Forward‐backward method with a spectral acceleration algorithm for capacitance extraction of planar structures on a single‐layered medium

In this paper, the multiple sweep method of moments (MSMM) with the spectral acceleration (SA) algorithm and the genetic algorithm (GA) is proposed to design non-uniform spacing collinear dipole antenna arrays in free space. The SA algorithm is employed to accelerate the MSMM to be O(N), and the GA is incorporated to find optimum array parameters, where N is the total number of unknowns. Under this appropriate combination, numerical results are presented to demonstrate the accuracy and efficiency of the MSMM/SA/GA method for electrically large non uniform spacing collinear dipole antenna arrays in free space. It is found that the MSMM/SA/GA method provides more accurate radiation pattern than the pattern multiplication method. Moreover, the computational time and the memory storage requirement tend to be O(N) with the array increment in one direction.

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).

To numerically calculate bistatic scattering from a fractal rough surface with high permittivity, a comprehensive approach of the forward-backward method (FBM) with spectral acceleration algorithm (SAA) combined with the physics-based two-grid (PBTG) method is developed. Bistatic scattering from and transmitting through one-dimensional (1-D) fractal rough surface with high permittivity, under TE and TM tapered wave incidence, are numerically simulated. Angular reflectivity and transmittivity demonstrate the energy conservation and the functional dependences upon the surface parameters.

A fast integral-equation fast Fourier transform (IE-FFT) algorithm is developed, analyzed, and applied to the electromagnetic solution of radiation problems. The solution begins by the method-of-moments solution of a mixed potential integral equation on electrically large antenna arrays. Similar to other grid-based algorithms, the IE-FFT uses a Cartesian grid to significantly reduce memory requirement and speed up CPU time for both matrix assembly and matrix-vector multiplication when used with an iterative solver. The IE-FFT algorithm employs two discretizations, one for unknown current on an unstructured triangular mesh and the other on a uniform Cartesian grid for interpolating the layered medium's Green's functions. The uniform interpolation of the Green's functions allows us a global FFT for well-separated far-interaction terms. However, the near-interaction terms should be effectively corrected. A simple and efficient Lagrangian interpolation of the Green's functions is proposed. For a 2.5-D planar layered structure problem, the complexity of an IE-FFT is found to approximately $O(N)$ and $O({N\,{\rm{log}}\,N})$ for memory and CPU time, respectively.

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.

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.

The method of moments is an important tool for solving boundary integral equations arising in a variety of applications. It transforms the physical problem into a dense linear system. Due to the large number of variables and the associated computational requirements, these systems are solved iteratively using methods such as GMRES and CG and its variants. The core operation of these iterative solvers is the application of the system matrix to a vector. This requires $\theta(n^2)$ operations and memory using accurate dense methods. The computational complexity can be reduced to $O(n \log n)$ and the memory requirement to $\Theta(n)$ using hierarchical approximation techniques. The algorithmic speedup from approximation can be combined with parallelism to yield very fast dense solvers. In this paper, we present efficient parallel formulations of dense iterative solvers based on hierarchical approximations for solving potential integral equations of the first kind. We study the impact of various parameters on the accuracy and performance of the parallel solver. We demonstrate that our parallel formulation incurs minimal parallel processing overhead and scales up to a large number of processors. We present two preconditioning techniques for accelerating the convergence of the iterative solver. These techniques are based on an inner-outer scheme and a block-diagonal scheme based on a truncated Green's function. We present detailed experimental results on up to 256 processors of a Cray T3D. Our code achieves raw computational speeds of over 5 GFLOPS. When compared to the accurate solver, this corresponds to a speed of approximately 776 GFLOPS.

The Forward-Backward (FB) method and its accelerated version (SA-FB, Spectral Accelerated Forward-Backward) were developed to compute the electromagnetic scattering from ocean-like rough surfaces. The FB algorithm provides very accurate scattering results and a very fast convergence, but its computational cost is still O(N2) per iteration, being N the number of unknowns used to discretize the surface. The Spectral Acceleration Algorithm proposed later reduces this cost to O(N). Nevertheless, the SA-FB can only be applied to quasi-planar structures or slightly rough surfaces (such as the sea surface), but it cannot be used to solve problems involving very undulating surfaces such as terrain profiles. In this paper the SA-FB method is modified to enhance its scope of application to considerable undulating surfaces. It will be seen that significant changes with respect to the original formulation as well as modifications of the integration path are necessary to get accurate results when dealing with terrain profiles. The proposed method is presented for vertical and horizontal polarizations and for PEC and non-PEC surfaces.

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.

For antennas that are mounted on the same object, coupling through surface waves typically is very significant. The accurate characterization of this coupling is instrumental to the design of antennas with required isolation between its multiple functions. When the antennas consist of only conducting elements, they can be efficiently modeled using the method of moments (MoM). However, most MoM programs developed so far are not suitable to the accurate calculation of mutual coupling. For example, MoM programs based on wire-grid models do not accurately model surface-wave coupling. Furthermore, the MoM yields a full matrix equation, the solution of which is very memory intensive and extremely time consuming for a large scale modeling problem when the number of unknown is large. This is because both the memory requirements and the CPU time per matrix vector multiply are proportional to N/sup 2/. To overcome these problems, we considered the application of the multilevel fast multipole algorithm (MLFMA) to reduce the memory requirements and computational complexity per matrix-vector multiply to O(NlogN) (Chew et al. 1997, and Chao 1998). Our preliminary investigation shows that the MLFMA can predict accurately the S-parameters that characterize the mutual coupling/isolation between antennas. It is a useful tool for the design and performance evaluation of multi-antenna systems. We consider two antenna configurations to demonstrate the accuracy of our algorithms. The first configuration consists of two inverted-L antennas on a finite ground plane and the second composes two loop antennas, also on a finite ground plane.

The electromagnetic radiation and scattering from a body of revolution (BOR) of arbitrary shape have been widely discussed during several decades. The objects can contain perfect electric conductor (PEC), homogeneous dielectric bodies, coated conducting bodies and combined dielectric and conducting bodies [1][2]. The traditional method used to solve BOR with integral equations is the Method of Moments (MoM). And the computational time consumed in solving the integral equation of the BOR problem depends on the evaluation of modal Green's function (MGF), which is a time consuming process. Some research has been done to reduce this computational complexity. For example, Abdelmageed used spherical Bessel function to expansion to evaluate the MGF [3]. In this work, we extend the fast inhomogeneous plane wave algorithm (FIPWA) [4][5] to accelerate the computation of the MoM for composite homogeneous dielectric and conducting bodies of revolution. PMCHW [6] (Poggio-Miller-Chang-Harrington-Wu) equations and electric field integral equation are used for solving the homogeneous dielectric and conducting objects, respectively. Both the memory requirement and CPU time are reduced for large-scale BOR problems. Numerical results are given to demonstrate the validity and efficiency of the FIPWA.

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 introduce a method to compress the impedance matrix of the method of moments (MoM) for the modeling of high-fidelity multiscale structures at low- to moderate-frequencies. We start from a method recently proposed to compress static (scalar) problems, proved to have O(N) computational complexity. We represent far coupling between groups through equivalent source distributions on properly defined, automatically generated equivalence surfaces. The equivalent sources are obtained via an inverse-source process that enforces equivalence of radiated fields on testing surfaces within a prescribed accuracy, and are intrinsically multiscale. This results in an O(N) complexity scaling of matrix-vector products, but reduces multiplicative constants (i.e., reduces time and memory requirements) for all structures. It affords an improved representation of couplings in multiscale structures, resulting in a fast convergence of iterative solvers. Our approach is Green's function independent and easy to be implemented in existing MoM codes; the present version is based on the electric field integral equation (EFIE). Numerical results prove the effectiveness of the proposed algorithm for complex multiscale structures.

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