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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 18, Issue 4

Issues

Numerical Modeling of Optical Fibers Using the Finite Element Method and an Exact Non-reflecting Boundary Condition

Rafail Z. Dautov / Evgenii M. Karchevskii
  • Corresponding author
  • Department of Applied Mathematics, Kazan Federal University, 18 Kremliovskaya street, Kazan 42008, Russia
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Published Online: 2017-11-17 | DOI: https://doi.org/10.1515/cmam-2017-0049

Abstract

The original problem for eigenwaves of weakly guiding optical fibers formulated on the plane is reduced to a convenient for numerical solution linear parametric eigenvalue problem posed in a disk. The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. Properties of dispersion curves are investigated for the new formulation of the problem. An efficient numerical method based on FEM approximations is developed. Error estimates for approximate solutions are derived. The rate of convergence for the presented algorithm is investigated numerically.

Keywords: Finite Element Method; Exact Non-Reflecting Boundary Condition; Spectral Problem; Optical Fiber

MSC 2010: 65N30; 65N25; 65Z05

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About the article

Received: 2017-04-21

Revised: 2017-10-10

Accepted: 2017-10-23

Published Online: 2017-11-17

Published in Print: 2018-10-01


Funding Source: Russian Foundation for Basic Research

Award identifier / Grant number: 16-01-00408

This work was partly supported by the Russian Foundation for Basic Research, project no. 16-01-00408 (R. Z. Dautov) and was performed according to the Russian Government Program of Competitive Growth of Kazan Federal University (E. M. Karchevskii).


Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 581–601, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.1515/cmam-2017-0049.

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