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Volume 16, Issue 2
A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

Jan Nordström, Qaisar Abbas, Brittany A. Erickson & Hannes Frenander

DOI: 10.4208/cicp.020313.120314a

Commun. Comput. Phys., 16 (2014), pp. 541-570.

Published online: 2014-08

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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.

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@Article{CiCP-16-541, author = {Jan Nordström, Qaisar Abbas, Brittany A. Erickson and Hannes Frenander}, title = {A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain}, journal = {Communications in Computational Physics}, year = {2014}, volume = {16}, number = {2}, pages = {541--570}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.020313.120314a}, url = {http://global-sci.org/intro/article_detail/cicp/7053.html} }
TY - JOUR T1 - A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain AU - Jan Nordström, Qaisar Abbas, Brittany A. Erickson & Hannes Frenander JO - Communications in Computational Physics VL - 2 SP - 541 EP - 570 PY - 2014 DA - 2014/08 SN - 16 DO - http://doi.org/10.4208/cicp.020313.120314a UR - https://global-sci.org/intro/article_detail/cicp/7053.html KW - AB -

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.

Jan Nordström, Qaisar Abbas, Brittany A. Erickson and Hannes Frenander. (2014). A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain. Communications in Computational Physics. 16 (2). 541-570. doi:10.4208/cicp.020313.120314a
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