The Nystr\"{o}m method for elastic wave scattering by unbounded rough surfaces
Numerical Analysis
2021-08-06 v1 Numerical Analysis
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.2108.02600,
title = {The Nystr\"{o}m method for elastic wave scattering by unbounded rough surfaces},
author = {Jianliang Li and Xiaoli Liu and Bo Zhang and Haiwen Zhang},
journal= {arXiv preprint arXiv:2108.02600},
year = {2021}
}