Comparison of the Muller and PMWCHT surface integral formulations for the locally corrected Nystrom method

Two surface integral formulations, the Muller and PMCHWT methods, are compared for the computation of the electromagnetic scattering by composite dielectric objects via the locally corrected Nystrom (LCN) method. The Muller formulation leads to a second-kind integral equation, whereas the PMCHWT formulation leads to a first-kind integral equation with a hypersingular kernel. For the high-order LCN solution of these integral formulations, it is shown that the Muller formulation leads to faster convergence rates and smaller condition numbers, and is more efficient for the same level of accuracy for moderate to low contrast materials. For high contrast materials, while the PMCHWT simulation converges at a slower rate, it can still realize the desired precision with fewer unknowns than a Muller formulation.