RWG Basis Research Articles

Windowed Green Function MoM for Second-Kind Surface Integral Equation Formulations of Layered Media Electromagnetic Scattering Problems

This paper presents a second-kind surface integral equation method for the numerical solution of frequency-domain electromagnetic scattering problems by locally perturbed layered media in three spatial dimensions. Unlike standard approaches, the proposed methodology does not involve the use of layer Green functions. It instead leverages an indirect M\"uller formulation in terms of free-space Green functions that entails integration over the entire unbounded penetrable boundary. The integral equation domain is effectively reduced to a small-area surface by means of the windowed Green function method, which exhibits high-order convergence as the size of the truncated surface increases. The resulting (second-kind) windowed integral equation is then numerically solved by means of the standard Galerkin method of moments (MoM) using RWG basis functions. The methodology is validated by comparison with Mie-series and Sommerfeld-integral exact solutions as well as against a layer Green function-based MoM. Challenging examples including realistic structures relevant to the design of plasmonic solar cells and all-dielectric metasurfaces, demonstrate the applicability, efficiency, and accuracy of the proposed methodology.

Application of the Method of Moments with RWG Basis Functions in Problems of Diffraction by Plates with Similar Geometries

Application of the Method of Moments with RWG Basis Functions in Problems of Diffraction by Plates with Similar Geometries

CFIE-Based DDM With Full Exploitation of BoR Basis for Scattering From Compound BoR-and-Non-BoR PEC Object

A true domain decomposition method based on a combined field integral equation has been developed for scattering analysis of a combinational PEC structure comprising body of revolution (BoR) and non-BoR parts. Utilizing the method of moments (MoM), the surface currents of BoR and non-BoR parts are expanded by the BoR and RWG basis functions, respectively. BoR basis functions are exploited in calculating both self-coupling and mutual-coupling matrices. The proposed method has the accuracy of MoM, while the number of unknowns is considerably reduced due to converting the 3-D problem to a 2-D one in the BoR part. The correctness and robustness of this approach are verified by numerical results, and significant improvement in the efficiency in terms of both the computational time and memory consumption in comparison with the conventional RWG-RWG IE-domain decomposition method (DDM) is observed.

Multibranch Rao–Wilton–Glisson Basis Functions for Electromagnetic Scattering Problems

A multibranch Rao–Wilton–Glisson (MB-RWG) basis function is proposed in this article, which is composed of one positive triangle with a larger edge length and several negative triangles with smaller edge lengths. All negative triangles are aggregated to replace the negative triangle in the traditional RWG basis function, with exactly the same function expression defined on the triangles. The number of negative triangles can be changed in different mesh structures. Similar to traditional RWG basis functions, the proposed MB-RWG basis functions guarantee normal current continuity across the common edges. No line charges exist and the total charge on one MB-RWG is zero. MB-RWG basis functions can be used very conveniently to connect one surface with a coarse mesh scheme to another with a fine mesh scheme and can be flexibly applied in the domain decomposition method (DDM). Numerical results validate the accuracy and demonstrate the versatility of the proposed basis function in modeling multiscale perfect electrically conducting (PEC) objects.

On the Use of Hybrid CFIE–EFIE for Objects Containing Closed–Open Surface Junctions

To effectively solve the electromagnetic scattering or radiation properties from the perfect electric conductor objects containing closed-open surface junctions, how to establish the hybrid combined field integral equation-electric field integral equation (CFIE-EFIE) is studied, which is different from the existing scheme for the objects, where the closed and open parts are separate. Furthermore, it is found that when the integral equation is solved using the method of moments, if the widely used RWG basis functions are employed to expand the induced surface current, the CFIE-EFIE may give inaccurate numerical results for the objects containing fine structures. The numerical accuracy can be improved by introducing the linear-linear (LL) basis functions. Moreover, to pursue a high computational efficiency, the LL and RWG basis functions are simultaneously used to expand the current on the fine structures and other relatively smooth surfaces, respectively, whose validity is verified by the numerical results.

A Chebyshev-Based High-Order-Accurate Integral Equation Solver for Maxwell’s Equations

This article introduces a new method for discretizing and solving integral equation formulations of Maxwell's equations, which achieves spectral accuracy for smooth surfaces. The approach is based on a hybrid Nyström-collocation method using Chebyshev polynomials to expand the unknown current densities over curvilinear quadrilateral surface patches. As an example, the proposed strategy is applied to the magnetic field integral equation (MFIE) and the N-Müller formulation for scattering from metallic and dielectric objects, respectively. The convergence is studied for several different geometries, including spheres, cubes, and complex NURBS geometries imported from CAD software, and the results are compared against a commercial Method-of-Moments solver using RWG basis functions.

A well‐conditioned integral equation for electromagnetic scattering from composite inhomogeneous bi‐anisotropic material and closed perfect electric conductor objects

A well-conditioned volume-surface integral equation, called the volume integral equation-combined field integral equation, is applied to analyse electromagnetic (EM) scattering from arbitrarily shaped three-dimensional composite objects comprising both inhomogeneous bi-anisotropic material and closed perfect electric conductors (PECs). The equivalent surface and volume currents are respectively expanded using the commonly used RWG and SWG basis functions, while a matrix equation is derived by the method of moments. Because the magnetic field integral equation is involved in modelling the surface electric current, and the constitutive parameters are all tensors, some new kinds of singularities are encountered and properly handled in the filling process of the impedance matrix. Several numerical results of EM scattering from composite bi-anisotropy and closed PEC objects are shown to illustrate the accuracy and efficiency of the proposed scheme. The validity of the continuity condition of electric flux enforced on the bi-anisotropy-PEC interfaces, which can be used to eliminate the volumetric electric unknowns, is also verified.

The research of magnetic-field integration method based on linear-linear basis functions

Abstract When calculating electromagnetic scattering problems, the RWG basis function is usually used to discretize the target surface. However, the calculation error of magnetic field integral equation based on RWG basis function is often large. In order to solve this problem, linear-linear basis functions are proposed to be applied to the magnetic field integral equation to calculate the scattering of the target structure. In this paper, the matrix impedance elements of the magnetic field integral equation filled with linear-linear basis functions are derived and programmed, and then the RCS of the target structure is calculated. The results show that the linear-linear basis function can effectively improve the accuracy and educe the error of the magnetic field integral equation while using the same or even larger sectionals to fit the surface of the target scatterer, that is, while ensuring that the calculation amount is not increased, compared with the RWG basis function.

An adaptive nested complex source beam method for electromagnetic scattering of composite conducting-dielectric objects

A new nested complex source beam (NCSB) method based on the volume-surface integral equation (VSIE) is proposed for fast electromagnetic scattering analysis of composite conducting-dielectric objects. This scheme is based on the nested equivalent structure of the complex source beams to approximate the far-field interactions of both the RWG basis functions and SWG basis functions with an acceptable accuracy. An adaptive grouping technique is introduced in the traditional NCSB method to adaptively group the model based on the distribution of unknowns. Therefore, the new NCSB method is termed as adaptive nested complex source beam (ANCSB) method. The computational complexity and memory storage with a quasi-linear variation can be realized same as NCSB, and numerical results demonstrate the accuracy and higher efficiency than traditional NCSB for the electromagnetic scattering analysis of composite conducting-dielectric objects.

Uncertainty RCS Computation for Multiple and Multilayer Thin Medium-Coated Conductors by an Improved TDS Approximation

An efficient uncertainty RCS computation technology is proposed to analyze the EM scattering from 3-D medium-coated targets with varying geometrical shapes. First, the scattering target is described by a nonuniform rational B-spline surface, where the uncertain units are described by several independent random variables. Then, an improved thin dielectric sheet-based method of moments is presented to model the scattering from the multiple and multilayer thin medium-coated objects. As a result, only unknowns exist on the target’s outer surface, and the computational resources can significantly be saved in comparison with solvers that associate unknowns with all the surfaces and interfaces. It should also be noted that the half RWG basis functions are introduced at the interface of different media for multiple medium-coated conductors. Finally, both the mean value and variance of the scattering electric current are derived by applying a perturbation approach to account for the target’s uncertain variable geometry. Moreover, the validity of the proposed method is verified in comparison with the traditional Monte Carlo (MC) method, which is used to solve several certain problems, and it is found that the proposed method can provide higher efficiency compared with the MC method.

Electromagnetic scattering from an arbitrarily shaped PEC object coated by spherical dielectric material using equivalence principle algorithm

A new method is presented for the analysis of electromagnetic scattering from arbitrarily shaped PEC object coated by homogeneous spherical dielectric material. The analysis of the internal PEC objects is performed using the equivalence principle algorithm (EPA). First, the scattering operator of EPA is evaluated for the PEC object in terms of RWG basis functions where the background is filled by coating material. Then a translation procedure is introduced to translate scattering operator evaluated in terms of RWG basis functions to a new scattering operator in terms of spherical wave harmonics (SWHs). This new scattering operator relates SWH coefficients of the scattered wave by internal PEC to those of the incident wave. By invoking the boundary conditions on the surface of spherical coating using the mode-matching technique, the coefficients of the scattered wave outside the coating material are evaluated. Since the scattering operator is independent from the coating radius, the problem may be solved by only analysis of boundary conditions on the surface of spherical coating for various values of coating radii without needing to repeat the analysis of internal PEC object. Several numerical examples are investigated to evaluate validity and efficiency of the proposed method.

Application of Equivalence Principle for EM Scattering From Irregular Array of Arbitrarily Oriented PEC Scatterers Using Both Translation and Rotation Addition Theorems

Electromagnetic scattering from irregular array of arbitrarily oriented PEC scatterers is investigated using a novel domain decomposition method based on equivalence principle algorithm (EPA) in conjunction with addition theorems for spherical wave harmonics (SWHs). Each element is considered to be enclosed by a spherical equivalence surface as a single domain. The primary unknowns on each element are replaced by the equivalent electric and magnetic current distributions on the equivalence sphere in terms of RWG basis functions. From these current distributions, the scattered field outside its equivalence sphere is evaluated in terms of SWHs in the local coordinates system fixed to each element body. The SWHs in rotated local coordinates are translated as a new set of SWHs in other local coordinates with the same origin but axes parallel to the global coordinate’s axes using the rotation addition theorem. Furthermore, the mutual coupling effects among the separated domains are considered using the translation addition theorem for parallel local coordinate systems. It is shown that the proposed method effectively reduces the computational costs by reducing the number of unknowns versus the conventional EPA. The efficiency and validity of the proposed method are investigated through several numerical examples.

Combination of MLFMA and ACA to Accelerate Computation of Scattering from Underground Targets

Electromagnetic nondestructive evaluation of underground targets is of great significance for the safety of urban construction. Based on the accurate and efficient simulation of scattering, we can detect the underground targets successfully. As one of the most popular numerical methods in electromagnetics, surface integral equations solved by method of moments (MoM) are used to simulate the scattering from underground targets in this paper. The integral equation is discretized by RWG basis and Galerkin testing. Multilevel fast multipole algorithm (MLFMA) is used to decrease the computation complexity and memory cost. However, the octree used in MLFMA is not applied for rough surfaces and targets together; both the surface and target need to construct octree separately. Since the combination of MLFMA and ACA can build a more efficient method to compute scattering from underground targets, adaptive cross approximation (ACA) is used to compress the impedance matrix instead of MLFMA for the coupling action between the rough surface and target. That is to say that, when calculating the scattering of two targets, target self-interaction is suitable for MLFMA calculation and the coupling between targets is approximated by ACA. Numerical results demonstrate the accuracy and efficiency of our proposed method.

Efficient Solution of Scattering From Composite Planar Thin Dielectric-Conductor Objects by Volume-Surface Integral Equation and Simplified Prism Vector Basis Functions

Scattering from composite planar thin dielectric-conductor objects is calculated by the hybrid volume-surface integral equation (VSIE) approach. To highly efficient model such objects, the prism elements are used for volume regions instead of general tetrahedral elements, and the simplified prism vector basis functions are proposed so that the volume integral can be simplified into either surface integral or line integral. As a pair, the RWG basis is used for arbitrarily shaped conductor surface. This proposed method has several advantages for objects comprising planar thin dielectric materials. First of all, the use of prism elements can significantly reduce the number of unknowns compared with the general tetrahedral mesh scheme so that the CPU time consumption and memory occupation are reduced. In addition, the prism elements also result in a more convenient meshing procedure. Finally, the simplification of volume integral further reduces the CPU time consumption, while maintaining comparable accuracy. Since the proposed scheme can be easily accelerated by fast algorithms, our VSIE method combined with the multilevel fast multipole algorithm is employed for the scattering analysis from the electrically large objects. Several numerical results are reported to show the good accuracy and efficiency of the proposed method.

A Low-Frequency EFIE-MLFMA Solver Based on Approximate Diagonalization of Green’s Function

The low-frequency fast multipole algorithm (LFFMA) based on the approximate diagonalization of Green’s function for the electric field integral equation (EFIE) is proposed for open and complex structures with high accuracy. Moreover, the multiresolution preconditioner is employed to the mixed potential form of EFIE with RWG basis functions for stability. Herein, a triangle-grouping scheme is adopted for the scalar potential so that the accuracy of the LFFMA can be guaranteed. Furthermore, the computational resources can be reduced largely since part of the radiation pattern of vector potential can share one of the scalar potentials by taking advantage of some mathematical deductions.

An Efficient Marching-on-in-Degree Solution of Transient Multiscale EM Scattering Problems

A marching-on-in-degree (MOD)-based time-domain domain decomposition method is proposed to efficiently analyze the transient electromagnetic scattering from electrically large multiscale targets. The algorithm starts with an octree that divides the whole scattering target into several subdomains. Then using the equivalence principle algorithm, each subdomain is enclosed by an equivalence sphere (ES), where both the RWG and BoR spatial basis functions are employed to expand the unknown currents. The interactions of the near-field subdomains are directly calculated by the method of moments, while the far-field interactions can be converted into the interactions of corresponding ESs. This scheme implicitly satisfies the current continuity condition, and the convergence can be accelerated as well. By harnessing the rotational symmetry of the ESs, the computational resources are reduced significantly compared with the traditional MOD method. Several numerical examples are presented to demonstrate the accuracy and efficiency of the proposed algorithm.

Electromagnetic scattering analysis using nonconformal meshes and monopolar curl-conforming basis functions

A scheme for electromagnetic scattering analysis of perfect electric conducting (PEC) objects using nonconformal meshes is developed in this paper. The difference of the integral operators for the electric field integral equation (EFIE) and the magnetic field integral equation (MFIE) are analyzed in detail. It is shown theoretically that basis functions used to expand the surface currents for the MFIE may not necessarily be divergence-conforming. The nonconformal meshes and monopolar n×RWG basis functions are used together to solve the MFIE. Details for the implementation of the proposed method are presented. The method is verified through the numerical results for electromagnetic scattering analysis from several PEC objects. It is shown that this method is a suitable choice for using nonconformal meshes when solving electromagnetic scattering problems with the MFIE.

Design of a Dual-Band Bidirectional Antenna Using Superellipse-Monopole-Fed Rectangular Ring for IEEE 802.11 a/b/g/n Applications

This paper presents the design of a dual-band bidirectional ring antenna fed by a superellipse surface probe for 2.4/5 GHz WLAN applications. The Method of Moments (MoM) with RWG basis function was utilized in the study and design processes. A prototype antenna was fabricated successfully with the advantages of simple and low-cost structure. The measured impedance bandwidth of 810 MHz (2.10–2.91 GHz) and 2.39 GHz (3.57–5.96 GHz) is achieved for the first and second band, respectively. The peak gains are also feasible, 4.67 dBi at 2.45 GHz and 7.83 dBi at 5.5 GHz, with bidirectional radiation patterns for both bands. From the experimental field tests, the proposed antenna was suitable for most applications in long and narrow communication sites in 2.4/5 GHz bands as desired. Also, the measured and calculated results were in good agreement.

Higher Order MoM Analysis of Traveling-Wave Waveguide Antennas with Matched Waveports

The method of mode matching (MM) is used to construct ideal waveports in the context of the method of moments (MoM). The waveports can provide not only excitations as sources but also perfectly matched loads for traveling-wave slotted waveguide antennas. Additionally, the application of the higher order basis functions (HOBs) in MoM significantly reduces the number of unknowns compared to the RWG basis functions. Numerical results show that the proposed method is accurate and efficient for traveling-wave slotted waveguide antennas. Finally, a Ka-band waveguide array with 1976 narrow-wall slots is solved using a high-performance cluster.

Charge Recovery for the RWG-Based Method of Moments

This letter is concerned with methods of obtaining a better approximation to the true surface charge density on a structure by post-processing the surface divergence of an RWG-based method-of-moments (MoM) solution current. It is shown that derivative recovery techniques developed for the finite element method (FEM) are not suitable. A simple and inexpensive recovery technique based on the properties of RWG basis functions is introduced for charge recovery in the MoM. Satisfactory performance of the proposed method is demonstrated, and its application to a posteriori error estimation is shown.