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A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

Published online by Cambridge University Press:  03 June 2015

Jan Nordström ,
Qaisar Abbas ,
Brittany A. Erickson  and
Hannes Frenander
Jan Nordström*
Affiliation:
Department of Mathematics, Division of Computational Mathematics, Linköping University, SE-581 83 Linköping, Sweden
Qaisar Abbas*
Affiliation:
Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden
Brittany A. Erickson*
Affiliation:
Department of Geological Sciences, San Diego State University, San Diego, CA 92182-1020, USA
Hannes Frenander*
Affiliation:
Department of Mathematics, Division of Computational Mathematics, Linköping University, SE-581 83 Linköping, Sweden
*
Corresponding author.Email:[email protected]
Email:[email protected]
Email:[email protected]
Email:[email protected]
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Abstract

A new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary procedure is cheap, easy to implement and suitable for all numerical methods, not only finite difference methods, that employ weak boundary conditions. Numerical results that corroborate the analysis are presented.

Keywords

35L0535L6535Q3565M0665M1265Z05Summation-by-partsweak boundary conditionspenalty techniquehigh-order accuracyfinite difference schemesstabilitysteady-statenon-reflecting boundary conditions.
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 2 , August 2014 , pp. 345 - 358
Copyright
Copyright © Global Science Press Limited 2014

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