The effect of near-zone preconditioning on electromagnetic integral equations of first and second kind

The linear equation systems which arise from the discretization of surface integral equations are conveniently solved with iterative methods because of the possibility to employ fast integral methods like the Multilevel Fast Multipole Method. However, especially integral equations of the first kind often lead to very ill-conditioned systems, which require the usage of effective preconditioners. In this paper, the regularization property of near-zone preconditioning operators on the Electric Field Integral Equation is demonstrated and investigated for problems of different size. Furthermore, comparisons are drawn to second-kind integral equations such as the Combined Field Integral Equation.