High-order quasi-curl conforming functions for multiplicative Calderón preconditioning of the EFIE

Method of moments (MoM)-based electric field integral equation (EFIE) solvers are widely used for analyzing time-harmonic electromagnetic scattering from perfect electrically conducting (PEC) surfaces. In the last decade, MoM-based EFIE solvers using high-order basis functions have been shown to be more accurate as well as CPU and memory efficient than their zeroth-order predecessors leveraging Rao-Wilton-Glisson (RWG) functions. Due to the spectral properties of the EFIE operator, and their effects on the MoM interaction matrices, the use of Calderon identities for preconditioning the EFIE has been studied extensively. In this context, Buffa-Christiansen (BC) basis functions recently have been shown to permit a robust discretization of the Calderon preconditioned EFIE. Unfortunately, the BC basis functions are zeroth-order in nature, and only can be used in conjunction with RWG basis functions. This limitation imposes a severe constraint on the accuracy and efficiency of present Calderon preconditioned EFIE solvers. In this paper, a new set of basis functions is presented, that extends the qualities of the (zeroth-order) BC functions to high-order.