A space–time BIE method for 2D wave equation problems with mixed boundary conditions

In this paper we consider the 2D exterior problem for the non homogeneous wave equation, with mixed type boundary conditions and non homogeneous initial conditions, these latter having local supports. First we derive a space–time boundary integral equation formulation to solve the problem. Then we propose a numerical approach for its solution, which couples a Lubich discrete convolution quadrature with a classical collocation method. For the computation of the extra “volume” integrals generated by the initial data, having local supports, we propose a new numerical approach. Finally, we solve some test problems and present some of the numerical results we have obtained.