Fast adaptive high-order integral equation methods for electromagnetic scattering from smooth perfect electric conductors

Abstract

Many integral equation-based methods are available for problems of time-harmonic electromagnetic scattering from perfect electric conductors. Among the many challenges that arise in such calculations are the avoidance of spurious resonances, robustness of the method to scatterers of non-trivial topology or multiscale features, stability under mesh refinement, ease of implementation with high-order basis functions, and behavior in the static limit. Since three-dimensional scattering is a challenging, large-scale problem, many of these issues have been historically difficult to investigate. It is only with the advent of fast algorithms for matrix-vector multiplies coupled with modern iterative methods that a careful study of these issues can be carried out effectively. Our focus here is on comparing the behavior of several integral equation formulations with regard to the issues noted above, namely: the well-known, standard electric, magnetic, and combined field integral equations with standard RWG basis functions, and the more modern non-resonant charge-current and decoupled potential integral equation. Numerical results are provided to demonstrate the behavior of each of these schemes. Furthermore, we provide some analytical properties and comparisons with the electric charge-current integral equation and the augmented regularized combined source integral equation.