Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization

Nosich, A.A.; Gandel, Y.V.; Magath, T.; Altintas, A.

doi:10.1364/josaa.24.002831

Cited by 26 publications

(14 citation statements)

References 21 publications

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“…, where is the real position vector and ib is the complex vector, which characterizes the beam direction and its width (see [3][4][5] and [9,10] for details).…”

Section: Formulationmentioning

confidence: 99%

“…However these papers did not present reliable numerical data for arbitrary profiles; nor they attacked electrically larger geometries. A different numerical approach is based on the Nystrom-type interpolation techniques, which are efficient for large reflectors up to quasioptical size and multi-reflector configurations [8][9][10]. In all above mentioned studies the solutions have been performed only for perfectly electric conducting (PEC) zero-thickness surfaces.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of an arbitrary profile reflector antenna having resistive-type surface — H-polarization case

Oğuzer

Altintas

Nosich

2008

2008 12th International Conference on Mathematical Methods in Electromagnetic Theory

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A regularization-based numerical solution is obtained for arbitrary-shape conic section profile reflector antenna in 2-D, for the H-polarization case. New point is that the reflector surface is assumed a resistive-type material. The problem is treated by reducing the singular integral equation obtained from the boundary condition to the dual series equations and application of the Riemann Hilbert Problem (RHP) technique. The resulting matrix equation has regularized form. Sample numerical results are obtained for various values of the eccentricity of the conic section contour of reflector and the resistivity of its surface. INTRODUCTION:Reflector antennas have originally 3-D geometry but sometimes nearly 2-D cylindrical reflectors are also used in practice; besides, these 2-D reflectors can be considered as canonical shapes to validate the numerical analysis methods. In real applications large dishes are mostly used and can be simulated by high-frequency ray-tracing techniques like GTD, UTD, PO and PTD. However, these techniques do not produce a single solution valid in all directions. Still they are erroneous in the caustic and transition regions. In the simulations of 2-D reflectors, Wiener-Hopf method based analytical treatment has been applied and certain asymptotic results have been obtained in [1], however they have a limited validity. On the other hand purely numerical techniques can also be applied to the reflector antenna problems. Method-of-Moments (MoM) with local basis functions is a standard tool in electromagnetics, however it is efficient only for small or medium size single-reflector geometries. Moreover, MoM does not guarantee the accuracy and the convergence of the performed numerical solution.An alternative for the same 2-D reflector antenna problem is the method of analytical regularization (MAR) [2]. With MAR, a part of the full-wave operator is inverted analytically and the resulting operator equation having favorable features is solved numerically. RHP based solutions are examples of the MAR. In [3], RHP based solutions were built for the analysis of the circular-strip 2-D reflector antenna problems for the both polarizations. These RHP based solutions provide fast convergence and easily controlled accuracy. In [4] and [5], the conic-section-profile reflectors excited by complex-source-point (CSP) feeds were analyzed and the regularized solutions were obtained. Similar MAR-type algorithms have been also proposed based on different techniques. For example, projection on Chebyshev polynomials and Jacobi polynomials was suggested in [6] and [7], respectively. However these papers did not present reliable numerical data for arbitrary profiles; nor they attacked electrically larger geometries. A different numerical approach is based on the Nystrom-type interpolation techniques, which are efficient for large reflectors up to quasioptical size and multi-reflector configurations [8][9][10]. In all above mentioned studies the solutions have been performed only for perfectly electric cond...

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“…, where is the real position vector and ib is the complex vector, which characterizes the beam direction and its width (see [3][4][5] and [9,10] for details).…”

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of an arbitrary profile reflector antenna having resistive-type surface — H-polarization case

Oğuzer

Altintas

Nosich

2008

2008 12th International Conference on Mathematical Methods in Electromagnetic Theory

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“…The Nystrom-type methods are popular methods of numerical solution of boundary integral equations of mathematical diffraction theory [1,2,3,4]. In the countries of the former Soviet Union, some variants of Nystromtype methods are called methods of discrete vortices [5,6] or methods of discrete singularities [7].…”

Section: Introductionmentioning

confidence: 99%

“…In the countries of the former Soviet Union, some variants of Nystromtype methods are called methods of discrete vortices [5,6] or methods of discrete singularities [7]. In the articles [1,2,3,4] and many others (see. [8]) the solution of mathematical electrodynamics problems is carried out in two stages.…”

Section: Introductionmentioning

confidence: 99%

The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

V.N.¹,

V.²,

Dushkin³

2014

AJAMS

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In this article the method for numerical solution of boundary integral equations of the original problem is proposed. This method is one of the modifications of Nystrom-type methods; particularly the method of discrete vortices. The convergence of the numerical solutions to the exact solution of the problem is guaranteed by propositions proved in this article. Also, the rate of convergence of the approximate solutions to the exact solution had been found. Keywords: singular integral equation, modification of method of discrete vortices, existence of approximate solution, the rate of convergence of the approximate solutionsCite This Article: Maurya V.N., Gandel Yu. V., and Dushkin V.D., "The Approximate Method for Solving the Boundary Integral

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“…The alternative to MAR is the meshless Nystrom-type numerical algorithms having guaranteed convergence and developed recently for 2-D problems [11], [12], [31]. Here, the current density is sought as a product of unknown smooth function and known weight.…”

Section: Introductionmentioning

confidence: 99%

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

Bulygin

Nosich

Gandel³

2012

IEEE Trans. Antennas Propagat.

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Time-harmonic electromagnetic wave diffraction by a perfectly electrically conducting (PEC) finite rotationally symmetric surface located in free space is investigated. The problem is split to independent azimuth orders and reduced to the sets of coupled hypersingular and singular integral equations (IEs) for the surface current components. These IEs are discretized by the Nystrom-type method of discrete singularities using the interpolation type quadrature formulas. From the solutions of corresponding matrix equations the near-and the far-field patterns are obtained. The presented method has guaranteed convergence for arbitrary not axially symmetric primary field.Index Terms-Body of revolution (BOR), focusing, interpolation type quadrature formulas, radar cross-section, scattering, singular and hypersingular integral equations.

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Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom's discretization

Cited by 26 publications

References 21 publications

Analysis of an arbitrary profile reflector antenna having resistive-type surface — H-polarization case

Analysis of an arbitrary profile reflector antenna having resistive-type surface — H-polarization case

The Approximate Method for Solving the Boundary Integral Equations of the Problem of Wave Scattering by Superconducting Lattice

Nystrom-Type Method in Three-Dimensional Electromagnetic Diffraction by a Finite PEC Rotationally Symmetric Surface

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