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Mathematics of Computation

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Non-reflecting boundary conditions
for waveguides


Authors: A. Bendali and Ph. Guillaume
Journal: Math. Comp. 68 (1999), 123-144
MSC (1991): Primary 35Q60, 35J05, 65N12, 65N15, 65N30, 78A50
DOI: https://doi.org/10.1090/S0025-5718-99-01016-9
MathSciNet review: 1609674
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Abstract | References | Similar Articles | Additional Information

Abstract: New non-reflecting boundary conditions are introduced for the solution of the Helmholtz equation in a waveguide. These boundary conditions are perfectly transparent for all propagating modes. They do not require the determination of these propagating modes but only their propagation constants. A quasi-local form of these boundary conditions is well suited as terminating boundary condition beyond finite element meshes. Related convergence properties to the exact solution and optimal error estimates are established.


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Additional Information

A. Bendali
Affiliation: Département de Génie Mathématique, INSA Toulouse & CNRS-UMR 5640 MIP, Avenue de Rangueil, 31077 Toulouse Cedex, France
Email: bendali@gmm.insa-tlse.fr

Ph. Guillaume
Affiliation: Département de Génie Mathématique, INSA Toulouse & CNRS-UMR 5640 MIP, Avenue de Rangueil, 31077 Toulouse Cedex, France
Email: guillaum@gmm.insa-tlse.fr

DOI: https://doi.org/10.1090/S0025-5718-99-01016-9
Keywords: Guided propagation, absorbing boundary conditions, waveguides, Helmholtz equation, acoustics, electromagnetics, finite element
Received by editor(s): May 26, 1996
Received by editor(s) in revised form: May 23, 1997
Article copyright: © Copyright 1999 American Mathematical Society