Analytical integrations for the approximation of 3D hyperbolic scalar boundary integral equations

The present note deals with 3D hyperbolic scalar problems modeled by integral equations [1]. It aims at showing analytical integrations for collocation in time [2] as well as “variational” [3] approximation schemes. Numerical solution is achieved adopting polynomial shape functions of arbitrary degree (in space and time) on a trapezoidal flat tiling of a polygonal domain. Analytical integrations are performed both in space and time for Lebesgue integrals, working in a local coordinate system. For singular integrals, both a limit to the boundary as well as the finite part of Hadamard approach have been pursued. Outcomes and computational issues are presented. Extension to elastodynamics will be the subject of forthcoming publications.