Before the emergence of ultra-wideband (UWB) radios, widely used wireless communications were based on sinusoidal carriers, and impulse technologies were employed only in specific applications (e.g. radar). In 2002, the Federal Communication Commission (FCC) allowed unlicensed operation between 3.1–10.6 GHz for UWB communication, using a wideband signal format with a low EIRP level (−41.3dBm/MHz). UWB communication systems then emerged as an alternative to narrowband systems and significant effort in this area has been invested at the regulatory, commercial, and research levels.

IEEE Transactions on Microwave Theory and Techniques and Antennas and Propagation Announce a Joint Special Issue on Ultra-Wideband (UWB) Technology

This paper presents the first FFT-based fast volume integral equation solver for inhomogeneous anisotropic magnetodielectric objects. The volume integral equations are formulated by employing mixed-order basis functions that expand the flux densities and vector potentials in the coupled field integral equations in terms of different sets of basis functions with different orders. Volumetric roof-top basis functions are used for flux densities whereas second-order curl conforming basis functions are used for vector potentials. A fast volume integral equations solver namely the BCGS-FFT method is then applied to accelerate the solution of this mixed-order weak-form formulation. Examples show that the mixed-order BCGS-FFT method has high accuracy compared to both analytical and numerical solutions. Examples also show the mixed-order BCGS-FFT method has high computational efficiency compared to commercial software.

The Mixed-Order BCGS-FFT Method for the Scattering of Three-Dimensional Inhomogeneous Anisotropic Magnetodielectric Objects

In this paper, the stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is used to solve the electromagnetic scattering problem for 3-D inhomogeneous uniaxial anisotropic objects embedded in a layered uniaxial medium. The optical axis of the background medium is perpendicular to the layer boundaries. However, the optical axis of the scatterer can be rotated through any angles. The electric field integral equation (EFIE) is formulated in the layered uniaxial anisotropic background medium. The volumetric roof-top function is used for the basis function as well as the testing function. The dyadic Green’s functions (DGFs) for both the electric field and the magnetic vector potential are used to solve the EFIE, and the results as well as the performance are compared. Several numerical simulations are carried out to validate the accuracy and efficiency of the proposed method. The major new contribution of this paper is to extend the BCGS-FFT method to accommodate the uniaxial anisotropy of the layered background medium. Therefore, the DGFs for the layered uniaxial medium are evaluated before solving the EFIE. In addition, the DGF for the electric field is also used to solve the 3-D scattering problem through BCGS-FFT iterations, which is different from the previous work.

Fast Solution of Electromagnetic Scattering for 3-D Inhomogeneous Anisotropic Objects Embedded in Layered Uniaxial Media by the BCGS-FFT Method

In this work, the electromagnetic scattering in general rotationally symmetric inhomogeneous anisotropic spheres is investigated. A rigorous full-wave solution is presented based on the volume integral equation. The solution is achieved by expanding the unknown fields in fully orthogonal Dini-type spherical vector wave functions. This formulation allows the study of general rotationally symmetric gyrotropic spheres with varying permittivity and permeability tensors. We investigate the validity of the developed method, which is next applied on the computation of the scattering cross sections of inhomogeneous rotationally symmetric gyroelectric and gyromagnetic spheres.

Electromagnetic Scattering by a General Rotationally Symmetric Inhomogeneous Anisotropic Sphere

3-D electromagnetic (EM) scattering and inverse scattering of magnetodielectric objects with arbitrary anisotropy embedded in layered uniaxial media are studied. The stabilized biconjugate gradient fast Fourier transform (BCGS-FFT) method is employed to solve the forward scattering problem formulated by the combined field volume integral equation (CFVIE). In the inversion, we use the variational Born iterative method (VBIM) enhanced by the structural consistency constraint (SCC) to reconstruct eighteen unknown dielectric parameters of the scatterers simultaneously. In order to further improve the accuracy of the reconstructed permittivity, permeability, and conductivity of the scatterers, we propose the structural continuity scanning (SCS) technique. Comparisons between the BCGS-FFT solution and simulated results from finite element method (FEM) are performed to verify the reliability and accuracy of the forward solver. Meanwhile, we reconstruct the multiple anisotropic parameters of several typical structures embedded in layered uniaxial media to show the feasibility and anti-noise ability of the inversion algorithm.

3-D Electromagnetic Scattering and Inverse Scattering by Magnetodielectric Objects With Arbitrary Anisotropy in Layered Uniaxial Media

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 Nystrom method and develop the corresponding multilevel fast multipole algorithm (MLFMA) for solving large highly anisotropic problems. The Nystrom 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.

Rui Peng Chen

Papers

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