Journal of Integral Equations and Applications

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

Roman Chapko and Leonidas Mindrinos

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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


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References

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Journal of Integral Equations and Applications

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