A Higher Order Hierarchical Solution to the Time-Domain Electric Field Integral Equation for Thin-Wire Antennas

In this paper, a new time-domain integral equation solution method for arbitrarily shaped, perfectly conducting thin-wire antennas is presented. The space-time discretization of the circumferentially invariant electric current along the wire axis is achieved by employing higher order hierarchical polynomials for the spatial basis functions and discretely causal piecewise polynomial interpolation functions for the temporal basis functions. The solution of the transient current along the wire is obtained by marching-on-in-time (MOT). The hierarchical nature of the spatial basis functions enables the efficient assembly of the space-time impedance matrices. Rigorous evaluation of the time-domain wire kernels is presented. Numerical test cases demonstrate the validity, accuracy, and applicability of the new method.