Convergence of infinite element methods for scalar waveguide problems

We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both the perfectly matched layer method and the Hardy space infinit...

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Bibliographic Details
Published inBIT Numerical Mathematics Vol. 55; no. 1; pp. 215 - 254
Main Authors Hohage, Thorsten, Nannen, Lothar
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.03.2015
Subjects
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Numeric Computing
Transparent boundary conditions
78A45
Perfectly matched layer
65N12
78M10
Waveguide
Hardy space infinite elements
65N30
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ISSN0006-3835
1572-9125
DOI10.1007/s10543-014-0525-x

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Summary:We consider the numerical solution of scalar wave equations in domains which are the union of a bounded domain and a finite number of infinite cylindrical waveguides. The aim of this paper is to provide a new convergence analysis of both the perfectly matched layer method and the Hardy space infinite element method in a unified framework. We treat both diffraction and resonance problems. The theoretical error bounds are compared with errors in numerical experiments.
ISSN:0006-3835
1572-9125
DOI:10.1007/s10543-014-0525-x