Convolution-in-time approximations of time domain boundary integral equations

We present a new temporal approximation scheme for the boundary integral formulation of time-dependent scattering problems (TDBIEs) which can be combined with either collocation or Galerkin approximation in space. It uses the ``backwards-in-time'' framework introduced in [PJ Davies and DB Duncan, submitted] with new temporal basis functions which share some properties with RBF multi-quadrics. We analyse the stability and convergence properties of the new scheme for associated Volterra integral equations, and perform extensive numerical tests for scattering from flat polygonal plates, open and closed cubes and spheres, which demonstrate effectiveness of this approach.