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Numerical computation of dispersion relations in wave guides
Author(s) -
Gravenkamp Hauke,
Song Chongmin,
Prager Jens
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210256
Subject(s) - computation , discretization , eigenvalues and eigenvectors , finite element method , dispersion relation , mathematical analysis , dispersion (optics) , boundary value problem , mathematics , wavenumber , wave propagation , cross section (physics) , physics , geometry , optics , algorithm , quantum mechanics , thermodynamics
Abstract In this paper a numerical approach, based on the Scaled Boundary Finite Element Method (SBFEM), is described to obtain dispersion relations for propagating modes in wave guides. While the formulation is developed for plate structures, it can easily be extended to wave guides with arbitrary cross‐section. The cross‐section is discretized in the Finite Element sense while all equations remain analytical in the direction of propagation. The wave numbers of all propagating modes are obtained as the solutions of a standard eigenvalue problem. The group velocities can be calculated accurately as the eigenvalue derivatives. The use of higher‐order elements drastically increases the efficiency and accuracy of the computation. This approach can be used for wave guides with arbitrary distribution of material parameters. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)