An accurate boundary element method for the exterior elastic scattering problem in two dimensions

TL;DR

This paper develops an accurate boundary element method for solving the two-dimensional exterior elastic wave scattering problem, employing advanced regularization and series expansion techniques to improve numerical precision.

Contribution

It introduces a new computational approach using Hankel function series expansions and an accurate regularization formula for hyper-singular operators in boundary element methods.

Findings

Demonstrates high accuracy through numerical examples

Effectively computes hyper-singular boundary integrals

Improves numerical stability and efficiency

Abstract

This paper is concerned with a Galerkin boundary element method solving the two dimensional exterior elastic wave scattering problem. The original problem is first reduced to the so-called Burton-Miller (\cite{BM71}) boundary integral formulation, and essential mathematical features of its variational form are discussed. In numerical implementations, a newly-derived and analytically accurate regularization formula (\cite{YHX}) is employed for the numerical evaluation of hyper-singular boundary integral operator. A new computational approach is employed based on the series expansions of Hankel functions for the computation of weakly-singular boundary integral operators during the reduction of corresponding Galerkin equations into a discrete linear system. The effectiveness of proposed numerical methods is demonstrated using several numerical examples.