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

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

Under Review 2013, SCEC Contribution #1806

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 at 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.

Citation
Nordström, J., Abbas, Q., Erickson, B. A., & Frenander, H. (2013). A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain . Communications in Computational Physics, (under review).