## Journal of Integral Equations and Applications

- J. Integral Equations Applications
- Volume 30, Number 4 (2018), 521-542.

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

Roman Chapko and Leonidas Mindrinos

#### 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 two-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-dependent problem to a sequence of stationary boundary value problems, which are solved by a boundary layer approach resulting in 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.

#### Article information

**Source**

J. Integral Equations Applications, Volume 30, Number 4 (2018), 521-542.

**Dates**

First available in Project Euclid: 29 November 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.jiea/1543482175

**Digital Object Identifier**

doi:10.1216/JIE-2018-30-4-521

**Mathematical Reviews number (MathSciNet)**

MR3881215

**Zentralblatt MATH identifier**

06989831

**Subjects**

Primary: 35L20: Initial-boundary value problems for second-order hyperbolic equations 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 45E05: Integral equations with kernels of Cauchy type [See also 35J15] 65N35: Spectral, collocation and related methods

**Keywords**

Elastic equation initial boundary value problem Laguerre transformation fundamental sequence single and double layer potentials boundary integral equations of the first kind trigonometrical quadrature method

#### Citation

Chapko, Roman; Mindrinos, Leonidas. On the numerical solution of the exterior elastodynamic problem by a boundary integral equation method. J. Integral Equations Applications 30 (2018), no. 4, 521--542. doi:10.1216/JIE-2018-30-4-521. https://projecteuclid.org/euclid.jiea/1543482175