Characteristic Mode Analysis Based on Rayleigh Quotient Iteration

Abstract

For radiation and scattering problems, characteristic mode analysis (CMA) can provide intuitively physical insight. Generally, eigenpairs (eigenvalue/eigenvectors) for CMA are computed discretely at each frequency and then assigned to corresponding modes within the investigated frequency range using tracking algorithms. These two-stage mode processing methods have low efficiency and can run into problems, including mode discontinuity and inappropriate crossing avoidance handling. Intrinsically, the Rayleigh quotient iteration (RQI)-based algorithm proposed in this article can simultaneously achieve CMA’s mode tracking and eigenpair calculation. Compared to traditional techniques, the tracking efficiency is enhanced with third-order convergence since the number of examined modes calculated by RQI is far fewer than the number of eigenpairs solved by the impedance matrix. In addition, together with the von Neumann–Wigner theorem, the enhanced RQI can detect mode overlap and undesired switching caused by crossing avoidance and correct them on the spot without increasing the computational cost.