A spectral boundary integral method for the elastic obstacle scattering problem in three dimensions

TL;DR

This paper introduces a spectral boundary integral method for solving elastic obstacle scattering problems in three dimensions, combining Helmholtz decomposition with a novel integral equation formulation.

Contribution

The paper develops a new spectral boundary integral approach for elastic scattering, improving computational efficiency and accuracy in 3D elastic obstacle problems.

Findings

Demonstrates high accuracy of the spectral method through numerical experiments

Shows superior computational performance compared to traditional methods

Validates the approach for complex obstacle geometries

Abstract

In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a coupled boundary value problem for the Helmholtz and Maxwell equations. A novel system of boundary integral equations is formulated and a spectral boundary integral method is developed for the coupled boundary value problem. Numerical experiments are presented to demonstrate the superior performance of the proposed method.