Highly accurate quadrature schemes for singular integrals in energetic BEM applied to elastodynamics

We consider an exterior linear elastodynamics problem with vanishing initial conditions and Dirichlet datum on the scatterer. We convert the Navier Equation, governing the wave behaviour, into two space–time Boundary Integral Equations (BIEs) whose solution is approximated by the energetic Boundary Element Method (BEM). To apply this technique, we have to set the BIEs in a weak form related to the energy of the differential problem solution at the final time instant of analysis. After the space–time discretization of the weak formulation, we have to deal with double space–time integrals, with a weakly singular kernel depending on primary and secondary wave speeds and multiplied by Heaviside functions. The main purpose of this work is the analysis of these peculiar integrals and the study of suitable quadrature schemes for their approximation. •Elastodynamics exterior problem is taken into account.•The solution of the related vectorial equation is approximated by energetic BEM.•The geometry of the integration domains resulting from the discretization phase is analysed in dept.•An innovative domain splitting is introduced for an efficient numerical integration.•Several numerical results are discussed.