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Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems, Ying He

Open Access Dissertations

This dissertation focuses on the development of high-order numerical methods for acoustic and electromagnetic scattering problems, and nonlinear fluid-structure interaction problems.

For the scattering problems, two cases are considered: 1) the scattering from a doubly layered periodic structure; and 2) the scattering from doubly layered, unbounded rough surface. For both cases, we first apply the transformed field expansion (TFE) method to reduce the two-dimensional Helmholtz equation with complex scattering surface into a successive sequence of the transmission problems with a plane interface. Then, we use Fourier-Spectral method in the periodic structure problem and Hermite-Spectral method in the unbounded rough surface …