Solution of a time-domain magnetic-field integral equation for arbitrarily closed conducting bodies using an unconditionally stable methodology

In this work, we present a new and efficient numerical method to obtain an unconditionally stable solution for the time-domain magnetic-field integral equation (TD-MFIE) for arbitrarily closed conducting bodies. This novel method does not utilize the customary marching-on-in-time (MOT) solution method often used to solve a hyperbolic partial-differential equation. Instead, we solve the wave equation by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives in the TD-MFIE formulation can be handled analytically. Since these weighted Laguerre polynomials converge to zero as time progresses, the electric surface currents also converge to zero when expanded in a series of weighted Laguerre polynomials. In order to solve the wave equation, we introduce two separate testing procedures: spatial and temporal testing. By introducing the temporal testing procedure first, the marching-on in time procedure is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials. The other novelty of this approach is that through the use of the entire domain Laguerre polynomials for the expansion of the temporal variation of the currents, the spatial and the temporal variables can be separated. To verify our method, we do a comparison with the results of an inverse Fourier transform of a frequency domain MFIE.