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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Half-space kinetic equations with general boundary conditions
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by Qin Li, Jianfeng Lu and Weiran Sun PDF
Math. Comp. 86 (2017), 1269-1301 Request permission

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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Additional Information
  • Qin Li
  • Affiliation: Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Drive, Madison, Wisconsin 53705
  • MR Author ID: 1016753
  • Email: qinli@math.wisc.edu
  • 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: jianfeng@math.duke.edu
  • 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