Decoupled potential integral equation applied to complex geometries

In this paper we present a numerical implementation of the Decoupled Potential Integral Equation DPIE. The DPIE formulation allows to describe the scattered electromagnetic field by solving a boundary value problem for the vector and scalar potentials A
^scat
and ø
^scat
separately. The formulation allows to obtain the exact scattered electric and magnetic fields for any frequency ω ≥ 0. The formulation is immune to low frequency breakdown, high density mesh breakdown and internal resonances. The formulation can be applied to multiply connected geometries without loop search. In this paper we present a low frequency multilevel fast multipole implementation of the DPIE based on a flat triangular discretization with piecewise constant basis functions and collocation method.