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.
"On the numerical solution of the exterior elastodynamic problem by a boundary integral equation method." J. Integral Equations Applications 30 (4) 521 - 542, 2018. https://doi.org/10.1216/JIE-2018-30-4-521