On solving volume integral equations with highly anisotropic media

Solving volume integral equations (VIEs) with anisotropic media usually relies on the method of moments (MoM) with the divergence-conforming Schaubert-Wilton-Glisson (SWG) basis function or curl-conforming edge basis function. However, the basis functions may not be suitable to represent unknown functions when the anisotropy of media is strong. In this work, we replace the MoM with a point-matching method to solve such problems and the method characterizes the unknown functions at discrete points with directional components and more degrees of freedoms. Also, the method allows the use of JM-formulation which does not explicitly include material property in the integral kernels. A typical numerical example is presented to demonstrate the approach.