A highly accurate boundary integral method for the elastic obstacle scattering problem

TL;DR

This paper introduces a highly accurate boundary integral method for elastic obstacle scattering, reducing the problem to coupled integral equations and demonstrating superior numerical performance for various obstacle types.

Contribution

A novel boundary integral formulation based on Helmholtz decomposition for elastic scattering, with regularization and convergence analysis, enhancing accuracy and efficiency.

Findings

High accuracy demonstrated through numerical experiments

Effective handling of singular kernels and degenerated operators

Superior performance on smooth and nonsmooth obstacles

Abstract

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate numerical method is developed for the elastic obstacle scattering problem. More specifically, based on the Helmholtz decomposition, the model problem is reduced to a coupled boundary integral equation with singular kernels. A regularized system is constructed in order to handle the degenerated integral operators. The semi-discrete and full-discrete schemes are studied for the boundary integral system by using the trigonometric collocation method. Convergence is established for the numerical schemes in some appropriate Sobolev spaces. Numerical experiments are presented for both smooth and nonsmooth obstacles to demonstrate the superior performance of the proposed method.