Tie Jun Cui

Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buried objects

This paper presents a fast method for electromagnetic scattering and radiation problems pertinent to three-dimensional (3D) buried objects. In this approach, a new symmetrical form of the Greens function is derived, which can reduce the number of Sommerfeld integrals involved in the buried objects problem. The integration along steepest descent paths and leading-order approximations are introduced to evaluate these Sommerfeld integrals, which can greatly accelerate the computation. Based on the fast evaluation of Sommerfeld integrals, the radiation of an arbitrarily oriented electric dipole buried in a half space is first analyzed and computed. Then, the scattering by buried dielectric objects and conducting objects is considered using the method of moments (MOM). Numerical results show that the fast method can save tremendous CPU time in radiation and scattering problems involving buried objects.

Inverse scattering of two-dimensional dielectric objects buried in a lossy earth using the distorted Born iterative method

An efficient inverse-scattering algorithm is developed to reconstruct both the permittivity and conductivity profiles of two-dimensional (2D) dielectric objects buried in a lossy earth using the distorted Born iterative method (DBIM). In this algorithm, the measurement data are collected on (or over) the air-earth interface for multiple transmitter and receiver locations at single frequency. The nonlinearity due to the multiple scattering of pixels to pixels, and pixels to the air-earth interface has been taken into account in the iterative minimization scheme. At each iteration, a conjugate gradient (CG) method is chosen to solve the linearized problem, which takes the calling number of the forward solver to a minimum. To reduce the CPU time, the forward solver for buried dielectric objects is implemented by the CG method and fast Fourier transform (FFT). Numerous numerical examples are given to show the convergence, stability, and error tolerance of the algorithm.

Diffraction tomographic algorithm for the detection of three-dimensional objects buried in a lossy half-space

A diffraction tomographic (DT) algorithm has been proposed for detecting three-dimensional (3-D) dielectric objects buried in a lossy ground, using electric dipoles or magnetic dipoles as transmitter and receiver, where the air-earth interface has been taken into account and the background is lossy. To derive closed-form reconstruction formulas, an approximate generalized Fourier transform is introduced. Using this algorithm, the locations, shapes, and dielectric properties of buried objects can be well reconstructed under the low-contrast condition, and the objects can be well detected even when the contrast is high. Due to the use of fast Fourier transforms to implement the problem, the proposed algorithm is fast and quite tolerant to the error of measurement data, making it possible to solve realistic problems. Reconstruction examples are given to show the validity of the algorithm.

A FAFFA-MLFMA algorithm for electromagnetic scattering

Based on the multilevel fast multipole algorithm (MLFMA), an efficient method is proposed to accelerate the solution of the combined field integral equation in electromagnetic scattering and radiation, where the fast far-field approximation (FAFFA) is combined with MLFMA. The translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many k/spl circ/ directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k/spl circ/ direction is involved in the translator. The condition for using FAFFA and the way to efficiently incorporate FAFFA with MLFMA are discussed. Complexity analysis illustrates that the computational cost in FAFFA-MLFMA can be asymptotically cut by half compared to the conventional MLFMA. Numerical results are given to verify the efficiency of the algorithm.

Magnetic field integral equation at very low frequencies

It is known that there is a low-frequency breakdown problem when the method of moments (MOM) with Rao-Wilton-Glisson (RWG) basis is used in the electric field integral equation (EFIE); it can be solved through the loop and tree basis decomposition. The behavior of the magnetic field integral equation (MFIE) at very low frequencies is investigated using MOM, where two approaches are presented based on the RWG basis and loop and tree bases. The study shows that MFIE can be solved by the conventional MOM with the RWG basis at arbitrarily low frequencies, but there exists an accuracy problem in the real part of the electric current. Although the error in the current distribution is small, it results in a large error in the far-field computation. This is because a big cancellation occurs during the far field computation. The source of error in the current distribution is easily detected through the MOM analysis using the loop and tree basis decomposition. To eliminate the error, a perturbation method is proposed, from which a very accurate real part of the tree current has been obtained. Using the perturbation method, the error in the far-field computation is also removed. Numerical examples show that both the current distribution and the far field can be accurately computed at extremely low frequencies by the proposed method.

Novel diffraction tomographic algorithm for imaging two-dimensional targets buried under a lossy Earth

A novel diffraction tomographic algorithm has been proposed to detect two-dimensional (2D) dielectric cylinders buried under a lossy Earth. In this algorithm, the air-Earth interface has been taken into account and the exact treatment of Sommerfeld-like integrals has been considered. Using the algorithm, all locations, shapes, and dielectric properties of buried cylinders can be accurately reconstructed under the low-contrast condition. For high-contrast targets, this algorithm can also be used to determine their locations and approximate their dielectric properties. Due to the use of fast Fourier transforms to implement the problem, this algorithm is very fast and quite tolerant to the error of measurement data. Numerical examples are given to show the validity of the algorithm.

Efficient Evaluation of Sommerfeld Integrals for Tm Wave Scattering By Buried Objects

Unlike the scattering problem in homogeneous space, intensive computations of Sommerfeld integrals are involved in the EM scattering of buried scatterers. There are mainly three bottlenecks of the CPU time for such problem: matrix filling, matrix inversion and calculation of the scattered fields. For moderately sized problems, extensive numerical experience shows that the CPU time used in the first and third items (concerned with the Sommerfeld integrals) is much more than that used in the matrix inversion. Therefore an efficient method for solving such buried object problems requires the fast evaluation of such Sommerfeld integrals. In this paper, several efficient methods are presented to evaluate the integrals that appear in the TM wave scattering by two-dimensional buried dielectric and conducting cylinders. In the numerical integration method, the original integrating path is deformed to the steepest-descent paths to expedite the numerical integration and yield a more stable computation result. In th...

Accurate model of arbitrary wire antennas in free space, above or inside ground

An accurate model of wire antennas in free space, above or inside lossy ground is presented in which the current is assumed to flow on the surface of the wire and the testing is also performed on the surface. To replace the traditional delta-gap source, a more accurate source model is developed by using the Huygens principle. From this principle and reciprocity theorem, a variational formulation of the input admittance is derived. When the triangle function is chosen as both basis and weighting functions, all the elements of impedance matrix and source vector are formulated in closed forms, which can be rapidly computed. Several numerical results are given. Comparing with measured data, both the current distribution and input impedance by this model are more accurate than those of delta-gap model.

Accurate analysis of wire structures from very-low frequency to microwave frequency

Based on the accurate model developed in our previous paper, a general method is proposed to analyze wire structures in the free space or above multilayered media, which is valid from very-low to microwave frequencies. In this method, loop-tree basis functions have been applied to overcome the low-frequency breakdown problem, which can represent the nature of the Helmholtz decomposition of the current. The proposed method can be used to study wire antennas, or it can be incorporated with other methods to analyze circuit problems containing wire structures.

Modeling of arbitrary wire antennas above ground

An efficient method for modeling wire antennas of arbitrary shapes and orientations above a lossy ground is presented by using Galerkin method. As opposed to the traditional point matching method, careful treatment is required for the electric-field integral equation (EFIE) and its numerical implementation. Comparing with the point matching method, only three simple Sommerfeld integrals are needed in the new method, and the convergence is much faster. To test the validity of this method, numerous numerical examples are given. Numerical results show that, for equivalent-accuracy solutions, the cell number used in this method is much fewer than that in the point matching method.