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

Abstract

A weakly singular form of the hypersingular boundary integral equation (BIE) (traction equation) for 3-D elastic wave problems is developed in this paper. All integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements, regular quadrature and collocation procedures used for conventional BIEs are sufficient for the discretization of the original hypersingular BIE. This weakly singular form of the hypersingular BIE is applied to the composite BIE formulation which uses a linear combination of the conventional BIE and the hypersingular BIE to remove the fictitious eigenfrequencies existing in the conventional BIE formulation for elastic wave problems. Numerical examples employing different types of boundary elements clearly demonstrate the effectiveness and efficiency of the developed formulation.