The Nystr\"{o}m method for elastic wave scattering by unbounded rough surfaces

TL;DR

This paper develops a Nyström method for simulating elastic wave scattering by unbounded rough surfaces, providing convergence analysis and numerical validation for the integral equation approach.

Contribution

It introduces a novel Nyström method tailored for elastic wave scattering on rough surfaces, with proven convergence and analysis of kernel singularities.

Findings

Method achieves accurate results in numerical experiments.

Convergence rate depends on surface smoothness.

Effective handling of boundary integral operator singularities.

Abstract

We consider the numerical algorithm for the two-dimensional time-harmonic elastic wave scattering by unbounded rough surfaces with Dirichlet boundary condition. A Nystr\"{o}m method is proposed for the scattering problem based on the integral equation method. Convergence of the Nystr\"{o}m method is established with convergence rate depending on the smoothness of the rough surfaces. In doing so, a crucial role is played by analyzing the singularities of the kernels of the relevant boundary integral operators. Numerical experiments are presented to demonstrate the effectiveness of the method.