  This paper introduces a new method for discretizing and solving integral
equation formulations of Maxwell's equations which achieves spectral accuracy
for smooth surfaces. The approach is based on a hybrid Nystr\"om-collocation
method using Chebyshev polynomials to expand the unknown current densities over
curvilinear quadrilateral surface patches. As an example, the proposed strategy
is applied the to Magnetic Field Integral Equation (MFIE) and the N-M\"uller
formulation for scattering from metallic and dielectric objects, respectively.
The convergence is studied for several different geometries, including spheres,
cubes, and complex NURBS geometries imported from CAD software, and the results
are compared against a commercial Method-of-Moments solver using RWG basis
functions.
