Generalized VSIE formulation for arbitrary high contrast objects

High contrast materials can be found in many useful metamaterial applications. However, traditional VIE methods for high contrast inhomogeneous materials require extremely high field resolution where the sampling rate is inversely proportional to the material parameters. To overcome the sampling rate growth, this paper proposes a factorization technique allowing high contrast inhomogeneous materials to he represented by an equivalent uniform medium and a perturbation representing its inhomogeneity. The resulting VSIE alleviates, to a large degree, the necessity for higher discretizations within these material regions allowing for simulation of recently proposed complex media.