A space–time BIE method for nonhomogeneous exterior wave equation problems. The Dirichlet case

Abstract

    To the memory of James N. Lyness

In this paper we consider the (two-dimensional and three-dimensional) exterior problem for the nonhomogeneous wave equation, with a Dirichlet boundary condition and nonhomogeneous initial conditions. First, we derive two alternative boundary integral equation formulations to solve the problem. Then we propose a numerical approach for the computation of the extra ‘volume’ integrals generated by the initial data and the equation known term. To show the efficiency of this approach we solve some test problems by applying a second-order Lubich discrete convolution quadrature for the discretization of the time integral, coupled with a classical collocation boundary element method. Some conclusions are finally drawn.

wave equation, nonhomogeneous conditions, space–time boundary integral equations, numerical methods