An Efficient Multilevel Fast Multipole Algorithm to Solve Volume Integral Equation for Arbitrary Inhomogeneous Bi-Anisotropic Objects

A volume integral equation (VIE) based on the mixed-potential representation is presented to analyze the electromagnetic scattering from objects involving inhomogeneous bi-anisotropic materials. By discretizing the objects using tetrahedrons on which the commonly used Schaubert-Wilton-Glisson (SWG) basis functions are defined, the matrix equation is derived using the method of moments (MoM) combined with the Galerkin's testing. Further, adopting an integral strategy of tetrahedron-to-tetrahedron scheme, the multilevel fast multipole algorithm (MLFMA) is proposed to accelerate the iterative solution, which is further improved by using the spherical harmonics expansion with a faster implementation and low memory requirement. The memory requirement of the radiation patterns of basis functions in the proposed MLFMA is several times less than that in the conventional MLFMA.