A nonconformal volume integral equation for electromagnetic scattering from anisotropic materials

The purpose of this study is to formulate integral equations for electromagnetic scattering by arbitrarily shaped anisotropic bodies with complex permittivity and permeability tensors, epsi_r and mu_r, respectively, and to develop a code for the efficient solution of such equations. A coupled integral equation is obtained that represents both the electric and magnetic fields, E^rarr(r ^rarr) and H^rarr(r^rarr), respectively, to account for both the electric and magnetic properties of the scatterer. To obtain a nonconformal volume integral equation (VIE), imposing divergence or curl operators on the unknown vectors are avoided by applying instead the gradient-gradient operator on the Green´s function. In the method of moments (MoM) solution of the presented VIE tetrahedral discretization is employed for accurate and flexible geometric modeling. Applying the gradient-gradient operator on the Green´s function gives the flexibility to choose piecewise constant functions to expand E^rarr(r^rarr) and H^rarr(r^rarr) and to test the electric and magnetic polarization currents, J^rarr(r^rarr) and M^rarr(r^rarr), respectively. Moreover, the resulting coefficient matrix is symmetric for a reciprocal medium due to the symmetry of the volume integral operators in the formulation