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.
Highlights
With the rapid development of material science, the electromagnetic (EM) radiation or scattering properties of complicated materials have aroused great interests in the field of computational electromagnetics
The method of moments (MoM) solution of the volume integral equation (VIE) [5], [6], in which the object is replaced by the equivalent volume currents according to the principle of volume equivalence, The associate editor coordinating the review of this manuscript and approving it for publication was Jenny Mahoney
A generalized VIE method was formulated for arbitrarily shaped complex objects with inhomogeneous bi-isotropy [9], where the threedimensional solenoidal function was incorporated as the basis function defined on each tetrahedron
Summary
With the rapid development of material science, the electromagnetic (EM) radiation or scattering properties of complicated materials have aroused great interests in the field of computational electromagnetics. In [7], an integral equation based scheme was presented to analyze scattering from inhomogeneous bodies with anisotropic EM properties. It was concluded that when the scatterer is extremely anisotropic, the behavior of the VIE formulation based on the equivalent currents is more stable than that based on fluxes or fields. This conclusion is tenable only for the uniaxial anisotropic materials. Reference [11] proposed a new generalized volume-surface integral equation to analyze the EM scattering from composite objects comprised of both conductors and inhomogeneous bi-isotropic materials
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