  Many integral equation-based methods are available for problems of
time-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 charge
densities, numerous quadrature methods that can be deployed, and numerous fast
methods that can be used to accelerate the solution of the large linear systems
which arise from discretization. Among the many issues that arise in such
scattering calculations are the avoidance of spurious resonances, the
applicability of the chosen method to scatterers of non-trivial topology, the
robustness of the method when applied to objects with multiscale features, the
stability of the method under mesh refinement, the ease of implementation with
high-order basis functions, and the behavior of the method as the frequency
tends to zero. 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 and modern iterative methods that
a 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 our
acceleration scheme in order to investigate some of these questions. In
particular, we compare the behavior of the following integral equation
formulations with regard to the issues noted above: the standard electric,
magnetic, and combined field integral equations with standard RWG basis
functions, the non-resonant charge-current integral equation, the electric
charge-current integral equation, the augmented regularized combined source
integral equation and the decoupled potential integral equation DPIE. Various
numerical results are provided to demonstrate the behavior of each of these
schemes.
