# On the numerical solution of the elastodynamic problem by a boundary integral equation method

## TL;DR

This paper introduces a numerical boundary integral method combining Laguerre transformation and quadrature for solving elastodynamic problems in unbounded 2D regions, demonstrated through numerical results.

## Contribution

It presents a novel approach that reduces time-dependent elastodynamic problems to stationary boundary value problems using Laguerre transformation, solved via boundary integral equations.

## Key findings

- Effective numerical solution for elastodynamic problems
- Reduction of time-dependent problems to stationary boundary problems
- Numerical results validate the method's accuracy

## Abstract

A numerical method for the Dirichlet initial boundary value problem for the elastic equation in the exterior and unbounded region of a smooth closed simply connected 2-dimensional domain, is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and a boundary integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the time-depended problem to a sequence of stationary boundary value problems, which are solved by a boundary layer approach resulting to a sequence of boundary integral equations of the first kind. The numerical discretization and solution are obtained by a trigonometrical quadrature method. Numerical results are included.