Split Formulation of the Charge and Current Integral Equations for Arbitrarily Shaped Dielectrics

The low-frequency instability in the method of moments can be resolved by reformulating the underlying integral equations to explicitly include charge as an unknown. A new technique based on this charge and current formulation that reduces the computational complexity, both in time and memory, will be introduced. Considerations when using a charge and current technique include the practical problems of basis functions and the evaluation of the singular surface integrals, well as more theoretical problems such as whether the continuity equation still holds. The technique is implemented using a simple set of basis and testing functions and has been verified quantitatively, checking the charge and current distributions against analytic solutions where existing, as well as qualitatively against the boundary conditions for the scattered field. These results show the method to be both stable and accurate.