Challenges in developing efficient Calderon preconditioners for resonating or high material contrast penetrable objects

Calderon preconditioning is a recently proposed technique for improving conditioning of ill-conditioned matrices arising from discretization of surface integral equations. In electromagnetics the method has been developed for both perfectly conducting and homogeneous penetrable objects. In the case of penetrable objects the large variety of possible material parameters poses additional challenges on the efficiency of the preconditioner. We demonstrate with numerical experiments that problems may appear in particular at high material parameter values, at the physical resonances of the object, and at negative or zero material parameters. As realistic examples of objects with zero or negative material parameters we consider plasmonic nanoparticles at optical wavelengths.