Spectral and algorithmic strategies for penetrable scatterers on simply and non-simply connected geometries

The Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) is a widely used integral equation for simulating radiation and scattering from penetrable objects. This formulation, however, is plagued from mesh refinement and low-frequency ill-conditioning. Existing techniques for handling these problems, however, suffer from very low-frequency numerical cancellations or they require the detection of global loops. This work presents a new Calderon-like strategy for the PMCHWT which, leveraging on the quasi-Helmholtz projectors, solves both frequency and refinement ill-conditioning without detecting global loops. Moreover the technique is immune from very low-frequency numerical cancellations. Numerical results confirms all theoretical developments and show the practical impact of the new scheme.