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Multigrid schemes for high order discretizations of hyperbolic problems
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-7972-6183
2019 (English)In: 2019 AIAA Aerospace Sciences Meeting, AIAA Scitech Forum, American Institute of Aeronautics and Astronautics, 2019, p. 1-25, article id AIAA 2019-0103Conference paper, Published paper (Refereed)
Abstract [en]

Total variation diminishing multigrid methods have been developed for first order accurate discretizations of hyperbolic conservation laws. This technique is based on a so-called upwind biased residual interpolation and allows for algorithms devoid of spurious numerical oscillations in the transient phase. In this paper, we justify the introduction of such prolongation and restriction operators by rewriting the algorithm in a matrix-vector notation. This perspective sheds new light on multigrid procedures for hyperbolic problems and provides a direct extension for high order accurate difference approximations. The new multigrid procedure is presented, advantages and disadvantages are discussed and numerical experiments are performed.

Place, publisher, year, edition, pages
American Institute of Aeronautics and Astronautics, 2019. p. 1-25, article id AIAA 2019-0103
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-154393DOI: 10.2514/6.2019-0103ISBN: 978-1-62410-578-4 (electronic)OAI: oai:DiVA.org:liu-154393DiVA, id: diva2:1287393
Conference
2019 AIAA Aerospace Sciences Meeting, AIAA Scitech Forum, San Diego, California, 7-11 January 2019
Available from: 2019-02-11 Created: 2019-02-11 Last updated: 2019-02-11

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Ruggiu, Andrea AlessandroNordström, Jan
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