Systems of singular integral equations of certain mixed boundary-value problems of mathematical physics

Gandel, Y.V.; Polyanskaya, Tatyana

doi:10.1007/bf01095791

Cited by 8 publications

(3 citation statements)

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“…To satisfy the radiation conditions, we choose γ (λ) from the conditions Re γ (λ) ≥ 0 and Im γ (λ) ≤ 0 . As shown in [1,[4][5][6][7][8], the boundary-value problem (1) (with regard for all imposed conditions) is reduced to the following two dual integral equations:…”

Section: Statement Of the Problem And Dual Integral Equationsmentioning

confidence: 99%

Discrete Mathematical Model of the Problem of Diffraction for E -Polarized Waves on Slots in the Impedance Plane

Nesvit

2015

J Math Sci

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We consider the problem of diffraction for E -polarized plane monochromatic waves on slots in the impedance plane. A discrete mathematical model of the boundary integral equations of this problem is constructed. We also perform a numerical experiment based on the use of the efficient numerical method of discrete singularities.A stationary electromagnetic field (its time dependence is specified by the factor e −iωt ) is described by the Maxwell equations. In the two-dimensional case, these equations lead to two independent boundary-value problems for the steady-state wave equation. The two-dimensional diffraction problems for monochromatic electromagnetic waves on perfectly conducting structures lead to the Dirichlet and Neumann two-dimensional external boundary-value problems for the Helmholtz equation.In the present paper, we construct and perform the numerical analysis of a discrete mathematical model of the problem of diffraction on slots in the impedance plane. This model enables one to find the required characteristics of the electromagnetic fields and, in particular, to construct directional diagrams.The problems of scattering and diffraction of electromagnetic waves by impedance metallic and superconducting thin tapes were investigated in the monograph [5] and paper [4] by the method of discrete singularities. The same problems for the pre-Cantor tapes were studied in [12].The mathematical models of diffraction problems based on hypersingular integral equations [10] were also numerically investigated by the method of discrete singularities. Statement of the Problem and Dual Integral EquationsWe consider a problem of the mathematical theory of diffraction of E -polarized plane monochromatic electromagnetic waves on a finite set of slots in the impedance plane.The surface impedance of the metal is an important physical characteristic specifying the amplitude and phase relationships between the electric and magnetic fields on the surface.The model studied in the present work can be regarded as an approximation of actual fractal [11] antennas for the case where the field depends on two Cartesian coordinates. Fractal antennas are used in various contemporary mobile devices because their compactness and broadband properties made them irreplaceable for the purposes of wireless communications in the Bluetooth, Wi-Fi, and GSM standards. Their theoretical investigation is important from the viewpoint both of the development of mathematical methods capable of the solution of complex boundary-value problems of electrodynamics and of the construction of new physical models as close to the reality as possible.

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Section: Statement Of the Problem And Dual Integral Equationsmentioning

confidence: 99%

Discrete Mathematical Model of the Problem of Diffraction for E -Polarized Waves on Slots in the Impedance Plane

Nesvit

2015

J Math Sci

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“…The proposed new approach is based on two main steps: a) reduction of the initial two-dimensional boundary problem for Maxwell equations to the system of one-dimensional singular integral equations (SSIE); b) rigorous numerical solving of the SSIE by direct numerical methbd analogous to that developed in [2]. It allow us to correctly describe multimode regimes of the interaction to be usually realized in high power electronic devices with predicted exactness.…”

Section: Wherementioning

confidence: 99%

“…in parallel with the cavity shunt impedance. [2,3] The response of the gain cavities is modified by the same admittance, Y, . In a magnicon.…”

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Field analysis of beam loading and detuning in magnicon deflection cavities

Hafizi

Gold

1995

International Conference on Plasma Science (Papers in Summary Form Only Received)

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Improved Algorithm for Approximate Solution of Integral Equations of Diffraction Problems on Periodic Structures

Dushkin

2024

2024 IEEE 29th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED

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Systems of singular integral equations of certain mixed boundary-value problems of mathematical physics

Cited by 8 publications

References 1 publication

Discrete Mathematical Model of the Problem of Diffraction for E -Polarized Waves on Slots in the Impedance Plane

Discrete Mathematical Model of the Problem of Diffraction for E -Polarized Waves on Slots in the Impedance Plane

Field analysis of beam loading and detuning in magnicon deflection cavities

Improved Algorithm for Approximate Solution of Integral Equations of Diffraction Problems on Periodic Structures

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