Current and charge integral equation formulation

A new stable frequency domain surface integral equation formulation is proposed for the three dimensional electromagnetic scattering of composite metallic and dielectric objects. The developed formulation does not suffer from the low frequency breakdown and leads to a well balanced and stable system on a wide frequency band. Surface charge densities are used as unknowns in addition to the traditional surface current densities. The balance of the system is achieved by using normalized field quantities and by enforcing the continuity of the fields across the boundaries with carefully chosen scaling factors. The linear dependence between the currents and charges is taken into account with an integral operator, and the linear dependence in charges is removed with the deflation method. A combined field integral equation form of the formulation is proposed to remove the internal resonance problem associated to the closed metallic objects. Due to the good balance in the new formulation, fast converging iterative solutions on a very wide frequency band can be obtained. The new formulation and its convergence is verified with numerical examples.