1536-1225 (c) 2016 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/LAWP.2016.2577599, IEEE Antennas and Wireless Propagation Letters > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) < 1 Abstract—The finite element method is applied to the modeling of fringe currents and fields in a diffraction problem where a perfectly conducting wedge is illuminated by a line source. A spatial superposition approach is employed to compute the fringe currents. The locally-conformal perfectly matched layer (PML) approach is used to truncate the infinitely-long conducting structure in a finite-sized domain. MATLAB codes are developed and some numerical examples are demonstrated. The results are compared with those of the physical theory of diffraction and the method of moments. Index Terms—Diffraction, finite element method (FEM), locally-conformal PML, high frequency asymptotics, physical theory of diffraction (PTD), wedge, fringe waves, fringe currents. I. INTRODUCTION symptotic techniques, such as geometric optics (GO), physical optics (PO), geometric theory of diffraction (GTD), uniform theory of diffraction (UTD) and physical theory of diffraction (PTD), use simplified models of electromagnetic wave reflection, refraction and diffraction for numerical modeling of wave propagation at high frequencies [1]-[7]. The GO method, in homogeneous media, models the electromagnetic waves as rays traveling in straight lines, whereas the PO method deals with more wave-like properties based on Huygens’ principle. Both methods obtain only the reflected and refracted fields on the illuminated side of the object. The PTD method supplements the PO method by considering source induced currents on the surface of the object. It uses non-uniform ("fringe") edge currents to compute the diffracted fields. The PTD computes the fringe fields by subtracting the PO fields from the exact solution. One limitation of high frequency asymptotic methods is that they are defined for some canonical geometries in a homogeneous medium, and it is a difficult task to model complex geometries, inhomogeneous media and arbitrary impedance boundary conditions. Integral or differential equation-based numerical methods [such as finite element method (FEM), method of moments (MoM), finite difference time domain method (FDTD), etc.] Manuscript received February 21, 2016. O. Ozgun is with the Department of Electrical and Electronics Engineering, Hacettepe University, Beytepe, Ankara, Turkey. (e-mail: ozgunozlem@gmail.com, ozlem@ee.hacettepe.edu.tr) L. Sevgi is with the Department of Electrical and Electronics Engineering, Okan University, Istanbul, Turkey. (e-mail: ls@leventsevgi.net) have certain advantages for modeling complex geometries and arbitrary materials. However, they have been rarely used for diffraction and fringe wave modeling because of computational difficulties in handling electrically-large geometries in a finite-sized computational domain. For example, infinitely-long structures must be truncated properly to eliminate artificial reflections due to abrupt truncation of the geometry. There are some studies that apply the numerical methods to the computation of diffracted fields [8]-[12]. In [11], the FEM was applied to the computation of diffracted fields. In this study, the FEM is extended to the extraction of “fringe” currents and fields in a wedge diffraction problem by means of a spatial superposition approach. It is different from [11] in the sense that it focuses on the extraction of fringe fields and currents, which require additional special treatments due to the field-based nature of the FEM. This paper is indeed the first attempt in the literature to show how FEM can be utilized for fringe current and field computations. The proposed approach is validated through various simulations. The results are compared with those of the PTD and MoM. The paper is organized as follows: In Sec. II, the problem is defined and formulated by FEM. In Sec. III, numerical results are demonstrated. In Sec. IV, some conclusions are drawn. II. FORMULATION An electromagnetic (EM) scattering problem is considered, where a wedge structure is illuminated by a line source as shown in Fig. 1(a). The source can be outside or inside the domain. Assuming that the suppressed time-dependence is exp(), the total field outside the wedge satisfies the scalar Helmholtz equation with boundary conditions (BCs) on the perfect electric conductor (PEC) wedge surface as follows: ( ) ( ) ( ) 2 2 s u ku δ ∇ + =- - r r r r (1.a) BC: 0 u = (soft/TMz) (1.b) BC: / 0 u n ∂ ∂ = (hard/TEz) (1.c) where k is the free-space wave number; δ is the Dirac delta function; and rs is the position vector of the source point. For TMz (or soft) polarization, u represents the z-component of the electric field (Ez), whereas it represents the z-component of the magnetic field (Hz) for TEz (or hard) polarization. The FEM is a type of variational method that formulates the problem as a boundary value problem governed by a partial differential equation. The FEM is implemented by using the scattered field formulation. The Helmholtz equation in terms Finite Element Modeling of Fringe Fields in Wedge Diffraction Problem Ozlem Ozgun, Senior Member, IEEE, and Levent Sevgi, Fellow, IEEE A