Analysis of Volume Integral Equation Formulations for Scattering by High-Contrast Penetrable Objects

The volume integral equation method is applied in electromagnetic scattering from arbitrarily shaped three-dimensional inhomogeneous objects. The properties of the volume electric and magnetic field integral equations (VEFIE and VMFIE) are investigated. Numerical experiments show that if the Galerkin´s method with the lowest mixed-order basis functions is used to discretize the equations the accuracy of the VMFIE can be significantly poorer than the accuracy of the VEFIE, in particular, for high-contrast objects at high frequencies. The accuracy of the VMFIE can be essentially improved with full first order (linear) basis functions. The linear basis functions are found to be useful also when a single volume integral equation is used to model a general scatterer where both permittivity and permeability differ from the background.