Perturbation-based electric field integral equation for low frequency capacitive problems

Abstract

At low frequencies, the electric field integral equation (EFIE) usually breaks down when the Rao-Wilton-Glisson (RWG) basis function is employed. The physical reason is the decoupling between the electric field and magnetic field. In the integral representation of the EFIE, the electric field is decomposed into the vector potential part and the scalar potential part. When the frequency approaches zero, the vector potential part is much smaller than the scalar potential part and its contribution will be lost during the numerical process. Due to the divergence operator, the remaining scalar potential part has a null space, which makes the system matrix extremely ill-conditioned. In this work, the perturbation method is directly applied on the EFIE. We can observe that the starting term of resultant current is on the order of ω1. It means that the zeroth-order of the current has been lost during the numerical process in the original EFIE. This will lead to wrong results for plane wave scattering problems. However, for a circuit problem with capacitive surfaces, the leading term of the current is rightly aligned on the same order. Therefore, the low-frequency capacitive current at the first order of frequency can be accurately captured. Moreover, the nullspaces of the divergence operator are carefully studied, where the eigenvectors with small eigenvalue terms are not excited and the convergence of the iterative solution is ensured.