A Refinement and High-Degree Stable Marching-on-in-Degree Method for Wideband Scattering From Perfect Conductors

This communication presents a time-domain electric field integral equation (TDEFIE) solver, specifically designed to analyze ultrawideband (the ratio of highest and lowest frequency is over 1033) scattering from perfect electric conductors (PEC). The solver addresses the challenges associated with dense-mesh breakdown and high-degree collapse. To be specific, the Calderón preconditioning technique and a narrow temporal excitation are adopted to avoid the ill-conditioning in space and time dimensions. Meanwhile, the Filon-type method is integrated, resulting in a Calderón-stability-improved marching-on-in-degree (SIMOD) approach during the matrix construction. This method effectively addresses the oscillatory property of the generalized Laguerre polynomials. To obtain accurate results at low frequencies, we introduce two strategies based on Calderón-SIMOD to eliminate the adverse effects of static error current (SEC): the static error current subtraction (SECS) method and its approximate version (ASECS). Consequently, numerical results demonstrate that the proposed approach is both stable and highly accurate over an ultrawideband. It also indicates that the proposed method offers significant improvements over the existing marching-on-in-degree (MOD) methods, as well as providing a valuable tool for analyzing broadband electromagnetic scattering.