Nonconformal Discretization of Electric Current Volume Integral Equation with Higher Order Hierarchical Vector Basis Functions

A nonconformal discretization of the electric current volume integral equation (JVIE) is presented for the electromagnetic scattering analysis of inhomogeneous dielectric objects. This JVIE is based on higher order geometrical and current modeling, where curved tetrahedral elements and higher order hierarchical vector (HOHV) basis functions are adopted. In order to implement the nonconformal discretization, the half face-based HOHV basis function is introduced to address the nonconformal volumetric elements. Compared to the conventional low-order conformal/nonconformal VIE, our nonconformal HOHV-based JVIE has the advantage of improving the computational efficiency and accuracy. Compared to the previous VIE discretized by other higher order functions, our nonconformal JVIE is based on the higher order geometric modeling and the HOHV bases. In order to improve the efficiency, the basis expansion and recombination technique is introduced to significantly accelerate the matrix filling. Moreover, the flexibility of basis order selection is further enhanced by the mixed order schemes. Numerical results are given to demonstrate its accuracy, efficiency, and flexibility.