On the numerical solution of the elastodynamic problem by a boundary integral equation method
This work addresses the numerical solution of elastodynamic problems for exterior domains, which is relevant for wave propagation and scattering applications.
The paper proposes a numerical method for solving the Dirichlet initial boundary value problem for the elastic equation in exterior 2D domains, combining Laguerre transformation in time with boundary integral equations. Numerical results demonstrate the method's effectiveness.
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.