Fast Solutions of Volume Integral Equations for Electromagnetic Scattering by Large Highly Anisotropic Objects

Accurate analysis of electromagnetic problems including inhomogeneous or anisotropic structures requires solving volume integral equations (VIEs) in the integral-equation approach. When the structures are electrically large in dimensions or constitutively complicated in materials, fast numerical algorithms are desirable to accelerate the solution process. Traditionally, such fast solvers are developed based on the method of moments (MoM) with the divergence-conforming Schaubert-Wilton-Glisson basis function or curl-conforming edge basis function, but the basis functions may not be appropriate to represent unknown functions in anisotropic media. In this work, we replace the MoM with the Nyström method and develop the corresponding multilevel fast multipole algorithm (MLFMA) for solving large highly anisotropic problems. The Nyström method characterizes the unknown functions at discrete quadrature points with directional components and more degrees of freedom and it also allows the use of JM-formulation, which does not explicitly include material property in the integral kernels in the VIEs. These features, with its other well-known merits, can greatly facilitate the implementation of MLFMA for anisotropic structures. Typical numerical examples are presented to demonstrate the algorithm and good results have been observed.