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Shari Moskow's Abstract
An Approximate Method for Scattering by Thin Structures
(with F. Santosa and J. Zhang)
Scattering of waves by a thin structure is considered in this work.
Helmholtz's equation with variable coefficients models the wave
phenomena. The scatterer is assumed to have a high index of
refraction while at the same time it is very small in one of the
dimensions. We show that if the index scales as $O(1/h)$ where $h$ is
the thickness of the scatterer, then an approximate solution, based on
perturbation analysis, can be obtained. The approximate solution
consists of a leading order term plus a corrector, each of which solves an
integral equation in 2D for a 3D problem. We provide error analysis
on the approximation. The approximate method can be viewed as an
efficient computational approach since it can potentially greatly
simplify scattering calculations. Numerical results provide an assessment
of the accuracy of the approximate solution.
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