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- W1964239095 abstract "We investigate Frechet 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 Frechet 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." @default.
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- W1964239095 date "2002-12-08" @default.
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- W1964239095 title "The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory" @default.
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- W1964239095 doi "https://doi.org/10.1098/rspa.2002.0999" @default.
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