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Simon N. Chandler-Wilde
Brunel University, UK
Title of the talk: Integral Equation Methods for
Scattering by One-Dimensional Rough Surfaces
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Abstract : We consider the Dirichlet boundary value
problem for the Helmholtz equation in a non-locally perturbed half-plane which arises in a
study of time harmonic acoustic scattering of an incident field by a sound-soft,
infinite rough sourface where the total field vanishes. We propose a second kind boundary
integral equation formulation of this problem, the novel feature of which is that it uses
a half-plane Green´s function in place of the standard free-field fundamental solution.
This has the advantage that the integral equation is well posed in the space of bounded
continuous functions in the L^p spaces, pÎ [ 1,¥ ] and the results can be obtained on
convergence of the finite section method (truncating the range of integration) and on
convergence of a banded matrix iteration algorithm. Numerical results suggest the
theoretically predicted advantages are seen in practice. |
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