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An augmented electric field integral equation for low frequency electromagnetic analysis

The surface integral equations solved by the method of moments (MoM) using the Rao-Wilton-Glisson (RWG) or roof-top basis functions are widely applied to scattering, antenna and microwave circuit problems. For the analysis of high speed interconnects, solutions are mainly expected in the full-field regime, where the electric field and magnetic field have to be simulated together to capture the equally important circuit physics and wave physics. It is a difficult regime for the conventional RWG based electric field integral equation (EFIE), because the small electrical size of the fine geometry details poses the well-known low frequency breakdown. The problem is usually remedied by employing the Helmholtz decomposition. It provides a valid solution from zero to microwave frequencies, but is burdened by the global loop search for complicated structures. In addition, the wave phenomenon across the whole structure causes the representation of loops and trees physically improper, so that the iterative solvers fail to converge.