A Calderón Preconditioner for the Electric Field Integral Equation With Layered Medium Green's Function

Abstract

A Calderón preconditioner is developed for the analysis of electromagnetic scattering of perfect electrically conducting (PEC) objects embedded in a layered medium. The electric field integral equation (EFIE) is formulated with the kernel of layered medium Green's function to account for the effects from the multilayered background. The Calderón projector is derived based on the general source-field relationship and the extinction theorem for inhomogeneous environment in electromagnetic theory. The Calderón identities can be naturally deduced based on this projector, which is then leveraged to precondition the EFIE with layered kernel. An alternative implementation is then proposed to make the implementation of the preconditioner as efficient as the one in free space. Different numerical examples are designed to show the performance of the preconditioner, where the objects are located in different positions with respect to the layered medium, or different types of excitation are adopted. It is shown that the proposed effective and robust preconditioner makes the EFIE system converge rapidly in all cases, independent of the discretization density.