TE-Polarized Electromagnetic Wave Diffraction by a Circular Slotted Cylinder

The problem of diffraction of a TE-polarized electromagnetic wave by a circular slotted cylinder is investigated. The boundary value problem in question for the Helmholtz equation is reduced to an infinite system of linear algebraic equations of the second kind (SLAE-II) using integral summation ide...

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Bibliographic Details
Published in:Mathematics (Basel) 2023-04, Vol.11 (9), p.1991
Main Authors: Abgaryan, Garnik V., Shestopalov, Yury V.
Format: Article
Language:English
Subjects:
Boundary conditions
Boundary value problems
Cylinders
diffraction problem
Electric waves
Electromagnetic radiation
Electromagnetic waves
Electromagnetism
Fredholm property
Helmholtz equation
Helmholtz equations
Hilbert space
Identities
infinite linear algebraic equation system
Linear algebra
Mathematics
Operators (mathematics)
slot resonator
Wave diffraction
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Summary:The problem of diffraction of a TE-polarized electromagnetic wave by a circular slotted cylinder is investigated. The boundary value problem in question for the Helmholtz equation is reduced to an infinite system of linear algebraic equations of the second kind (SLAE-II) using integral summation identities (ISI). A detailed study of the matrix operator of the problem is performed and its Fredholm property in the weighted Hilbert space of infinite sequences is proven. The convergence of the truncation method constructed in the paper for the numerical solution of SLAE-II is justified and the results of computations are presented and discussed, specifically considering the determination of resonance modes.
ISSN:2227-7390
2227-7390
DOI:10.3390/math11091991