Fatih Dikmen

Well-conditioned algorithm for scattering by a few eccentrically multilayered dielectric circular cylinders

The new regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering by a few eccentrically multilayered homogenous circular cylinders is presented. It is found out that a regularization of this formulation is absolutely necessary. The two-sided regularization that we made is based on the integral formulation of the mentioned problem. The polarization of the fields are parallel to the longitudinal axes of the cylinders; thus, a two dimensional problem for each both polarizations are under consideration. The condition number of the resulting algebraic system is uniformly bounded while its truncation number increases. The numerical results are validated by existing results such as near and far fields obtained under various geometrical and electrical parameters of the scattering problem. Numerical results including the condition numbers of the regularized and nonregularized systems show that only regularized system gives numerically stable results with any desired accuracy in a wide range of frequencies from quasistatic to rather high-frequency range, limited only by the capabilities of the computer with the guarantee of the physical reliability of the solution.

On Analytical Evaluation of Retarded-Time Potentials for SWG Bases

The Radon transform interpretation of impulsively excited time-domain integrals is recently shown to provide the time samples of these integrals in closed analytical form. Here, the derivation of such formulas for the time samples of the retarded-time scalar and vector potentials due to an impulsively excited Schaubert-Wilton-Glisson (SWG) basis function is accomplished. It was proven conceptually before that the aforementioned potentials are related to the geometrical quantities of the surface of intersection between the tetrahedral supports of the SWG basis and the hyper-cone centered at the observation point with radius ct where c is the speed of light. Analytical evaluation of these quantities involves proper introduction of the corresponding solid-angle and its gradient. Rigorously obtained formulas and numerical results are presented for them.

Modified superformula contours optimized via genetic algorithms for fastly converging 2D solutions of EFIE

It is known that solutions of the integral equations converge at the smoothness rate of the parametrical function representing the boundary contour. Thus using an infinitely smooth parametrical representation with derivatives of all orders results into exponentially converging solutions. A version of superformula tailored for this purpose is exposed to optimization of its parameters via genetic algorithms to obtain smooth parameterization for desired boundaries in two dimensional problems. The convergence of the resulting solutions of the electric-field integral equation will be presented.

Rigorous solution by analytical regularization method to the problem of 2D E-Polarized wave diffraction by a set of PEC surfaces

The analytical regularization method is applied to the problem of 2D E-Polarized wave diffraction by perfectly conductive surfaces consisting of a set of closed and unclosed surfaces. The electromagnetic boundary value problem is reduced to the infinite algebraic system of the second kind which in principal can be solved with any predetermined accuracy by means of truncation procedure. Numerical results, including condition number behavior, current density, and fields space distribution for obstacles are presented.

Scalar wave diffraction from infinitely thin perfectly conducting circular ring

A new strong mathematically rigorous and numerically efficient method for solving the boundary value problem of scalar wave diffraction by an infinitely thin circular ring screen is proposed. The method is based on the combination of the orthogonal polynomials approach and the ideas of the methods of analytical regularization. As a result of the suggested regularization procedure, the initial boundary value problems was equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e., to an equation of the type (I+H)x=b, x, b/spl isin/l/sub 2/ in the space l/sub 2/ of square summable sequences. This equation was solved numerically by means of a truncation method with, in principle, any required accuracy.

A numerically stable algorithm for eccentrically metamaterial covered circular cylinders

The regularization for monochromatic TM/TE-z polarized waves scattering from multiple non intersecting circular penetrable boundaries has recently been proven to be a requisite for its stable numerical implementation for a wide scope of parameters. The validity and necessity of corresponding regularization algorithm will be demonstrated for medium parameters which are from a double negative (DNG) material media. The preliminary numerical results which already prove the properties mentioned above are given in this paper.

Correction to “Analytical Evaluation of Retarded-Time Potentials for SWG Bases” [Sep 14 4860-4863]

A missing scaling and a comparison of results post correction thereof are presented.

Modeling of waveguides of various cross section by analytical regularization method

New efficient approach for simulation of waveguides and cylindrical resonators of arbitrary profile is suggested. Numerical investigations for the abilities of algorithm and comparison with known results show high efficiency and accuracy of the method.

Analytical Regularization Method as a tool for cylindrical antenna design

Mirror antennae formed by curvilinear perfectly conducting screens are classic objects of theoretical and experimental investigations, which already resulted in numerous scientific and engineering publications. The most typical full wave models of such antennae are based on mathematical approach of infinitely thin and perfectly conductive screens. In many cases screen is formed by a surface in 3D space. At the same time, cylindrical antennae and their models as homogenous and infinite in longitudinal direction cylindrical surfaces are also having their place in modern radio science. Our presentation is focused on such cylindrical antennae models both infinitely thin and of finite thickness with various shapes and screen thickness. Namely, we try to estimate how finite thickness influences the antenna characteristics and, in particular, estimate validity of the models based on infinitely thin screens relatively to different physical purposes of modeling. We have chosen Analytical Regularization Method (ARM) as a tool for our investigation. In publications [1, 2] aiming the similar investigation, where Semi-Inversion Procedure (SIP) [3] was used, it was claimed that ARM was used. This mistaken claim occurred due to mismatching of the standard terminology [4, 5, 6 and references therein]. Using ARM instead of SIP gives possibility to obtain algorithms of essentially better quality than those of [1, 2]. Moreover, we implement ARM in such a way that it is super-algebraically (faster than any negative power of the reduced algebraic system) convergent.

Arbitrary shaped hollow resonators and waveguides modeling. Analytical regularization method

Mathematically strong and efficient approach for simulation of resonators and waveguides of arbitrary profile is suggested. The approach is based on new implementation of Analytical Regularization Method. Numerical results of E-polarized wave diffraction by waveguide resonant structures demonstrate the method efficiency and reliability.