Calderón Preconditioned PMCHWT Equations for Analyzing Penetrable Objects in Layered Medium

We study Calderón preconditioners for analyzing electromagnetic scattering by penetrable objects in a layered medium. To account for the scattering effects of the multilayered background, the layered medium Green´s function is adopted in the Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) method. However, similar to the free-space case, the spectrum of the resulting equation is undesirable. This leads to a slow convergence of an iterative solver, especially when the geometry is densely meshed. To improve the convergence, a highly effective preconditioner is proposed. Different from its free-space counterpart, the preconditioning operator is constructed based on the Calderón identities for inhomogeneous medium. To reduce the relatively high construction cost of the preconditioning operator, several alternative simplified schemes are proposed and analyzed. Finally, the performances of different preconditioners are examined and compared carefully through different numerical examples. It is shown that the convergence of the PMCHWT system in a layered medium can be significantly improved by using the proposed Calderón preconditioners.