Olga Suvorova

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.

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.

Analytical regularization method for arbitrary hollow waveguides with spline-parameterized cross sections

This paper presents a numerically efficient simulation method and its implementation based on spline interpolation technique for solving waveguide problems of arbitrary cross sections. In this work, analytical regularization method is used as the key approach.

An analytical formulation with ill-conditioned numerical scheme and its remedy: Scattering by two circular impedance cylinders

The regularization of the well-known analytical formulation of the monochromatic electromagnetic wave scattering problem from two neighbor impedance circular cylinder system is presented. It is the improvement and extension of the work done for scattering from two perfectly conducting circular cylinders. Numerical results show that it is numerically much safer to solve the obtained infinite algebraic system at a lower truncation number also by ensuring the reliability of the solution.

Rigorous solution by analytical regularization method to the problem of 3D TM-ϕ wave diffraction by a set of axially symmetrical annular PEC surfaces

The analytical regularization method is applied to the problem o f 3D TM-ϕ wave diffraction by perfectly conductive axially symmetrical a nnular surfaces consisting a set of closed and unclosed ones. The electromagnetic boundary value problem is reduced to t he 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 and fields space distribution for obstacles will be presented.

Super-algebraically convergent mathematical model of hollow waveguldes by Analytical Regularization Method

An accurate and efficient simulation of hollow waveguides is in demand for many practical applications including those in the area of microwave engineering. But very many numerical methods produce ill conditioned matrix that getting correct results needs various numerical experiments (see, for example, [1], where the authors mentioned the instability of the method for the matrices of big sizes). Thus, some alternative numerically stable and efficient approach is in demand. Our algorithm based on Analytical Regularization Method [2]–[3], adopted in this paper for spectral problems, brings just such alternative to, at least, the hollow waveguide modeling considered herein.

Analytical Regularization Method for TE-modes in hollow waveguides modelling

Mathematically strong and numerically efficient approach for simulation of waveguides and cylindrical resonators of arbitrary profile in the case of H-(TE-) polarized waves is suggested. The approach is based on new implementation of Analytical Regularization Method. Special attention paid to methods of the profiles infinitely smoothing, which gives a possibility to achieve a super-algebraic (faster any algebraic) rate of the method convergence.