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On the numerical solution of the exterior elastodynamic problem by a boundary integral equation method. (English) Zbl 1408.65093

Summary: 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.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
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
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
65D32 Numerical quadrature and cubature formulas
74S15 Boundary element methods applied to problems in solid mechanics
65R20 Numerical methods for integral equations
35Q70 PDEs in connection with mechanics of particles and systems of particles
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References:

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