Browsing by Subject "Integral equations"

Now showing 1 - 20 of 111

Open Access
A novel machine-learning-based method for the fast solution of integral equations for electromagnetic scattering problems
(Institute of Electrical and Electronics Engineers, 2024-09-30) Koç, Enes; Kalfa, Mert; Ertürk, Vakur Behçet
A novel method is proposed for the efficient and accurate iterative solution of frequency domain integral equations that can be used for large-scale electromagnetic scattering problems. The proposed method uses a novel group-by-group interaction scheme for the fast and accurate evaluation of far-zone interactions based on the one-box-buffer scheme during the matrix-vector multiplication at each iteration. Briefly, subdomain basis functions (that are used to model the scatterer) at each box are replaced by a fixed uniform distribution of Hertzian dipoles, and the dipole-to-dipole interactions are inferred in a group-wise manner by using machine learning algorithms. The efficiency and accuracy of the proposed method are assessed by comparing our results for scattering from several conducting geometries with those obtained by the Mie series and multilevel fast multipole algorithm (MLFMA) solutions.
Open Access
Accurate simulation of reflector antennas by the complex source-dual series approach
(Institute of Electrical and Electronics Engineers, 1995-08) Oğuzer, T.; Altıntaş, A.; Nosich, A. I.
The radiation from circular cylindrical reflector antennas is treated in an accurate manner for both polarizations. The problem is first formulated in terms of the dual series equations and then is regularized by the Riemann-Hilbert problem technique. The resulting matrix equation is solved numeridy with a guaranteed accuracy, and remarkably Little CPU time is needed. The feed directivity is included in the analysis by the complex source point method. Various characteristic patterns are obtained for the front and offset-fed reflector antenna geometries with this analysis, and some comparisons are made with the high frequency techniques. The directivity and radiated power properties are also studied.
Open Access
Algebraic acceleration and regularization of the source reconstruction method with the recompressed adaptive cross approximation
(IEEE, 2014) Kazempour, Mahdi; Gürel, Levent
We present a compression algorithm to accelerate the solution of source reconstruction problems that are formulated with integral equations and defined on arbitrary three-dimensional surfaces. This compression technique benefits from the adaptive cross approximation (ACA) algorithm in the first step. A further error-controllable recompression is applied after the ACA. The numerical results illustrate the efficiency and accuracy of the proposed method. © 2014 IEEE.
Open Access
Analysis of a thin, penetrable, and nonuniformly loaded cylindrical reflector illuminated by a complex line source
(Institution of Engineering and Technology, 2017) Oğuzer, T.; Kuyucuoglu, F.; Avgin, I.; Altıntaş, A.
A thin, penetrable, and cylindrical reflector is illuminated by the incident field of a complex source point. The scattered field inside the reflector is not considered and its effect is modelled through a thin layer generalised boundary condition (GBC). The authors formulate the structure as an electromagnetic boundary value problem and two resultant coupled singular integral equation system of equations are solved by using regularisation techniques. The GBC provides us to simulate the thin layer better than the resistive model which is applicable only for very thin sheets. Hence, the more reliable data can be obtained for high-contrast and low-loss dielectric material. The scattering and absorption characteristics of the front-fed and offset reflectors are obtained depending on system parameters. Also, the effects of the edge loading are examined for both E- and Hpolarisations. The convergence and the accuracy of the formulation are verified in reasonable computational running time.
Open Access
Analysis of an arbitrary-profile, cylindrical, impedance reflector surface illuminated by an E-polarized complex line source beam
(VSP BV, 2014) Kuyucuoglu, F.; Oǧuzer, T.; Avgin, I.; Altintas, A.
Electromagnetic scattering from a cylindrical reflector surface having an arbitrary conic section profile is studied. We assumed an electrically thin layer antenna illuminated by a complex line source in E-polarization mode. Our boundary value formulation, without loss of generality, involves an integral equation approach having impedance-type thin-layer boundary conditions. For simplicity, we also considered both faces of the reflector of the same uniform impedance value. Our computation employs the Method of Analytical Regularization (MAR) technique: the integral equations are converted into the discrete Fourier transform domain yielding two coupled dual series equations, which are then solved by the Fourier inversion and Riemann Hilbert Problem techniques. We demonstrate the accuracy and the convergence behaviors of our numerically solved MAR results that can serve as an accurate benchmark for comparison with widely used results obtained by approximate boundary conditions. © 2013 Taylor and Francis.
Open Access
Analysis of circular reflectors by complex source-dual series approach
(IEEE, 1993-06-07) Oğuzer, Taner; Altıntaş, Ayhan; Nosich, A. L.
In the present paper, two dimensional circular reflector antennas are analyzed by a rigorous analytical-numerical technique for both E and H polarization cases. The method is used in combination with the complex source approach. The convergence of the solution is guaranteed and any desired accuracy can be obtained. Some principal results of reflector antennas are examined by the exact circular reflector solution.
Open Access
Analysis of cylindrically conformal antennas using closed-form Green's function representations
(IEEE, 2015-04) Kalfa, Mert; Karan, S.; Ertürk, Vakur B.
Probe-fed microstrip patch antennas and slotted sectoral waveguide array antennas embedded in cylindrically stratified media are analyzed with a hybrid Method of Moments/Green's function technique, where closed-form Green's function representations for electric and magnetic current sources are used as the kernel of the associated integral equations. Various patch and slot antennas are analyzed using the proposed method. Numerical results in the form of input impedance, S-parameters, and radiation patterns are presented and compared to the results obtained from CST Microwave Studio™ and HFSS™.
Open Access
Analysis of double-negative materials with surface integral equations and the multilevel fast multipole algorithm
(IEEE, 2011) Ergül O.; Gürel, Levent
We present a fast and accurate analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). DNMs are commonly used as simplified models of metamaterials at resonance frequencies and are suitable to be formulated with surface integral equations. However, realistic metamaterials and their models are usually very large with respect to wavelength and their accurate solutions require fast algorithms, such as MLFMA. We consider iterative solutions of DNMs with MLFMA and we investigate the accuracy and efficiency of solutions when DNMs are formulated with two recently developed formulations, namely, the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Numerical results on canonical objects are consistent with previous results in the literature on ordinary objects. © 2011 IEEE.
Open Access
Analysis of finite arrays of axially directed printed dipoles on electrically large circular cylinders
(IEEE, 2004) Ertürk, V. B.; Rojas, R. G.; Lee, K. W.
Various arrays consisting of finite number of printed dipoles on electrically large dielectric coated circular cylinders are investigated using a hybrid method of moments/Green's function technique in the spatial domain. This is basically an "element by element" approach in which the mutual coupling between dipoles through space as well as surface waves is incorporated. The efficiency of the method comes from the computation of the Green's function, where three types of spatial domain Green's function representations are used interchangeably, based on their computational efficiency and regions where they remain accurate. Numerical results are presented in the form of array current distributions, active reflection coefficient and far-field pattern to indicate the efficiency and accuracy of the method. Furthermore, these results are compared with similar results obtained from finite arrays of printed dipoles on grounded planar dielectric slabs. It is shown that planar approximations, except for small separations, can not be used due to the mutual coupling between the array elements. Consequently, basic performance metrics of printed dipole arrays on coated cylinders show significant discrepancies when compared to their planar counterparts. © 2004 IEEE.
Open Access
Analysis of finite arrays of circumferentially oriented printed dipoles on electrically large cylinders
(Wiley, 2004) Ertürk, V. B.; Güner, B.
An efficient and accurate hybrid method of moments (MoM)/Green's function technique in the spatial domain is developed for the rigorous analysis of large, finite phased arrays of circumferentially oriented printed dipoles on electrically large, dielectric-coated, circular cylinders. Basic performance metrics (in the form of array current distribution, active reflection coefficient, far-field patterns, and so forth) of several arrays have been obtained and compared with similar printed arrays on grounded planar substrates. Certain discrepancies have been observed and discussed. © 2004 Wiley Periodicals, Inc.
Open Access
Analysis of Lossy Dielectric Objects with the Multilevel Fast Multipole Algorithm
(IEEE, 2011) Ergul, O.; Gurel, Levent
Rigorous solutions of electromagnetics problems involving lossy dielectric objects are considered. Problems are formulated with two recently developed formulations, namely, the combined-tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE), and solved iteratively using the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of solutions are compared for different objects and conductivity values. We show that iterative solutions of CTF are significantly accelerated as the conductivity increases and CTF becomes a good alternative to JMCFIE in terms of efficiency. Considering also its high accuracy, CTF seems to be a suitable formulation for the analysis of lossy dielectric objects.
Open Access
Anisotropy sensitivity of an acoustic lens with slit aperture
(IEEE, 1993) Atalar, Abdullah; Ishikawa, I.; Ogura, Y.; Tomita, K.
A conventional spherical acoustic lens is modified by restricting its aperture in the form of a slit to provide directional sensitivity. The spacing between the two parallel absorbing sheets forming the slit is adjustable to obtain varying slit widths. The resulting lens can be used in conjunction with V(Z) method to obtain leaky wave velocities of the sample under investigation as a function of direction. The theoretical V(Z) analysis of the lens involves a two-dimensional integral rather than one-dimensional integral of the conventional lens. Single crystal anisotropic materials are chosen as test samples. Reflection coefficients for anisotropic single crystals of given surface cut and orientation are calculated. Numerically evaluated V(Z) curves are used to deduce the surface wave velocity of the object for the given orientation. This is compared with the surface wave velocity directly calculated from the elastic parameters of the object. Results show the compromise between signal-to-noise ratio and angular resolution as the slit width is varied. V(Z) measurement results of a slitted lens are presented to be compared with calculated curves. The new lens is used to measure the acoustic velocity on the (001) surface of GaAs along varying directions with differing slit widths.
Open Access
Approaches for inequity-averse sorting
(Elsevier, 2016) Karsu, Ö.
In this paper we consider multi-criteria sorting problems where the decision maker (DM) has equity concerns. In such problems each alternative represents an allocation of an outcome (e.g. income, service level, health outputs) over multiple indistinguishable entities. We propose three sorting algorithms that are different from the ones in the current literature in the sense that they apply to cases where the DM's preference relation satisfies anonymity and convexity properties. The first two algorithms are based on additive utility function assumption and the third one is based on the symmetric Choquet integral concept. We illustrate their use by sorting countries into groups based on their income distributions using real-life data. To the best of our knowledge our work is the first attempt to solve sorting problems in a symmetric setting.
Open Access
Approximate MLFMA as an efficient preconditioner
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.
Open Access
Approximate Schur preconditioners for efficient solutions of dielectric problems formulated with surface integral equations
(IEEE, 2009-07) Malas, Tahir; Gürel, Levent
We propose direct and iterative versions of approximate Schur preconditioners to increase robustness and efficiency of iterative solutions of dielectric problems formulated with surface integral equations. The performance of these preconditioners depends on the availability of fast and approximate solutions to reduced matrix systems. We show that sparse-approximate-inverse techniques provide a suitable mechanism for this purpose. The proposed preconditioners are demonstrated to significantly improve convergence rates of dielectric problems formulated with two different surface integral equations. ©2009 IEEE.
Open Access
Closed-form Green's functions for general sources and stratified media
(Institute of Electrical and Electronics Engineers, 1995-07) Dural, G.; Aksun, M. I.
The closed-form Green's functions of the vector and scalar potentials in the spatial domain are presented for the sources of horizontal electric, magnetic, and vertical electric, magnetic dipoles embedded in general, multilayer, planar media. First, the spectral domain Green's functions in an arbitrary layer are derived analytically from the Green's functions in the source layer by using a recursive algorithm. Then, the spatial domain Green's functions are obtained by adding the contributions of the direct terms, surface waves, and complex images approximated by the Generalized Pencil of Functions Method (GPOF). In the derivations, the main emphasis is to put these closed-form representations in a suitable form for the solution of the mixed potential integral equation (MPIE) by the method of moments in a general three-dimensional geometry. The contributions of this paper are: 1) providing the complete set of closed-form Green's functions in spectral and spatial domains for general stratified media; 2) using the GPOF method, which is more robust and less noise sensitive, in the derivation of the closed-form spatial domain Green's functions; and 3) casting the closed-form Green's functions in a form to provide efficient applications of the method of moments.
Open Access
Combined-field solution of composite geometries involving open and closed conducting surfaces
(IEEE, 2005-04) Ergül, Özgür; Gürel, Levent
Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative solutions of these problems are now achieved with significantly improved efficiency compared to the EFIE solution, without sacrificing the accuracy. © 2005 ACES.
Open Access
Compact optical temporal processors
(Optical Society of America, 1995) Mendlovic, D.; Melamed, O.; Özaktaş, Haldun M.
Optical signal processing can be done with time-lens devices. A temporal processor based on chirp-z transformers is suggested. This configuration is more compact than a conventional 4-f temporal processor. On the basis of implementation aspects of such a temporal processor, we did a performance analysis. This analysis leads to the conclusion that an ultrafast optical temporal processor can be implemented.
Open Access
Comparison of surface-modeling techniques
(IEEE, 1997-07) Sertel, Kubilay; Gürel, Levent
Solution techniques based on surface integral equations are widely used in computational electromagnetics. The accurate surface models increase the accuracy solutions by using exact and flat-triangulation models for a sphere. For a required solution accuracy, the problem size is significantly reduced by using geometry models for the scatterers. The dependence of the accuracy of the solution on the geometry modeling is investigated.
Open Access
Comparisons of FMM implementations employing different formulations and iterative solvers
(IEEE, 2003-06) Gürel, Levent; Ergül, Özgür
The implementation of multi-level fast multipole algorithm (MLFMA) requires the consideration of several parameters. The preferred combination of the parameters given is not trivially obvious and requires a careful investigation. This paper extensively investigates such parameters by using a series of scattering problems of various sizes containing different numbers of unknowns as a testbed.