Calderón preconditioned time-domain integral equation solvers

Marching on in time MOT-based electric field integral equation (EFIE) solvers represent an increasingly appealing avenue for analyzing electromagnetic transients on multiscale and geometrically complex circuits and antennas. Unfortunately, time-domain EFIEs discretized via marching on in time (MOT) recipes suffer from a dense-grid breakdown phenomenon whenever the time step becomes large compared to the spatial grid size. This breakdown phenomenon manifests itself in the form of ill- conditioned MOT matrices and slow convergence rates of the MOT iterative solver. The time-domain breakdown phenomenon has a direct frequency domain counterpart: frequency domain EFIEs discretized via the method of moments result in ill-conditioned matrices when the spatial grid size is small compared to the wavelength. In this paper, a preconditioner for the time-domain EFIE is developed that gives rise to an accurate stable system after discretization. To this end, the Calderon preconditioned time-domain EFIE is discretized using Buffa-Christiansen basis functions. Numerical results that demonstrate the performance of the new analytical preconditioner are presented.