An accurate time-marching solution method for the electric field integral equation using a bandlimited extrapolator

Despite their advantages in the analysis of transient electromagnetic scattering phenomena, the widespread implementation of time domain integral equation (TDIE) based methods was hampered by the fact that they tended to be unstable and computationally expensive. The recent rediscovery of TDIE based methods springs from two different sources: (i) fast methods ameliorate the computational complexity, (ii) implicit time stepping schemes make TDIE solutions stable enough for use in practical simulations (see Rao, S.M. and Wilton, D.R., 1991). Although these advances have made TDIE methods practical, the accuracy of TDIE methods remains largely unstudied. Though methods for improving the accuracy and convergence properties of the spatial discretization of TDIEs can be based on the well-known frequency domain method of moments (MoM) techniques, temporal discretization methods are still poorly understood. While exponentially convergent TDIE temporal discretization methods exist, they use basis functions that are noncausal and thus preclude the possibility of a time marching solution (see Weile, D.S. et al., 2000). We show how such methods can be modified to create a very accurate and stable time marching approach for the solution of TDIEs.