A study of combined field formulations for material scattering for a locally corrected Nyström discretization

A study of the error convergence and condition number of three integral-equation formulations derived for penetrable material scattering objects-the Poggio, Miller, Chang, Harrington, Wu and Tsai (PMCHWT), the Müller, and the PMCHWT(-) formulations-is presented for a variety of problems when discretized via a locally corrected Nyström method. The PMCHWT formulation is a first-kind integral equation with a hypersingular operator. The Müller formulation leads to a second-kind equation consisting of a diagonal term plus a compact operator. This form is both frequency and mesh stable. However, unlike the PMCHWT formulation, the error grows with the refractive index. The PMCHWT(-) formulation is in the form of a second-kind equation, but has a hypersingular term.