Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering

Abstract

We introduce a new version of the combined field integral equation (CFIE) for the solution of electromagnetic scattering problems in three dimensions. Unlike the conventional CFIE, the new CFIE is well-conditioned, meaning that it is a second kind integral equation that does not suffer from spurious resonances and does not become ill conditioned for fine discretizations (the so-called "low-frequency problem"). The new CFIE combines the standard magnetic field integral operator with an analytically preconditioned electric field integral operator. We also report numerical results showing that the new formulation stabilizes the number of iterations needed to solve the CFIE on closed surfaces. This is in contrast to the conventional CFIE, where the number of iterations grows as the discretization is refined.