Transient analysis of air layer in a dielectric medium using wavelet-based implicit TDIE formulation

The interaction of a transient electromagnetic pulse with an air layer in a dielectric medium is formulated in terms of a time-domain integral equation and solved numerically via the method of moments. Application of the standard marching-on-in-time approach in this case can not yield a solution. Hence, we utilize an implicit modeling scheme, and, to reduce the computational complexity, resort to a previously proposed time-domain impedance matrix compression method. This method uses spatio-temporal wavelet basis functions to construct and solve a reduced-rank matrix equation. Furthermore, by modeling the problem simultaneously at all the time steps, we can obtain a solution which roughly has the same level of accuracy for all these times.