On a Calderón Preconditioned PMCHWT Integral Equation for Non-Perfectly Conductive Scatterers

The Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) equation is one of the most widespread full-wave integral formulations for modeling the electromagnetic scattering from penetrable obstacles. Unfortunately, it suffers from sources of ill-conditioning that include the low-frequency and the densediscretization breakdowns, which manifest by an increase in condition number of the resulting discretized matrix both when the frequency goes to zero and when the mesh density increases. In addition, it also suffers from conductivity-related instabilities. These problems often limit the applicability of the equation in challenging scenarios. In fact, the low-frequency/highconductivity regimes, including the eddy current regime, are very relevant for industrial applications. In this work, we propose a new Calderón-like preconditioning strategy for the PMCHWT equation combined with the use of quasi-Helmholtz projectors, which cures at once all the ill-conditioning issues described above. The strategy proposed here is compatible with several fast solvers and can be implemented on top of a standard PMCHWT code.