A Nyström implementation of an augmented electric field integral equation for low frequency electrical analysis

The electric field integral equations (EFIE) solved by method of moments (MOM) is widely used in scattering, antenna, and microwave circuit problems. However, it is well known that EFIE will break down when applied to electrically small structures or low frequency problems. A loop-star decomposition for the RWG discretization overcomes this problem and provides a valid solution from zero to microwave frequencies. But the global loop search becomes a obstacle for complicated geometries. The separated potential integral equation (SPIE) augmented with continuity equations uses charge as additional unknowns to remove the imbalance of the vector potential and scalar potential in the conventional EFIE. With the enforcement of the current continuity constraint and proper frequency scaling, the augmented electric field integral equation with RWG discretization avoids the low frequency breakdown and provides an accurate representation of the electric fields.