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

A closed waveguide of a constant cross section with perfectly conducting walls is considered. It is assumed that its filling is described by function and invariable along the waveguide axis and piecewise continuous over the waveguide cross section. The aim of the paper is to show that, in such a sys...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2019-02, Vol.59 (2), p.330-342
Main Authors: Malykh, M. D., Sevast’yanov, L. A.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Continuity (mathematics)
Cross-sections
Electromagnetic fields
Magnetic fields
Mathematical analysis
Mathematics
Mathematics and Statistics
Representations
Sobolev space
Waveguides
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Summary:A closed waveguide of a constant cross section with perfectly conducting walls is considered. It is assumed that its filling is described by function and invariable along the waveguide axis and piecewise continuous over the waveguide cross section. The aim of the paper is to show that, in such a system, it is possible to make a change of variables that makes it possible to work only with continuous functions. Instead of discontinuous transverse components of the electromagnetic field , it is proposed to use potentials and related to the field as and, instead of discontinuous transverse components of the magnetic field , to use the potentials and related to the field as . It is proven that any field in the waveguide admits the representation in this form if the potentials are elements of the Sobolev space and are elements of the space .
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542519020118