High-order integral equation methods for high-frequency rough surface scattering applications.

摘要

In this thesis, a new numerical scheme is introduced for three-dimensional acoustic and electromagnetic rough-surface scattering simulations that can deliver highly accurate results from low to high frequencies at a cost that is independent of the wavelength of the incoming radiation. The method is based on high-order asymptotic expansions of the oscillatory integrals that enter potential theoretic formulations of the scattering problems in the high-frequency regime, in a manner that bypasses the need to resolve the fields on the scale of the wavelength of radiation. Indeed, the solutions of the integral equations (e.g. the normal velocity in acoustics and the current in electromagnetics) are sought in the form of slow modulations of highly oscillatory exponentials of known phases, and series expansions in inverse powers of the wavenumber are chosen to represent the unknown slowly varying envelopes. As shown, this framework can be made to yield an efficiently computable recursion for the terms of the series to any arbitrary order. The resulting algorithms generally provide a very significant improvement over classical (e.g. Kirchhoff's) approximations in both accuracy and applicability and they can, in fact, efficiently produce results with full double-precision accuracy for configurations of practical interest, including rough surfaces that exhibit composite roughness.