On the convergence the barycentric method in solving diffraction problems on conductive thin screens

2020 ◽  
Vol 23 (3) ◽  
pp. 34-43
Author(s):  
Anatolii S. Il’inskii ◽  
Ivan S. Polyanskii ◽  
Dmitry E. Stepanov ◽  
Nikolay I. Kuznetsov
Keyword(s):  
Numerical Solution ◽  
Electromagnetic Waves ◽  
Barycentric Coordinates ◽  
Bernstein Type ◽  
Polygonal Region ◽  
Basic Functions ◽  
Comparative Results ◽  
The Galerkin Method ◽  
Simply Connected ◽  
Equivalent Conditions

Annotation In this article, the use of the barycentric method is proposed for the numerical solution of problems of diffraction of electromagnetic waves on infinitely thin perfectly conducting screens of arbitrary shape. The numerical solution is formed in the projection formulation of the Galerkin method. The essence of the barycentric method is to form a global system of basic functions for opening the screen when determining the approximation of the desired function of the current plane on its surface. Basis functions are defined by Bernstein-type polynomials in terms of barycentric coordinates that are entered for opening the screen when it is represented as a closed simply connected polygonal region. The features of the algorithmic implementation of the barycentric method in solving diffraction problems on conducting thin screens are considered. The rate of convergence is estimated. Comparative results of calculations performed under equivalent conditions using the barycentric method and the RWG method are presented.

scholarly journals Эффективная диэлектрическая проницаемость анизотропного композита из сфероидных частиц в диэлектрической матрице

2021 ◽  
Vol 47 (23) ◽  
pp. 22
Author(s):  
Б.А. Беляев ◽  
В.В. Тюрнев ◽  
С.А. Ходенков
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Electromagnetic Waves ◽  
Effective Permittivity ◽  
Transverse Polarization ◽  
Dielectric Matrix ◽  
Anisotropic Composite ◽  
Concentration Dependences ◽  
The Matrix

The concentration dependences of the effective permittivity of an anisotropic composite containing co-directional particles in the form of oblate or elongated ellipsoids of rotation – spheroids – in the dielectric matrix are obtained. The calculation is made by the numerical solution of a system of coupled quadratic and integral equations obtained by a strict modification of the quasi-static Bruggeman theory. It is shown that the traditional (simplified) modification of the Bruggeman theory, widely used for calculating anisotropic composites, gives errors of different signs for the longitudinal and transverse polarization of electromagnetic waves relative to the axis of spheroids. In this case, the dependences of errors on the concentration of particles are non-monotonic, and the extremes observed on them can exceed 100%. Moreover, the position and magnitude of the extremes strongly depend on the ellipticity of the particles, as well as on the contrast of their permittivity with the matrix.

On Simple Connectedness of Minimal Representation-Infinite Algebras

2015 ◽  
Vol 22 (04) ◽  
pp. 639-654
Author(s):  
Hailou Yao ◽  
Guoqiang Han
Keyword(s):  
Cohomology Group ◽  
Hochschild Cohomology ◽  
Closed Field ◽  
Minimal Representation ◽  
Algebraically Closed Field ◽  
Hochschild Cohomology Group ◽  
Simple Connectedness ◽  
Simply Connected ◽  
Equivalent Conditions ◽  
Infinite Algebras

Let A be a connected minimal representation-infinite algebra over an algebraically closed field k. In this paper, we investigate the simple connectedness and strong simple connectedness of A. We prove that A is simply connected if and only if its first Hochschild cohomology group H1(A) is trivial. We also give some equivalent conditions of strong simple connectedness of an algebra A.

scholarly journals On the convergence of the barycentric method in solving internal Dirichlet and Neumann problems in $\mathbb{R}^2$ for the Helmholtz equation

2021 ◽  
Vol 31 (1) ◽  
pp. 3-18
Author(s):  
A.S. Il'inskii ◽  
I.S. Polyanskii ◽  
D.E. Stepanov
Keyword(s):  
Helmholtz Equation ◽  
Piecewise Linear ◽  
Linear Representation ◽  
Barycentric Coordinates ◽  
Neumann Problems ◽  
Convergence Rate Estimate ◽  
Simply Connected Domain ◽  
Piecewise Linear Representation ◽  
Uniqueness Of The Solution ◽  
Simply Connected

The application of the barycentric method for the numerical solution of Dirichlet and Neumann problems for the Helmholtz equation in the bounded simply connected domain $\Omega\subset\mathbb{R}^2$ is considered. The main assumption in the solution is to set the $\Omega$ boundary in a piecewise linear representation. A distinctive feature of the barycentric method is the order of formation of a global system of vector basis functions for $\Omega$ via barycentric coordinates. The existence and uniqueness of the solution of Dirichlet and Neumann problems for the Helmholtz equation by the barycentric method are established and the convergence rate estimate is determined. The features of the algorithmic implementation of the method are clarified.

scholarly journals Scattering, absorption, and thermal emission by large cometary dust particles: Synoptic numerical solution

2019 ◽  
Vol 631 ◽  
pp. A164 ◽  
Author(s):  
Johannes Markkanen ◽  
Jessica Agarwal
Keyword(s):  
Light Scattering ◽  
Numerical Solution ◽  
Electromagnetic Waves ◽  
Random Media ◽  
Thermal Emission ◽  
Interplanetary Dust ◽  
Dust Particles ◽  
Conductive Heat ◽  
Interplanetary Dust Particles ◽  
Cometary Dust

Context. Remote light scattering and thermal infrared observations provide clues about the physical properties of cometary and interplanetary dust particles. Identifying these properties will lead to a better understanding of the formation and evolution of the Solar System. Aims. We present a numerical solution for the radiative and conductive heat transport in a random particulate medium enclosed by an arbitrarily shaped surface. The method will be applied to study thermal properties of cometary dust particles. Methods. The recently introduced incoherent Monte Carlo radiative transfer method developed for scattering, absorption, and propagation of electromagnetic waves in dense discrete random media is extended for radiative heat transfer and thermal emission. The solution is coupled with the conductive Fourier transport equation that is solved with the finite-element method. Results. The proposed method allows the synoptic analysis of light scattering and thermal emission by large cometary dust particles consisting of submicrometer-sized grains. In particular, we show that these particles can sustain significant temperature gradients resulting in the superheating factor phase function observed for the coma of comet 67P/Churyumov–Gerasimenko.

scholarly journals Fast methods for the solution of singular integro-differential and differential equations

1981 ◽  
Vol 4 (4) ◽  
pp. 775-794
Author(s):  
L. F. Abd-Elal
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Numerical Solution ◽  
Integrodifferential Equations ◽  
Solution Time ◽  
First Order ◽  
Chebyshev Expansion ◽  
Fast Methods ◽  
The Galerkin Method

Uniform methods based on the use of the Galerkin method and different Chebyshev expansion sets are developed for the numerical solution of linear integrodifferential equations of the first order. These methods take a total solution time0(N2lnN)usingNexpansion functions, and also provide error extimates which are cheap to compute. These methods solve both singular and regular integro-differential equations. The methods are also used in solving differential equations.

scholarly journals NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS IN IRREGULAR PLANE REGIONS USING QUALITY STRUCTURED CONVEX GRIDS

2013 ◽  
Vol 04 (02) ◽  
pp. 1350004
Author(s):  
F. DOMÍNGUEZ-MOTA ◽  
P. FERNÁNDEZ-VALDEZ ◽  
S. MENDOZA-ARMENTA ◽  
G. TINOCO-GUERRERO ◽  
J. G. TINOCO-RUIZ
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Numerical Solution ◽  
Poisson Equation ◽  
Finite Differences ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Structured Grids ◽  
Simply Connected ◽  
Simply Connected Domains

The variational grid generation method is a powerful tool for generating structured convex grids on irregular simply connected domains whose boundary is a polygonal Jordan curve. Several examples that show the accuracy of a finite difference approximation to the solution of a Poisson equation using this kind of structured grids have been recently reported. In this paper, we compare the accuracy of the numerical solution calculated using those structured grids and finite differences against the solution obtained with Delaunay-like triangulations on irregular regions.

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