RWG Functions Research Articles

Analysis of scattering from multi-scale and multiple targets using characteristic basis function (CBFM) and integral equation discontinuous Galerkin (IEDG) methods

In this paper, the characteristic basis function method is adapted to analyze the problem of scattering from multiple and multi-scale impenetrable targets in conjunction with the discontinuous Galerkin method, and the monopolar RWG functions are chosen as the basis functions. This method enables us to analyze multiple and multi-scale targets using nonconforming discretizations. The use of the CBFs helps reduce the size of the impedance matrix of the associated method of moment significantly, enabling us to employ direct solvers as opposed to iterative solvers. The process of generating the reduced matrix is naturally parallel, and the reduced matrix is well conditioned, which obviates the need for pre-conditioning. In addition, the adaptive cross-approximation algorithm is implemented to reduce the complexity of the computation. Numerical results are included to demonstrate the accuracy and efficiency of the present approach when analyzing scattering from multiple and multi-scale targets using nonconforming discretizations.

Tangential-Normal Surface Testing for the Nonconforming Discretization of the Electric-Field Integral Equation

Nonconforming implementations of the electric-field integral equation (EFIE), based on the facet-oriented monopolar-RWG set, impose no continuity constraints in the expansion of the current between adjacent facets. These schemes become more versatile than the traditional edge-oriented schemes, based on the RWG set, because they simplify the management of junctions in composite objects and allow the analysis of nonconformal triangulations. Moreover, for closed moderately small conductors with edges and corners, they show improved accuracy with respect to the conventional RWG-discretization. However, they lead to elaborate numerical schemes because the fields are tested inside the body, near the boundary surface, over volumetric subdomains attached to the surface meshing. In this letter, we present a new nonconforming discretization of the EFIE that results from testing with RWG functions over pairs of triangles such that one triangle matches one facet of the surface triangulation and the other one is oriented perpendicularly, inside the body. This “tangential-normal” testing scheme, based on surface integrals, simplifies considerably the matrix generation when compared to the volumetrically tested approaches.

Uniform Surface Integral Equation Formulation for Mixed Impedance Boundary Conditions

A numerical approach based on the surface integral equation (SIE) method is developed for the analysis of time-harmonic electromagnetic scattering by impenetrable objects equipped with mixed impedance boundary conditions (MIBCs). MIBC is an axially anisotropic generalization of the conventional isotropic (Leontovich) impedance boundary condition. The developed SIE formulation utilizes surface Helmholtz decomposition, the self-dual formulation of Yan and Jin, and loop and star RWG functions. A combined field formulation is applied to avoid internal resonances.

Integral Equation-Based Nonoverlapping DDM Using the Explicit Boundary Condition

A new integral equation-based nonoverlapping domain decomposition method (NDDM) is proposed for analyzing electromagnetic (EM) scattering from electrically large PEC objects whose MLFMA models are too large for the user’s computer to accommodate. The integral equation is first built on the entire PEC surface, and the entire surface is partitioned into some nonoverlapping subsurfaces. The RWG functions are used to expand the surface current on the entire surface. Then, each full-RWG function across some boundary curve is split into two half-RWG functions whose unknown coefficients are constrained by the boundary current continuity (using the explicit boundary condition). The convergence of the outer-iterative scheme of the proposed NDDM is investigated theoretically and demonstrated to be very good, and hence a very large problem can be effectively solved in an ordinary computer. Some numerical examples are provided to demonstrate the correctness and robustness of the proposed method, and to compare the proposed method with the existing overlapping DDMs having similar attributes.

Comments on "The Use of Curl-Conforming Basis Functions for the Magnetic-Field Integral Equation

This paper discusses the author's comments regarding the sentence in the third paragraph of [(O. Ergul et al., 2005), subsection B in Section III], where the authors argue that "the diagonal elements of the impedance (MoM-MFIE) matrices are the same for the implementations of the nxRWG and RWG functions." The authors believe that this cannot be stated in general. The reply of the authors of (O. Ergul et al., 2005) regarding the comment made is also discussed in this paper.

Solution of volume‐surface integral equations using higher‐order hierarchical Legendre basis functions

The problem of electromagnetic scattering by composite metallic and dielectric objects is solved using the coupled volume‐surface integral equation (VSIE). The method of moments (MoM) based on higher‐order hierarchical Legendre basis functions and higher‐order curvilinear geometrical elements is applied to transform the VSIE into a system of linear equations. The higher‐order MoM provides significant reduction in the number of unknowns in comparison with standard MoM formulations using low‐order basis functions, such as RWG functions. Owing to the orthogonal nature of the higher‐order Legendre basis functions, the continuity condition at the interface between metal and dielectric can be satisfied explicitly, which further reduces the number of unknowns as well as improves the accuracy of the solution. Numerical results for a metallic sphere with dielectric coating show excellent agreement with the analytical Mie series solution. Scattering by more complex metal‐dielectric objects is also considered to compare the presented technique with other numerical methods.

TD-CFIE Formulation for Transient Electromagnetic Scattering from 3-D Dielectric Objects

In this paper, we present a time domain combined field integral equation formulation (TD-CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space-time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.

Accurate Analysis of Arbitrarily Shaped Wire Antenna-Dielectric Radome Structures

In this letter, the performance of wire antennas enclosed by a small/moderate-size dielectric radome with arbitrary shape is investigated by using the coupled surface integral equation (CSIE). PMCHWT formula is applied on the surfaces of the radome, while the EFIE is employed to model the equivalent strip structure of wire antennas. The advantages of this approach over other methods are (1) all of the mutual interactions between antennas and radome are taken into account so that the performance of the composite antenna-radome system can be predicted rigorously and accurately; (2) one can use only one type of basis function (e.g. RWG functions) to represent the equivalent currents on both antenna and radome surfaces; (3) A simple delta-gap feed model can be conveniently incorporated in the method of moments (MoM) with good accuracy. Numerical results of wire antenna covered by radomes with both spherical shell and Von Karman shapes are presented to validate the proposed method.

Using UV technique to accelerate the MM-PO method for three-dimensional radiation and scattering problem

An UV method, method of moments (MoM), physic-optic method (UV-MM-PO) hybrid technique is proposed to analyze the large-scale electromagnetic problems. In this new method, the UV decomposition technique is used to accelerate the conventional MM-PO hybrid method. With this hybrid technique, the problem is divided to MM region and PO region, and the currents are all expanded by RWG functions. The expression of interaction matrix between MM region and PO region are reformulated as a combination of two matrices: one is only related to the direction of basis functions and another is only related to the distance between source and field. The elements of the latter are smooth, and this matrix propitiously dealt with by using the UV technique. With the sampling process of the UV technique, only a few elements of the interaction matrix should be calculated, and the computational efficiency can be improved evidently. Calculated examples show that the results of this method approach those of the MM-PO method, while the computation time is much less than the latter. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1615–1618, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21685

Transmission through arbitrary apertures in metal-coated dielectric bodies

We present a new variational direct boundary integral equation approach for solving the scattering and transmission problem for dielectric objects partially coated with a PEC layer. The main idea is to use the electromagnetic Calderon projector along with transmission conditions for the electromagnetic fields. This leads to a symmetric variational formulation which lends itself to Galerkin discretization by means of divergence conforming discrete surface currents (aka RWG functions). Several numerical experiments confirm the efficacy of the new method.

Calculation of cfie impedance matrix elements with RWG and n x RWG functions

The method of moments (MoM) solution of combined field integral equation (CFIE) for electromagnetic scattering problems requires calculation of singular double surface integrals. When Galerkin's method with triangular vector basis functions, Rao-Wilton-Glisson functions, and the CFIE are applied to solve electromagnetic scattering by a dielectric object, both RWG and n/spl times/RWG functions (n is normal unit vector) should be considered as testing functions. Robust and accurate methods based on the singularity extraction technique are presented to evaluate the impedance matrix elements of the CFIE with these basis and test functions. In computing the impedance matrix elements, including the gradient of the Green's function, we can avoid the logarithmic singularity on the outer testing integral by modifying the integrand. In the developed method, all singularities are extracted and calculated in closed form and numerical integration is applied only for regular functions. In addition, we present compact iterative formulas for computing the extracted terms in closed form. By these formulas, we can extract any number of terms from the singular kernels of CFIE formulations with RWG and n/spl times/RWG functions.

Application of a novel CFIE for electromagnetic scattering by dielectric objects

AbstractIn this Letter a new type of combined field integral equation (CFIE) is proposed and applied for electromagnetic scattering by three‐dimensional dielectric objects of arbitrary shape. In this formulation, traditional CFIE is applied outside the object, and inside the object the electric and magnetic field integral equations are combined by changing their roles. This formulation gives a more stable solution than the traditional CFIE when the method of moments with Galerkin's type testing and RWG functions is applied. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 35: 3–5, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10500

Rigorous combined mode-matching integral equation analysis of horn antennas with arbitrary cross section

A combined rigorous method is presented for the analysis of horn antennas with arbitrary cross section and general outer surface. The horn taper is described by the mode-matching (MM) method where the cross-section eigenvalue problem is solved by a two-dimensional (2-D) finite element (FE) technique. For the exterior horn surface including the radiating aperture, the application of the Kirchhoff-Huygens principle yields two expressions for the admittance matrix which are based on the electric (EFIE) and the magnetic (MFIE) field integral equation, respectively. The equations are solved numerically by the method of moments (MoM). For the preferred EFIE formulation, the eigenvectors of the last waveguide taper section and RWG functions for triangular patches are utilized as basis-functions for the magnetic or electric surface current densities, respectively. The presented method is verified by available reference values or measurements for a waveguide radiator with a peripheral choke, a conical and a rectangular horn. Its flexibility is demonstrated at the example of a conical ridged waveguide horn.