On the numerical resolution of anisotropic equations with high order differential operators arising in plasma physics
| Autor: | Fabrice Deluzet, Jacek Narski, Chang Yang |
|---|---|
| Přispěvatelé: | Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Computer science Applied Mathematics Numerical analysis 010103 numerical & computational mathematics Differential operator 01 natural sciences Computer Science Applications 010101 applied mathematics Computational Mathematics Modeling and Simulation Bounded function Applied mathematics Polygon mesh 0101 mathematics Anisotropy Condition number Scaling ComputingMilieux_MISCELLANEOUS [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Resolution (algebra) |
| Zdroj: | Journal of Computational Physics Journal of Computational Physics, 2019, 386, pp.502-523. ⟨10.1016/j.jcp.2019.01.050⟩ Journal of Computational Physics, Elsevier, 2019, 386, pp.502-523. ⟨10.1016/j.jcp.2019.01.050⟩ |
| ISSN: | 0021-9991 1090-2716 |
| DOI: | 10.1016/j.jcp.2019.01.050⟩ |
| Popis: | In this paper, numerical schemes are introduced for the efficient resolution of anisotropic equations including high order differential operators. The model problem investigated in this paper, though simplified, is representative of the difficulties encountered in the modeling of Tokamak plasmas. The occurrence of high order differential operators introduces specific difficulties for the design of effective numerical methods. On the one hand, regular discretizations of the problem provide matrices characterized by a condition number that blows up with increasing anisotropy strength. On the other hand, matrices issued from Asymptotic-Preserving methods preserve a condition number bounded with respect to the anisotropy strength, nonetheless it scales very poorly as the mesh is refined. Both alternatives reveal to be inoperative in this specific framework to address the targeted values of anisotropy on refined meshes. We therefore introduce two successful methods offering the advantages of each approach: a condition number unrelated to the anisotropy strength and scaling as favorably as standard discretizations with the mesh refinement. |
| Databáze: | OpenAIRE |
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