Dissipation free low order convolution quadrature for TDBIE

In this paper we present a modified convolution quadrature (CQ) algorithm for the discretization of time-domain boundary integral equations as used for acoustic or electromagnetic scattering. Standard, low-order CQ schemes are strongly dissipative, especially for waves with energies at high frequencies. High-order, Runge-Kutta based schemes are much less dissipative and have proved to be very effective in applications. Still, the question remained whether the, simpler to implement, lower order methods can be improved. The modified version of low order CQ that we present in this paper is easy to implement, results in sparse matrices, and seems to require a fixed number of degrees of freedom per wavelength to achieve a fixed error. We describe the method in detail and illustrate it by numerical experiments in both 2D and 3D.