Rao-Wilton-Glisson Basis Research Articles

Exact Evaluation of Retarded-Time Potential Integrals for the RWG Bases

A new analytical approach for obtaining the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Rao-Wilton-Glisson (RWG) basis function is presented. The approach is formulated directly in the time-domain without any assumptions regarding the temporal behavior of the currents represented by the RWG bases. To the best knowledge of the authors, analytical evaluation of the potential integrals due to the RWG bases have not been formulated prior to the present work either in the time domain or the frequency domain. It is shown that the aforementioned potentials are related to the arc segments formed by the intersection of the triangular supports of the RWG basis and the sphere that is centered at the observation point and that has a radius R=ct, where c is the speed of light. In particular, the scalar potential is directly proportional to the total arc length and the vector potential is a function of the bisectors of these arc segments. A simple algorithm to evaluate these quantities is also presented. The validity of the obtained time-domain formulae is demonstrated through comparison of results to those obtained in the frequency domain by using numerical quadrature and transformed into time domain

Alternative implementation of combined‐field integral equation using Rao–Wilton–Glisson basis functions for conducting scatterers

AbstractThis paper presents an alternative combined‐field integral equation (CFIE) for conducting scatterers to surmount the nonuniqueness problem around the interior resonance frequencies. The implementation of an alternative CFIE is simplified by transforming the integrals of electric‐field (EFIE) and magnetic‐field (MFIE) integral equations to be of the same type. Through the method of moments (MoM), the commonly used Rao–Wilton–Glisson (RWG) basis and testing functions are exploited in the calculation of the alternative CFIE impedance matrix. The numerical results are illustrated and compared with those of the MFIE. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 753–756, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21465

Novel Monopolar MFIE MoM-Discretization for the Scattering Analysis of Small Objects

We present a novel method of moments (MoM)-magnetic field integral equation (MFIE) discretization that performs closely to the MoM-EFIE in the electromagnetic analysis of moderately small objects. This new MoM-MFIE discretization makes use of a new set of basis functions that we name monopolar Rao-Wilton-Glisson (RWG) and are derived from the RWG basis functions. We show for a wide variety of small objects -curved and sharp-edged-that the new monopolar MoM-MFIE formulation outperforms the conventional MoM-MFIE with RWG basis functions.

Incorporation of linear-phase progression in RWG basis functions

A linear-phase term is incorporated into the triangular-type Rao–Wilton–Glisson (RWG) vector basis functions in the method of moments (MoM) formulation. The objective consists of including the dominant phase variation of the current density within the basis-functions formulation, thus allowing an efficient representation of the induced current on large bodies using fewer unknowns. Assuming a good estimation of the phase variation, the new MoM formulation with linearly-phased RWG basis functions is shown to greatly relieve the storage and solution time of the conventional MoM with RWG basis functions, while accurately reproducing the scattered fields of some chosen problems. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 44: 106–112, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20560

Iterative-solver convergence for loop-star and loop-tree decompositions in method-of-moments solutions of the electric-field integral equation

Method-of-moments (MoM) solutions of the electric-field integral equation using Rao-Wilton-Glisson (RWG) basis functions suffer from the so-called low-frequency breakdown. Introduction of loop-tree or loop-star decompositions of the basis functions can effectively solve this problem, and a number of papers have been published discussing various aspects with respect to these techniques. Several papers imply that loop-tree or loop-star decompositions may help to improve iterative-solver convergence for the solution of the resulting linear-equation systems. Since only a few results with respect to this issue are available, a study of the frequency-dependent iterative-solver convergence for RWG, loop-tree, and loop-star basis functions was performed. Two metallic scattering objects, with meshes comprising up to 21060 unknowns, were considered. RWG functions were found to provide the best convergence behavior, as long as the frequency considered was high enough to prevent the low-frequency breakdown. Among the loop-tree and loop-star bases, the loop-tree functions were found to be superior to the loop-star functions. The loop-tree functions resulted in good and stable convergence behavior if the number of subdivisions per wavelength was larger than a few hundred. Moreover, it is shown that the so-called loop-tree decomposition can also be viewed as a loop-cotree decomposition if an alternative tree of edges connecting the free vertices of the mesh is constructed.

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.

First Order Triangular Patch Basis Functions for Electromagnetic Scattering Analysis

This paper analyzes a set of first order triangular patch basis functions for the method of moments (MoM) solution of electromagnetic scattering problems, and compares its performance to the traditional Rao-Wilton-Glisson (RWG) basis. These basis functions provide a faster convergence and a smoother surface current representation. It is shown that the computational complexity involved is about the same as the RWG basis, which means that existing computer codes can be adapted to use them with minimal modifications.

MoM antenna simulations, with Matlab: RWG basis functions

The Matlab implementation of an MoM antenna simulation code is presented, primarily (but not exclusively) for educational purposes. The PDE toolbox is used to generate the mesh. Evaluating the MoM matrix entries using the Rao-Wilton-Glisson (RWG) basis functions is discussed. The delta-function generator is used to model the feed point. Built-in Matlab functions are used for post-processing. Results for several examples, including thin-strip dipoles, a monopole on a ground plane and a wide-band slot antenna, are presented.

Implementation of a multilevel fast far-field algorithm for solving electric-field integral equations

The implementation of a multilevel algorithm for the accurate method-of-moments (MoM) solution of the electric-field integral-equation (EFIE) formulation of electromagnetic-wave scattering by arbitrarily shaped objects is described. The technique makes use of the fast far-field algorithm. The Rao–Wilton–Glisson basis set is employed to represent the surface current induced on the scatterer. Numerical results are presented to demonstrate the accuracy which can be achieved with the technique. Despite the use of the far-field approximation, the method presented is a general one and, because of its simplicity, possesses advantages over currently available accelerated numerical iterative solvers for the EFIE.