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A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-7972-6183
Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
Department of Geological Sciences, San Diego State University, San Diego, CA 92182-1020, USA.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Communications in Computational Physics, ISSN 1815-2406, E-ISSN 1991-7120, Vol. 16, no 2, 541-570 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Global Science Press, 2014. Vol. 16, no 2, 541-570 p.
Keyword [en]
Summation-by-parts, weak boundary conditions, penalty technique, high-order accuracy, finite difference schemes, stability, steady-state, non-reflecting boundary conditions.
National Category
Computational Mathematics
URN: urn:nbn:se:liu:diva-107508DOI: 10.4208/cicp.020313.120314aISI: 000340786500011OAI: diva2:729882
Available from: 2014-06-26 Created: 2014-06-13 Last updated: 2014-09-23

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