A Fast IE-FFT Algorithm to Analyze Electrically Large Planar Microstrip Antenna Arrays

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

An infinite medium Green's function is constructed for the boundary value problems of electron transport in the medium which is inhomogeneous and anisotropically scattering. A comparison scattering kernel method is discussed which provides a way of utilizing the well-known Case's normal modes in the spectral representation of Green's function. A numerical estimate of the difference between the exact and local solution for mono-directional scattering kernel is shown. In consequence and approximate spectral density function is constructed.

In this paper, a new multilevel Green's function interpolation method (MLGFIM) is presented to solve integral equations for large-scale electrostatic problems. In MLGFIM, the problem domain is first divided into multilevel cubes. Next, the peer-level Green's function interpolation technique is employed, and then, a new lower-to-upper-level Green's function interpolation technique is devised. They are used with the multilevel discretization to speed up the matrix-vector multiplications in the iterative solution in which a computational complexity of O(N) is achieved. The MLGFIM is used to extract the capacitances encountered in radio frequency integrated circuits (RFICs) and microelectromechanical systems. Moreover, to demonstrate its efficiency both in simulation speed and memory storage requirement, MLGFIM is compared with FastCap for free space problems and applied to extract capacitances from multilayered structures. For problems with 375,000 unknowns, the proposed method only requires 343 MB of computer memory.

Acceleration of the capacitance extraction of planar structures on a single‐layered medium is reported in this article, using the forward‐backward (FB) method with a spectral acceleration (SA) algorithm. The conventional spectral‐layered medium Green's function is modified appropriately so that it can be effectively incorporated into this method. The SA algorithm substantially speeds up the computational time involving in performing matrix‐vector multiplications in the iterative method of moments (MM). However, the memory requirement for the SA algorithm is comparable to that of the FB method. The computational complexity and the memory requirement are shown to be O(N) for large capacitance extraction problems, where N is the total number of unknowns in the MM for increasing one of the surface dimensions of planar structures and fixed neighborhood distance. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:694–700, 2014

The efficient computation of Green's functions for uniaxial anisotropic layered media is investigated. Both field and mixed‐potential layered medium Green's functions (LMGFs) are discussed for different applications. An asymptotic subtraction (singularity extraction) and the weighted average method are combined for the acceleration of LMGF computation. A full collection of Sommerfeld and related identities used in the acceleration is summarized and generalized to uniaxial anisotropic medium for both field and mixed‐potential LMGFs. When lossy media are considered, the effective distance from the source to the observation point becomes a complex number depending on the anisotropic ratio of the horizontal to vertical media parameters. In addition, the evaluation of half‐line source potentials, which are introduced to accelerate the scalar potential correction term for vertical currents, is generalized to the complex domain by analytic continuation. Several numerical examples are used to demonstrate the efficiency and accuracy of the resulting algorithms.

The FN method for anisotropic scattering in neutron transport theory: The critical slab problem

We extend the multilevel Green's function interpolation method (MLGFIM) developed for quasi-electrostatic problems to full-wave simulations. The difficulty in applying the interpolation approach lies in the additional rapidly changing phase term associated with the full-wave Green's functions. To enhance the efficiency and accuracy of the full-wave Green's function interpolation, a scattered point set consisting of two staggered Tartan grids in conjunction with radial basis function interpolation is employed. To further reduce the computational complexity, the QR factorization technique is applied to compress the low rank Green's function matrices. For electromagnetic scattering from PEC spheres up to a diameter of eight wavelengths, the proposed method compares well with Mie's scattering in accuracy and shows the O(NlogN) efficiency. As the method is "kernel independent", its extension to structures in layered medium is straightforward. In the numerical simulations of finite microstrip patch arrays up to 11 by 11 elements, the proposed method demonstrates very favorable dependencies of CPU time and memory storage requirement versus the number of unknowns

The through‐wall imaging (TWI) problem is studied within the context of EM inverse scattering in this article.A novel real time TWI algorithm is proposed by employing the spectrum Green's function and exploding source model under Born approximation. The complex scattering process because of the presence of the wall is well modeled in the imaging formulation through the layered medium Green's function. Inspired by the concept of time reversal imaging, a novel autofocusing strategy is incorporated in the proposed algorithm. The autofocusing is achieved by introducing a time factor in the TWI formulation to get a dynamic image at different focusing time. The image at the time instant, when the defined entropy is minimized, is stored as the output of the imaging result. Numerical and experimental results are presented to show that the proposed method can provide high quality focused image in a short computation time regardless of the estimated value of the wall parameters. © 2010 Wiley Periodicals, Inc. Microwave Opt Technol Lett 52: 732–736, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.25013

We study the electrodynamics of rigidly rotating micro-cavities and slow-light structures formed by a set of weakly coupled micro-cavities. Our analysis is performed in the rotating system rest-frame, using a tight-binding asymptotic theory adapted to rotating reference frame. New manifestations of the Sagnac effect are explored. The analytical results are tested against full-wave numerical solutions based on exact rotating medium Green's function theory. The new results can be used to design miniature optical gyroscopes.

In this study, an inverse scattering approach is investigated for the detection and imaging of an abnormal structure (a bleeding or a stroke) inside the human brain. The method is mainly based on the solution of an integral equation whose kernel is the Green’s function of the inhomogeneous medium (corresponding to a human head model) which is obtained by a numerical approach based on Method of Moments (MoM). In this context, an inverse scattering problem related to the difference of healthy and unhealthy brain models is formulated and a difference function is obtained which indicates the region where the anomaly is located by solving this inverse problem. In order to reduce the reflection effects caused by the electromagnetic differences between the free space and the brain, a matching medium is used as the background space.

This work presents a spectrally accurate method for electromagnetic scattering from objects with complex permittivity embedded in a layered medium. Two-dimensional (2D) layered medium Green's functions are computed adaptively by using Gaussian quadratures. The singular terms in the Green's functions and the non-smooth terms in their derivatives are handled appropriately to achieve exponential convergence. Numerical results, compared with the ones obtained by using other methods, demonstrate the spectral accuracy and high efficiency of the proposed method.

Accurate numerical analysis of electrically small structures embedded in a layered medium is presented in this letter. In our approach, the matrix‐friendly layered medium Green's function is implemented for its elegant expression and singularity of lowest order. The current is decomposed into divergence‐free part and nondivergence‐free part according to quasi‐Helmholtz decomposition when frequency tends to zero, to capture both capacitance and inductance physics. Frequency normalization is applied after analyzing frequency scaling properties of different blocks of the matrix system. Similar to the free space case, connection matrix is utilized to make the electro‐quasi‐static block amenable to iterative solvers. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1304–1308, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24302

This paper presents an efficient three-dimensional nonlinear electromagnetic inversion method in a multilayered medium for geophysical exploration. The stabilized biconjugate-gradient fast Fourier transform algorithm is used for forward modeling, whereas the distorted Born iterative method is used in the inversion. The conjugate-gradient method is applied at each inversion iteration to minimize the cost function. The usage of an iterative solver based on the FFT algorithm and the developed recursive matrix method combined with an interpolation technique to evaluate the layered medium Green's functions rapidly, make this method highly efficient, with the requirement of very low time and memory, O (N log N ) and O (N) respectively. Numerical experiments about the 3D forward modeling with application in Borehole to Surface Electromagnetic Method will be presented in this paper; in addition, we will show the examples about 3D inversion applied in geophysical exploration. All these results will demonstrate the high efficiency and accuracy of the proposed method.

A method of moment (MoM) analysis is developed for electromagnetic scattering from a generalized perfectly conducting target in the near field of a tree trunk in a layered medium environment. In this analysis, the tree trunk is modeled as a dielectric body of revolution and the layered medium electrical properties can be lossy and dispersive, of interest for simulating real soil. The MoM analysis employs the layered medium Green's function, which is evaluated efficiently via the method of complex images. To simplify the analysis, the conducting target is considered to be a flat plate. To rigorously account for the interaction between these disparate targets, the conducting target and tree trunk are modeled separately, with interactions handled via an efficient iterative procedure. In addition to yielding accurate results, this procedure has memory and run-time requirements that are significantly less than required of a straightforward brute force MoM approach. This latter issue is particularly important for the problem of interest here, since the tree trunk and conducting target are generally electrically large and because this work is ultimately directed towards modeling conducting targets in the near field of multiple tree trunks (that is, simulating targets concealed in tree foliage).

Accurate information about the locations of the targets inside a building and the layouts of the inner rooms of the building is very helpful in many search-and-rescue missions. In this paper the full scale building layout and interior target imaging is investigated using synthetic aperture radar (SAR) with a hybrid beamforming approach. An efficient freespace beamforming algorithm, implemented with the fast Fourier/inverse Fourier transform (FFT/IFFT), is presented for the building layout imaging. The far field layered medium Green's function is then employed in the through-wall beamformer to achieve a focused image of the targets inside the building. Numerical results are presented to show that detailed information of the building layout as well as focused imaging results of the target inside the building can be achieved with the proposed SAR imaging technique.