Scattering of elastic waves on a heterogeneous inclusion of arbitrary shape: An efficient numerical method for 3D-problems

The problem of scattering of plane monochromatic elastic waves on an isolated heterogeneous inclusion of arbitrary shape is considered. Volume integral equations for elastic displacements in heterogeneous media are used for reducing this problem to the region occupied by the inclusion. Discretization of this equation is carried out by Gaussian approximating functions. For such functions, the elements of the matrix of the discretized problem are calculated in explicit analytical forms. For regular grids of approximating nodes, the matrix of the discretized problem has the Toeplitz properties, and the matrix–vector products can be calculated by the Fast Fourier Transform technique. The latter strongly accelerates the process of the iterative solution of the discretized problem. Elastic displacements and differential cross-sections of a homogeneous spherical inclusion are calculated for longitudinal and transversal incident waves of various wave lengths. The numerical results are compared with exact solutions. The displacement fields and differential cross-sections of a cylindrical inclusion are calculated for incident fields of different directions with respect to the cylinder axis.

► Monochromatic elastic wave scattering on a heterogeneous inclusion is considered. ► Volume integral equations for the wave field inside the inclusion are used. ► Gaussian functions are applied for discretization of the integral equations. ► Fast Fourier Transform is employed for the solution of the discretized problem. ► Exact and numerical solutions are compared for a spherical inclusion.