Analysis of single unknown volume integral equation for general scatterers

The volume integral equation method is used to analyze electromagnetic scattering from arbitrarily shaped three-dimensional homogeneous objects whose permittivity and permeability differ from those of background medium. We consider three different types of formulations, the DB-formulation with flux densities as unknowns, the EH-formulation with fields as unknowns, and EE- and HH-formulations that contain only single unknown, either electric or magnetic field. The properties of the formulations are investigated with numerical examples. Numerical results show that at least fully linear curl conforming basis functions must be used when applying the single unknown volume intergal equation for general scatterers.