Improving Conditioning of the Surface Integral Equation Formulations using Normalized Fields and Currents

Surface integral equation (SIE) method is one of the most popular numerical methods in the electromagnetic analysis of metallic and dielectric objects. Unfortunately, in many cases discretization of a SIE leads to a matrix equation with a high condition number, which may cause problems in numerical solution. In the case of dielectric and composite metallic and dielectric objects, the poor conditioning of the SIE matrix is due to the difference in scales among the unknowns, the electric and magnetic surface current densities, and the matrix elements. This paper presents an efficient method to improve the balance between the unknowns and the matrix elements. The method is based on the use of normalized field quantities and unknowns, and carefully chosen scaling factors. Numerical results show that a significant reduction in the condition number of the matrix can be obtained with the new normalized and scaled SIE formulations