Abstract:We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various types of reflections, extending our previous work on half-space equations with incoming boundary conditions. As in our previous work, the main technique is a damping adding-removing procedure. We establish the well-posedness of linear (or linearized) half-space equations with general boundary conditions and quasi-optimality of the numerical scheme. The numerical method is validated by examples including a two-species transport equation, a multi-frequency transport equation, and the linearized BGK equation in 2D velocity space.
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- Qin Li
- Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53705
- MR Author ID: 1016753
- Email: firstname.lastname@example.org
- Jianfeng Lu
- Affiliation: Departments of Mathematics, Physics, and Chemistry, Duke University, Box 90320, Durham, North Carolina 27708
- MR Author ID: 822782
- ORCID: 0000-0001-6255-5165
- Email: email@example.com
- Weiran Sun
- Affiliation: Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby, British Columbia V5A 1S6, Canada
- Received by editor(s): September 9, 2015
- Received by editor(s) in revised form: December 2, 2015
- Published electronically: October 12, 2016
- Additional Notes: The research of the first author was supported in part by the AFOSR MURI grant FA9550-09-1-0613 and the National Science Foundation under award DMS-1318377
The research of the second author was supported in part by the Alfred P. Sloan Foundation and the National Science Foundation under award DMS-1312659 and DMS-1454939
The research of the third author was supported in part by the Simon Fraser University President’s Research Start-up Grant PRSG-877723 and NSERC Discovery Individual Grant #611626
- © Copyright 2016 American Mathematical Society
- Journal: Math. Comp. 86 (2017), 1269-1301
- MSC (2010): Primary 35Q20; Secondary 65N35
- DOI: https://doi.org/10.1090/mcom/3155
- MathSciNet review: 3614018