Elastic scattering from rough surfaces in three dimensions

Hu, Guanghui; Li, Peijun; Zhao, Yue

doi:10.1016/j.jde.2020.03.022

Cited by 3 publications

(1 citation statement)

References 37 publications

(82 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The paper [23] extends the method in [4] to the scattering by finite height inhomogeneous layer with the Nuemann and generarized impedance boundary boundary. The papers [18,19,21,26,22] also consider the scattering by electromagnetic and elastic waves.…”

Section: Introductionmentioning

confidence: 99%

A Nyström method for scattering by a two-layered medium with a rough boundary

Liu¹,

Li²,

Yang³

et al. 2023

Preprint

View full text Add to dashboard Cite

This paper presents a study on the integral equation method and the Nystöm method for the scattering of time-harmonic acoustic waves by a two-layered medium with an unbounded perturbed boundary. The medium consists of two layers separated by a plane interface, for which we assume transmission boundary conditions. We assume either Dirichlet or impedance boundary conditions for the rough surface boundary. Unlike classical rough surface scattering problems, the presence of a plane interface makes it difficult to establish the well-posedness of the scattering problem and to find a numerical treatment. We introduce the two-layered Green function and prove that this function has similar asymptotic decay properties to the half-space Green function. By using a similar approach to classical rough surface problems, we establish the uniqueness of the scattering problem. We derive the integral equation formulations using the two-layered Green function as the integral kernel and use them to prove the existence of the scattering problem. Furthermore, we propose the Nystöm method for discretizing the integral equations and establish its convergence. Finally, we perform numerical experiments to demonstrate the effectiveness of the Nystöm method.

show abstract