Hypersingular boundary integral equations for radiation and scattering of elastic waves in three dimensions (Q1309655)

This paper is an extension of the boundary integral equation (BIE) formulation developed by the authors recently for three-dimensional acoustic problems [Comput. Methods Appl. Mech. Eng. 96, No. 2, 271-287 (1992; Zbl 0754.76072)] to radiation and scattering of elastic waves. They employ the \textit{A. J. Burton} and \textit{G. F. Miller} [Proc. R. Soc. Lond., Ser. A 323, 201-210 (1971; Zbl 0235.65080)] composite BIE formulation using a linear combination of the conventional BIE and the hypersingular BIE to furnish unique solutions at all frequencies for external elastic wave problems. The authors derive systematically a weakly singular form of the hypersingular BIE before any discretization. The derived BIE are applied to time-harmonic scattering from a traction- free spherical void which is impinged upon by a plane longitudinal incident wave. Since the regularized hypersingular BIE requires the boundary density of the displacement vector to be \(C^ 1\) continuous, the authors employ \(C^ 1\) continuous elements, namely, the Overhauser elements and the non-conforming quadratic elements. Analysis of the numerical results is presented.