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

Abstract

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.

Keywords

• Bi-anisotropy
• method of moments (MoM)
• multilevel fast multipole algorithm (MLFMA)
• spherical harmonics expansion
• volume integral equation (VIE)