Mathematical modelling of the propagation of electromagnetic waves in a slotted transmission line

Ilinskii, A. S.; Smironov, Y. G.

doi:10.1016/0041-5553(87)90137-6

Cited by 3 publications

(5 citation statements)

References 1 publication

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“…which follows in its turn from the remark above and formulas (18). Inequalities (21) follow from (17).…”

Section: Eigenvalue Problem For Operator Pencilmentioning

confidence: 68%

“…For slot transmission lines the existence of eigenvalues was established in [14] . Localization of eigenvalues on the complex plane were studied in [18,11,13,14]. Note however that it is hardly possible to prove the existence and determine the spectrum location on the complex plane by these methods for a wide family of nonhomogeneously filled waveguides considered in this study.…”

Section: Introductionmentioning

confidence: 99%

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Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Smirnov¹,

Shestopalov²

2012

Preprint

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We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a nonempty set of isolated points localized in a strip with at most finitely many real points.

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“…which follows in its turn from the remark above and formulas (18). Inequalities (21) follow from (17).…”

Section: Eigenvalue Problem For Operator Pencilmentioning

confidence: 68%

Section: Introductionmentioning

confidence: 99%

Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Smirnov¹,

Shestopalov²

2012

Preprint

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“…Then, as was shown in [10, p. 55] (see also [7,8]), the projection method (3) is convergent, and the quasioptimal convergence rate estimate…”

Section: Direct Methods For Solving the Equationmentioning

confidence: 79%

“…The desired assertion follows from the invertibility of the operator L : Φ 0 → Φ 2 , the compactness of the operator (2), the representation (1), and the well-known Riesz theorem on the sum of an invertible and a compact operator [7,8]. Since the uniqueness of the representation (1) is assumed, it follows from the Fredholm equation for an equation of the second kind that there exists a solution of Eq.…”

Section: Assertion the Integral Equation (1) In The Operator Formmentioning

confidence: 94%

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Justification of the direct projection method for solving an integral equation of the potential theory

Ilinskii

2014

Diff Equat

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We justify the direct projection method for solving an integral equation with a logarithmic singularity in the kernel. The equation is treated as a mapping of one Hilbert space into another Hilbert space. The spaces are chosen from conditions ensuring the solution of a broad class of mathematical modeling problems with the use of a simple layer potential. The idea of the projection method is to choose finite-dimensional subspaces into which the exact solution and the right-hand side of the equation are projected. In this case, the problem of finding an approximate solution does not require computing the convolution of kernels. We prove an estimate for the solution error in the norm of the original operator equation.

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On the Representation of Electromagnetic Fields in Discontinuously Filled Closed Waveguides by Means of Continuous Potentials

Malykh

Sevastyanov

2019

Comput. Math. and Math. Phys.

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Mathematical modelling of the propagation of electromagnetic waves in a slotted transmission line

Cited by 3 publications

References 1 publication

Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Eigenwaves in Waveguides with Dielectric Inclusions: Spectrum

Justification of the direct projection method for solving an integral equation of the potential theory

On the Representation of Electromagnetic Fields in Discontinuously Filled Closed Waveguides by Means of Continuous Potentials

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