called a locally rough surface in thispaper). We propose a novel integral equation formulation for the directscattering problem which is defined on a bounded curve (consisting of a boundedpart of the infinite plane containing the local perturbation and the lower partof a circle) with two corners. This novel integral equation can be solvedefficiently by using the Nystrom method with a graded mesh introducedpreviously by Kress and is capable of dealing with large wavenumber cases. Forthe inverse problem, we propose a Newton iteration method to reconstruct thelocal perturbation of the plane from multiple frequency far-field data, basedon the novel integral equation formulation. Numerical examples are carried outto demonstrate that our reconstruction method is stable and accurate even forthe case of multiple-scale profiles.

A novel integral equation for scattering by locally rough surfaces and application to the inverse problem