Biryukov Vladislav Olegovich (Graduate student
Patrice Lumumba Peoples' Friendship University of Russia, Moscow
)
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The paper studies numerical methods for solving waveguide problems generated by a system of Maxwell's equations with given boundary conditions. The aim of the work was to develop and compare the finite-difference method and the finite element method modeling the propagation of eigensurface waves in a cylindrical dielectric weakly directional waveguide.
To achieve this goal, we described a mathematical model based on Maxwell's equations, implemented the methods and conducted a computational experiment in the Maple environment, compared the results in terms of accuracy, stability and computational costs, and analyzed the influence of geometry and model parameters.
We assumed that both methods provide comparable accuracy, but differ in stability and computational costs depending on the complexity of the geometry and model parameters.
The obtained values of the eigenfunction of both methods are in good agreement with each other, which is confirmed by the constructed graphs, allowing a visual comparison of the behavior of the solutions. It was found that the finite difference method is effective for simple geometry and requires fewer computational resources, while the finite element method is more versatile and stable when modeling in areas with complex boundaries.
Keywords:waveguides, Maxwell's equation, finite element method, finite difference method.
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Citation link:
Biryukov V. O. INVESTIGATION OF NUMERICAL METHODS FOR MODELING WAVEGUIDE PROPAGATION // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2025. -№07. -С. 46-51 DOI 10.37882/2223-2966.2025.07.04 |
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