A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain
Jan Nordstrom 1*, Qaisar Abbas 2, Brittany A. Erickson 3, Hannes Frenander 41 Department of Mathematics, Division of Computational Mathematics, Linkoping University, SE-581 83 Linkoping, Sweden.
2 Department of Information Technology, Division of Scientific Computing, Uppsala University, SE-751 05 Uppsala, Sweden.
3 Department of Geological Sciences, San Diego State University, San Diego, CA 92182-1020, USA.
4 Department of Mathematics, Division of Computational Mathematics, Linkoping University, SE-581 83 Linkoping, Sweden.
Received 2 March 2013; Accepted (in revised version) 12 March 2014
Available online 12 June 2014
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.AMS subject classifications: 35L05, 35L65, 35Q35, 65M06, 65M12, 65Z05
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Key words: Summation-by-parts, weak boundary conditions, penalty technique, high-order accuracy, finite difference schemes, stability, steady-state, non-reflecting boundary conditions.
Email: firstname.lastname@example.org (J. Nordstrom), email@example.com (Q. Abbas), firstname.lastname@example.org (B. A. Erickson), email@example.com (H. Frenander)