# Boundary integral equation methods for the elastic and thermoelastic waves in three dimensions

## TL;DR

This paper develops new regularized boundary integral equation formulations for elastic and thermoelastic wave problems in three dimensions, enabling more accurate and efficient numerical solutions using boundary element methods.

## Contribution

It introduces novel regularized formulations for hyper-singular boundary integral operators in 3D elastic and thermoelastic wave equations, simplifying numerical computations.

## Key findings

- Regularized formulations reduce singularity complexity.
- Numerical examples demonstrate high accuracy.
- Effective boundary element method implementation.

## Abstract

In this paper, we consider the boundary integral equation (BIE) method for solving the exterior Neumann boundary value problems of elastic and thermoelastic waves in three dimensions based on the Fredholm integral equations of the first kind. The innovative contribution of this work lies in the proposal of the new regularized formulations for the hyper-singular boundary integral operators (BIO) associated with the time-harmonic elastic and thermoelastic wave equations. With the help of the new regularized formulations, we only need to compute the integrals with weak singularities at most in the corresponding variational forms of the boundary integral equations. The accuracy of the regularized formulations is demonstrated through numerical examples using the Galerkin boundary element method (BEM).