Special infinite systems of linear algebraic equations

2021 ◽  
Author(s):  
Foma M. Fedorov ◽  
Oksana F. Ivanova ◽  
Nikifor N. Pavlov ◽  
Sargylana V. Potapova
Keyword(s):  
Algebraic Equations ◽  
Infinite Systems ◽  
Linear Algebraic Equations

scholarly journals Excitation of anisotropic impedance metasurface in the form of elliptical cylinder.

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A.I. Semenikhin ◽  
◽  
D.V. Semenikhin ◽  
Keyword(s):  
Elliptical Cylinder ◽  
Impedance Tensor ◽  
Reflection Coefficients ◽  
Algebraic Equations ◽  
Partial Reflection ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
External Sources ◽  
Surface Impedance Tensor ◽  
Special Case

The problem of arbitrary excitation of waves by a system of external sources near an anisotropic metasurface in the form of an elliptical cylinder with a surface homogenized impedance tensor of general form is solved. The solution to the problem is written as a superposition of E- and H-waves in elliptical coordinates. The partial reflection coefficients of waves were found from the boundary conditions using the orthogonality of the Mathieu angular functions. For these coefficients, four coupled infinite systems of linear algebraic equations of the second kind are obtained. The conditions under which the solution of the excitation problem by the method of eigenfunctions is obtained in an explicit form are found and analyzed. It is shown that for this, the surface impedance tensor of a uniform metasurface must belong to a class of deviators (have zero diagonal elements). In the particular case of a mutual (most easily realized) metasurface, its impedance tensor should only be reactance. In another special case, the impedance tensor of a set of deviators describes a class of anisotropic nonreciprocal metasurfaces with the so-called perfect electromagnetic conductivity (PEMC).

scholarly journals Quasihomogeneous Infinite Systems of Linear Algebraic Equations

2018 ◽  
Vol 1141 ◽  
pp. 012105
Author(s):  
F. M. Fedorov ◽  
N. N. Pavlov ◽  
O. F. Ivanova ◽  
S. V. Potapova
Keyword(s):  
Algebraic Equations ◽  
Infinite Systems ◽  
Linear Algebraic Equations

Electromagnetic field of the circular magnetic source in biconical section

2020 ◽  
Vol 2020 (48) ◽  
pp. 5-10
Author(s):  
O.M. Sharabura ◽  
◽  
D.B. Kuryliak ◽  
Keyword(s):  
Field Pattern ◽  
Geometrical Parameters ◽  
Algebraic Equations ◽  
Axially Symmetric ◽  
Reduction Procedure ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Regularization Techniques ◽  
Far Field Pattern ◽  
Analytical Regularization

The problem of axially-symmetric electromagnetic wave diffraction from the perfectly conducting biconical scatterer formed by the finite cone placed in the semi-infinite conical region is solved rigorously using the mode-matching and analytical regularization techniques. The problem is reduced to the infinite systems of linear algebraic equations (ISLAE) of the second kind. The obtained equations admit the reduction procedure and can be solved with a given accuracy for any geometrical parameters and frequency. The numerical examples of the solution are presented. The analysis of the source location influences on the far-field pattern for different geometrical parameters of the bicone is carried out.

The radiation and scattering of surface waves by a vertical circular cylinder in a channel

1992 ◽  
Vol 338 (1650) ◽  
pp. 325-357 ◽  
Keyword(s):  
Circular Cylinder ◽  
Gravity Waves ◽  
The Body ◽  
Far Field ◽  
Algebraic Equations ◽  
Surface Gravity Waves ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Correct Form ◽  
Body Boundary

In this paper we consider the problems of the radiation and scattering of surface gravity waves by a vertical circular cylinder placed on the centreline of a channel of width 2 d and depth H , and either extending from the bottom through the free surface or truncated so as to fill only part of the depth. These problems are solved, for arbitrary incident wavenumber k , by constructing appropriate multipoles for cylinders placed symmetrically in channels and then using the body boundary condition to derive a set of infinite systems of linear algebraic equations. For the general problems considered here, this method is superior to the more usual approach of using a set of image cylinders to model the channel walls, in particular the occurrence of modes other than the fundamental when kd > is accurately modelled and the correct form predicted for the far-field.

scholarly journals Analysis of a Coaxial Waveguide with Finite-Length Impedance Loadings in the Inner and Outer Conductors

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Feray Hacıvelioğlu ◽  
Alinur Büyükaksoy
Keyword(s):  
Reflection Coefficient ◽  
Boundary Value Problem ◽  
Finite Length ◽  
Formal Solution ◽  
Coaxial Waveguide ◽  
Algebraic Equations ◽  
Coaxial Cylinders ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Band Stop Filter

A rigorous Wiener-Hopf approach is used to investigate the band stop filter characteristics of a coaxial waveguide with finite-length impedance loading. The representation of the solution to the boundary-value problem in terms of Fourier integrals leads to two simultaneous modified Wiener-Hopf equations whose formal solution is obtained by using the factorization and decomposition procedures. The solution involves 16 infinite sets of unknown coefficients satisfying 16 infinite systems of linear algebraic equations. These systems are solved numerically and some graphical results showing the influence of the spacing between the coaxial cylinders, the surface impedances, and the length of the impedance loadings on the reflection coefficient are presented.

scholarly journals Diffraction of sound waves by a lined cylindrical cavity

2020 ◽  
Vol 19 (1-2) ◽  
pp. 38-56
Author(s):  
Burhan Tiryakioglu
Keyword(s):  
Mode Matching ◽  
Sound Waves ◽  
Algebraic Equations ◽  
Hopf Equation ◽  
Matching Method ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
The Fourier Transform ◽  
Sound Diffraction ◽  
Selection Of

In this paper, diffraction of sound waves through a lined cavity is analyzed rigorously. The inner–outer surfaces of the cavity and the base of the cavity are coated with three different absorbing linings. By using the Fourier transform technique in conjunction with the Mode-Matching method, the related boundary value problem is formulated as a Wiener–Hopf equation. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. Numerical solution of this system is obtained for various values of the parameters of the problem. The graphical results are also presented which show that how efficiently the sound diffraction can be reduced by selection of problem parameters.

scholarly journals Verification of Computing Grids with Special Edge Conditions by Infinite Petri Nets

2015 ◽  
Vol 19 (6) ◽  
pp. 21-33
Author(s):  
D. A. Zaitsev
Keyword(s):  
Petri Nets ◽  
Algebraic Equations ◽  
Square Grid ◽  
Parametric Solutions ◽  
Infinite Systems ◽  
Linear Algebraic Equations ◽  
Edge Conditions ◽  
Computing Grid

A technique of the computing grid verification using invariants of infinite Petri nets was presented. Models of square grid structures in the form of parametric Petri nets for such edge conditions as connection of edges and truncated devices were constructed. Infinite systems of linear algebraic equations were composed on parametric Petri nets for calculating p-invariants; their parametric solutions were obtained. P-invariant Petri nets are structuraly conservative and bounded that together with liveness are the properties of ideal systems. Liveness investigation based on siphons and traps can be implemented by using p-invariants of modified nets.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

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