Mathematics of Computation

Author(s): A. Bendali; Ph. Guillaume.
Journal: Math. Comp. 68 (1999), 123-144.
MSC (1991): Primary 35Q60, 35J05, 65N12, 65N15, 65N30, 78A50
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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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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: 10.1090/S0025-5718-99-01016-9
PII: S 0025-5718(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
Copyright of article: Copyright 1999, American Mathematical Society

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