A Nonconformal Volume Integral Equation for Electromagnetic Scattering From Penetrable Objects

A nonconformal volume integral equation (VIE) for electromagnetic scattering from inhomogeneous anisotropic scatterers with nontrivial complex permittivity and permeability tensors is presented. The integral equation is solved by the method of moments (MoM). Applying the gradient-gradient operator on the Green's function allows the choice of piecewise constant functions for expansion and testing. Hence, the tetrahedral mesh which discretizes the scatterer need not be conformal. Moreover, the coefficient matrix is symmetric for a reciprocal medium. However, applying the gradient-gradient operator on the Green's function leads to a hypersingular integral which needs to be evaluated using a regularization scheme. Furthermore, the same regularization scheme is applied to the integrals that represent interactions between neighbor elements to obtain a numerically convergent solution. The accuracy of the formulation is validated on a canonical example. The convergence study on a dielectric sphere demonstrates that the condition number of the coefficient matrix is bounded and the eigenvalue distribution preserves itself