Rao-Wilton-Glisson Basis Functions Research Articles

Numerical study of a novel MFIE formulation using monopolar RWG basis functions

Numerical character of a new magnetic field integral equation (MFIE) formulation solved by the method of moments (MoM) is studied. In this new formulation, monopolar Rao–Wilton–Glisson (RWG) functions are used as both the basis and the testing functions. Calculation details for the impedance matrix elements of this new formulation are presented with a form suitable for programming. Numerical results for electromagnetic scattering analysis of several small sharp-edged conducting objects show that the new formulation using the monopolar RWG basis functions is much more accurate than the traditional one using the RWG and the monopolar RWG basis functions.

Application of a novel formulation to the MFIE using RWG basis functions in method of moments

We investigate the inaccuracy of the traditional magnetic field integral equation (MFIE) in the analysis of scattering of small conducting objects, with the use of Rao–Wilton–Glisson (RWG) basis functions. As a remedy to such problems, we propose to use a novel impedance matrix elements (IME) formulation of the MFIE, which is suitable to use RWG basis functions. Techniques to calculate the IME of the new formulation are outlined. It is shown that similar technique to compute the IME of the MFIE resulted from the use of curl-conforming basis functions can also be used here. Based on the examples of several relatively small conducting objects, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained for this new IME formulation with the use of RWG basis functions.

Improving the accuracy of the magnetic field integral equation with the use of a new impedance matrix element formulation

The electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are widely used in conjunction with method of moments for electromagnetic scattering analysis of three-dimensional conducting objects with closed surfaces. However, the MFIE suffers from an accuracy problem compared with the EFIE with the use of the Rao–Wilton–Glisson (RWG) basis function. This accuracy problem is more serious for objects with sharp edges or corners. To solve this problem, a new technique to compute the impedance matrix elements (IME) of the MFIE using an RWG basis function is presented here. Details to compute the IME and the advantage of this new formulation are displayed. In addition, the relationship between this new IME formulation and the formulation using the low-order curl-conforming basis function for the MFIE is given. Through the computation of the RCS of several relatively small sharp-edged conducting objects, it is shown that the accuracy of the MFIE can be greatly improved by the use of the new IME formulation.

A Simple Strip Model in the Volume-Surface Integral Equation for Analysis of Arbitrary Probe-Fed Conformal Microstrip Antennas

A strip model is incorporated in the volume-surface integral equation (VSIE) to simplify the analysis of the probe-fed conformal microstrip antennas (CMSAs) with arbitrary shapes. The thin wire-surface junction of the feeding probe and the patch is transferred to the surface-surface junction that can be modeled by using Rao-Wilton-Glisson (RWG) basis functions easily. Thus, the use of complicated attachment mode basis function in the conventional VSIE is eliminated, which simplifies the calculation of the method-of-moments (MoM) matrix. The construction of RWG basis functions at the surface-surface junction is detailed as well. An effective remedy is also proposed to overcome the computation breakdown in the near-singularity treatment when the field point locates at the extension of one side of the source domain. Numerical results show the reliability and accuracy of the proposed method.

A quantitative study on the low frequency breakdown of EFIE

AbstractA quantitative study is presented for the low frequency breakdown of the electric‐field integral equation (EFIE) with the Rao–Wilton–Glisson basis function. The low frequency limit is ascertained hereby. Numerical experiments validate the conclusion. The line testing method is also compared with the Galerkin testing to dispel the misconception in the literature. The study thus provides a guideline for the application of EFIE in the full‐field regime. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1159–1162, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23324

Hybrid Lifting Wavelet-Like Transform for Solution of Electromagnetic Integral Equation

A hybrid lifting wavelet-like transform scheme is successfully applied to the solution of electric field integral equation using Rao–Wilton–Glisson basis functions. To speed up the matrix transform process, the lifting scheme is adopted. Numerical examples of different three-dimensional perfectly electric conducting objects are considered. Compared with the method of moments, the proposed matrix transform scheme can save considerable CPU time and memory.

The use of curl-conforming basis functions for the magnetic-field integral equation

Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming n~×RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel fast multipole algorithm. Based on the examples of electromagnetic modelling of conducting scatterers, it is demonstrated that significant improvement in the accuracy of the MFIE can be obtained by using the curl-conforming n~×RWG functions.

An RWG Basis Function Based Near- to Far-Field Transformation for 2-D Triangular-Grid Finite Difference Time Domain Method

A near- to far-field transformation (NTFT) based on the Rao-Wilton-Glisson (RWG) basis function is proposed for a 2-D triangular-grid FDTD method. The surface equivalence theorem is applied and the equivalent current density, J/sub z/ in the TM/sub z/ case or M/sub z/ in the TE/sub z/ case, on the radiation contour is interpolated by using RWG basis functions. The interpolation is valid for the NTFT in either the time or frequency domain. Formulations for the interpolation scheme and the NTFT are presented for the TM/sub z/ case. The scattering by an infinite dielectric circular cylinder due to an electric line source is simulated by using the triangular-grid FDTD as well as the proposed NTFT. Numerical results in both the time domain and frequency domain are demonstrated and verified by comparison with analytical solutions.

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.

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.