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Many integral equation-based methods are available for problems oftime-harmonic electromagnetic scattering from perfect electric conductors.Moreover, there are numerous ways in which the geometry can be represented,numerous ways to represent the relevant surface current and/or chargedensities, numerous quadrature methods that can be deployed, and numerous fastmethods that can be used to accelerate the solution of the large linear systemswhich arise from discretization. Among the many issues that arise in suchscattering calculations are the avoidance of spurious resonances, theapplicability of the chosen method to scatterers of non-trivial topology, therobustness of the method when applied to objects with multiscale features, thestability of the method under mesh refinement, the ease of implementation withhigh-order basis functions, and the behavior of the method as the frequencytends to zero. Since three-dimensional scattering is a challenging, large-scaleproblem, many of these issues have been historically difficult to investigate.It is only with the advent of fast algorithms and modern iterative methods thata careful study of these issues can be carried out effectively. In this paper,we use GMRES as our iterative solver and the fast multipole method as ouracceleration scheme in order to investigate some of these questions. Inparticular, we compare the behavior of the following integral equationformulations with regard to the issues noted above: the standard electric,magnetic, and combined field integral equations with standard RWG basisfunctions, the non-resonant charge-current integral equation, the electriccharge-current integral equation, the augmented regularized combined sourceintegral equation and the decoupled potential integral equation DPIE. Variousnumerical results are provided to demonstrate the behavior of each of theseschemes.

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