We shall present an analysis of convolution quadrature applied to the time domain Electric Field Integral Equation arising in the electromagnetic scattering of a wave by a perfectly conducting object. Numerical results pertaining to this analysis will also be presented. In particular we verify the predicted rates of convergence, but also note a long time instability related to low frequency components of the field. Methods to overcome this instability will be described. We will also present numerical results for scattering by a penetrable dispersive and conducting scatterer that are now the subject of a theoretical investigation.
This is joint work with Q. Chen, D. Weile, and X. Wang