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| Title: | April 2009 Full Issue |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 9648 KB |
| Title: | April 2009 Front/Back Matter |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 214 KB |
| Title: | An Incomplete Review of Fast Multipole Methods–from Static to Wideband–as Applied to Problems in Computational Electromagnetics |
| Abstract: | Fast multipole methods (FMM) and their immediate predecessors, tree codes, were developed in response to the need for solving Nbody problems that occur in applications as varied as biophysics, computational chemistry, astrophysics and electromagnetics. In all these areas, it is necessary to compute long range potentials of the form 1/R between a dense distribution of point charges, where R is the distance between any two charges. Often, repeated evaluation of these potentials is necessary. It is apparent that the cost of direct evaluation, which scales as O(N2) for N degrees of freedom, forms a fundamental bottleneck. FMM and tree methods ameliorate the cost associated with these computation; CPU times of these method scale as O(N). It stands to reason that FMM has had a seminal impact on a multitude of fields, so much so, that it was recognized as one of the top ten algorithms of the past century. A method to rapidly compute potentials of the form e-j κR/R soon followed. As the reader is aware, these potentials are the crux of integral equation based analysis tools in electromagnetics and the advent of these methods have transformed the face of computational electromagnetics. Consequently, the state of art of integral equation solvers has grown by leaps and bounds over the past decade. This paper attempts to present a detailed review of the state of art of FMM based methods that are used in computational electromagnetics, from the static to the high frequency regime. |
| Author(s): | M. Vikram, B. Shanker |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 889 KB |
| Title: | Analyzing PEC Scattering Structure Using an IE-FFT Algorithm” |
| Abstract: | In this paper a fast integral equation method, termed IE-FFT, is developed, analyzed and applied to the electromagnetic (EM) solution of scattering problems. The methodology is developed for the Method of Moments (MoM) solution of the Electric Field Integral Equation (EFIE) on electrically large Perfect Electric Conducting (PEC) structures. Similar to other Fast Fourier Transform (FFT) based algorithms, IEFFT uses a Cartesian grid to drastically decrease memory storage and speed up the matrix-vector multiplication. The IE-FFT algorithm employs two discretizations, one for the unknown current on an unstructured triangular mesh and the other on a uniform Cartesian grid for interpolating the Green’s function. The uniform interpolation of the Green’s function allows the fast computation of well-separated MoM interaction terms with the aid of a global FFT. Nevertheless, the coupling between near-interaction terms should be adequately corrected. The major contribution of this paper lies on the Lagrangian interpolation of the Green’s function. This not only allows simple and efficient algorithmic implementation, but also naturally suggests a rigorous error analysis of the algorithm. The efficiency of the method is based on the Toeplitz structure of the interpolated Green’s function. Therefore, it is applicable on both asymptotically-smooth and oscillatory kernels arisen in static and wave propagation problems, respectively. Through numerical simulations of electromagnetic wave scattering from a PEC sphere, the complexity of the IE-FFT algorithm is found to scale as O(N1.5) and O(N1.5logN) for memory and CPU time, respectively. Various numerical results verify the high accuracy and efficiency of the method. |
| Author(s): | S. M. Seo, C. Wang, J. F. Lee |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 595 KB |
| Title: | The Discontinuous Galerkin Finite-Element Time-Domain Method Solution of Maxwell’s Equation |
| Abstract: | A Discontinuous Finite-Element Time- Domain method is presented that is based on a high-order finite element discretization of Maxwell’s curl equations. The problem domain is decomposed into non-overlapping subdomains that couple through boundary integral terms. Within each subdomain, the tangential electric and magnetic fields are discretized via high-order curl conforming basis functions, leading to a highorder representation of the volume fields. For unbounded problems, a perfectly matched layer absorbing medium is used. The discrete equations are presented in a symmetric form. The method leads to an explicit time-dependent solution of Maxwell’s equations that is high-order convergent. |
| Author(s): | S. D. Gedney, C. Luo, J. A. Roden, R. D. Crawford, B. Guernsey, J. A. Miller, T. Kramer, E. W. Lucas |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 558 KB |
| Title: | Physics-Based Aggregate-Functions Approaches to Large Mom Problems |
| Abstract: | Aggregate functions approaches construct efficient MoM basis functions by suitably grouping standard (e.g. Rao-Wilton- Glisson) functions. The application domains, objectives and related means of achieving them can be significantly different. In this paper we review some recent advances in aggregatefunctions methods, putting them in a unifying perspective. We address matrix compression, multi-resolution sets, low- and high-frequency constructs. They can reduce the degrees of freedom of the problem so as to allow a direct, iteration-free solution, or can accelerate the convergence rate of iterative methods. We analyze compressive methods in more detail, providing general discussion and specific implementation examples. |
| Author(s): | L. Matekovits, G. Vecchi, F. Vico |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 941 KB |
| Title: | Diffraction-like Synthetic Functions to Treat the Scattering from Large Polyhedral Metallic Objects” |
| Abstract: | This paper presents an innovative procedure that allow for the Method of Moments (MoM) analysis of electrically large objects composed of flat faces, i.e. open or closed polyhedrons with or without attached plates. The method is framed within the category of iteration free, compressive basis function approaches. Two kinds of diffraction-like basis functions are introduced to achieve drastic memory requirement compression; relevant results compared with those obtained employing standard RWG basis functions are presented. |
| Author(s): | M. Casaletti, S. Maci, G. Vecchi |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 792 KB |
| Title: | Fast Solution of Multi-Scale Antenna Problems for the Square Kilometre Array (SKA) Radio Telescope using the Characteristic Basis Function Method (CBFM) |
| Abstract: | We present a numerically efficient technique, called the Characteristic Basis Function Method (CBFM), for computing the scan impedances of antenna elements located inside an electrically large subarray, which is surrounded by (many) other actively phase-steered subarrays. We construct a reduced moment matrix for a single subarray, and modify its entries in a manner that accounts for the mutual coupling between the surrounding subarrays. This enables us to circumvent the difficult problem of having to deal with the entire large array geometry in one step and reduces the total solve time significantly. Furthermore, the reduced moment matrix can be constructed in a time-efficient manner by exploiting the translation symmetry between pairs of Characteristic Basis Functions (CBFs). However, since we propose an overlapping domain decomposition technique for arrays of electrically interconnected antenna elements, symmetry can only be exploited if the mesh partitioning facilitates a one-to-one mapping of CBFs. To fully utilize the translation symmetry, a strategy has been developed to mesh the structure and to take advantage of this geometrical property. A numerical example is presented for a large array of subarrays of Tapered Slot Antennas (TSAs). The proposed method has good accuracy, excellent numerical efficiency, and reduced memory storage requirement. |
| Author(s): | R. Maaskant, R. Mittra, A. Tijhuis |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 537 KB |
| Title: | Application of the Characteristic Basis Function Method for the Electromagnetic Analysis of Electrically Large and Complex Bodies |
| Abstract: | An overview of a parallel implementation of the Characteristic Basis Function Method combined with the Multilevel Fast Multipole Algorithm is presented. This approach allows an accurate analysis of very large electromagnetic problems. The geometry is described by means of Non-Uniform Rational BSplines, and the macro-basis functions are expressed in terms of subsectional functions totally conformed to the original geometry. A number of representative examples are considered in order to show the performance of the proposed approach. |
| Author(s): | C. Delgado, E. García, F. Felipe Cátedra, R. Mittra |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 464 KB |
| Title: | Characteristic Basis Function Method (CBFM)—An Iteration-free Domain Decomposition Approach in Computational Electromagnetics |
| Abstract: | In this paper we review a novel Domain Decomposition (DD) approach, called the Characteristic Basis Function Method (CBFM), which tackles large-scale electromagnetic problems by generalizing the concept of principle of localization that forms the cornerstone of asymptotic methods. The paper shows that the problem of having to deal with large matrices that arise in the conventional formulation of large problems with the Method of Moments (MoM) can be obviated, by dividing the original large problem into a number of smaller sub-problems that are more manageable to handle. However, unlike the conventional DD approaches that typically rely upon iteration algorithms to account for the inter-coupling between the subdomains, the CBFM tackles the problem with direct solvers instead. It is possible to do this in the context of CBFM, because it reduces the original large system matrix into one whose size is orders of magnitude smaller, and is appropriately called the “reduced matrix.” Furthermore, an important salutary feature of CBFM is that the algorithm is naturally parallelizable, an attribute that distinguishes it from many other CEM solvers, and makes it well suited for parallel platforms that have become ubiquitous in recent years. This, in turn, enables us to take advantage of the power of these platforms and to solve, numerically efficiently, large problems that were well beyond our reach in the past. The paper also shows that the basic concepts of CBFM are quite general, and they not only apply to MoM, but can also be tailored for both FEM and FDTD. Index Terms─ Characteristic Basis Function Method (CBFM), Domain Decomposition, Method of Moments (MoM), Finite element Method (FEM), Finite Difference Time Domain (FDTD). |
| Author(s): | R. Mittra |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 1733 KB |
| Title: | Efficient numerical analysis of arrays of identical elements with complex shapes |
| Abstract: | A fast method-of-moments approach is proposed for the solution of finite arrays of complex identical elements, involving both metal and finite dielectric parts. The method is based on the use of Macro Basis Functions (MBF), also named “Characteristic” Basis Functions, among which interactions are computed very fast with the help of a Multipole approach. Fast evaluation of array patterns or embedded element patterns is obtained through decomposition into a finite series of pattern multiplication problems. Examples are provided for finite arrays of bowtie antennas embedded in dielectric boxes. For periodic arrays, results are compared with infinite-array solutions. The method is also extended to non-periodic structures, for which the Multipole approach appears very useful for interactions outside the near-field region. We show that interactions in the near-field region can benefit from an interpolation procedure. |
| Author(s): | C. Craeye, D. González-Ovejero, X. Dardenne |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 468 KB |
| Title: | A Mode Matching - Finite Element - Spectral Decomposition Approach for the Analysis of Large Finite Arrays of Horn Antennas |
| Abstract: | In this paper a Mode Matching / Finite Element / Spectral Decomposition (MM/FE/SD) approach is applied to the analysis of finite but large arrays of horn antennas. The proposed methodology retains advantages from the three involved techniques: the SD reduces the finite problem to a superposition of infinite periodic ones, whereas the flexibility of the FE method allows us to model complex irregular structures providing a very high degree of generality. A key step in the analysis consists of resorting to a stepped waveguide model of the longitudinal inner profile of the elementary horn antenna. The numerical efficiency of the MM procedure ensures the continuity of transverse fields over each waveguide discontinuity and over the radiating aperture. The methodology presented here is applied to array with elements arranged in polygonal shape. |
| Author(s): | A. Pellegrini, S. Bertini, A. Monorchio, G. Manara |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 438 KB |
| Title: | Iterative Physical Optics for Radar Scattering Predictions |
| Abstract: | The iterative physical optics (IPO) method is applied to compute the radar cross section of electrically large and realistically complex targets. The method is based on iterative refinement of the first-order physical optics currents to include multiple interactions up to a specified order. Unlike other high-frequency asymptotic methods, no ray tracing is required, and spurious diffraction effects from non-physical shadow boundaries are avoided. Numerical results are presented to demonstrate convergence, accuracy, efficiency and robustness. |
| Author(s): | R. J. Burkholder, Ç. Tokgöz, C. J. Reddy, W. O. Coburn |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 1439 KB |
| Title: | Fast Multipole Method Accelerated by Lifting Wavelet Transform Scheme |
| Abstract: | The lifting wavelet like transform (LWLT) is applied to the fast multipole method (FMM) to complete the scattering analysis of three-dimensional (3D) objects. The aggregation matrix and disaggregation matrix are sparsified by the LWLT scheme in time. Numerical results for different shaped three-dimensional objects are considered. It is shown that the proposed method can speed up FMM with lower memory required. |
| Author(s): | M. S. Chen, X. L. Wu, W. Sha, Z. X. Huang |
| File Type: | Journal Paper |
| Issue: | Volume: 24 Number: 2 Year: 2009 |
| Download Link: | Click here to download PDF File Size: 1471 KB |