Schmitt, Andreas ; Schreiber, Martin ; Peixoto, Pedro ; Schäfer, Michael (2018)
A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation.
In: Computing and Visualization in Science, 19 (1)
doi: 10.1007/s00791-018-0294-1
Artikel, Bibliographie
Kurzbeschreibung (Abstract)
This work focuses on the Parareal parallel-in-time method and its application to the viscous Burgers equation. A crucial component of Parareal is the coarse time stepping scheme, which strongly impacts the convergence of the parallel-in-time method. Three choices of coarse time stepping schemes are investigated in this work: explicit Runge--Kutta, implicit--explicit Runge--Kutta, and implicit Runge--Kutta with semi-Lagrangian advection. Manufactured solutions are used to conduct studies, which provide insight into the viability of each considered time stepping method for the coarse time step of Parareal. One of our main findings is the advantageous convergence behavior of the semi-Lagrangian scheme for advective flows.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2018 |
| Autor(en): | Schmitt, Andreas ; Schreiber, Martin ; Peixoto, Pedro ; Schäfer, Michael |
| Art des Eintrags: | Bibliographie |
| Titel: | A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation |
| Sprache: | Englisch |
| Publikationsjahr: | Juni 2018 |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Computing and Visualization in Science |
| Jahrgang/Volume einer Zeitschrift: | 19 |
| (Heft-)Nummer: | 1 |
| DOI: | 10.1007/s00791-018-0294-1 |
| URL / URN: | https://doi.org/10.1007/s00791-018-0294-1 |
| Kurzbeschreibung (Abstract): | This work focuses on the Parareal parallel-in-time method and its application to the viscous Burgers equation. A crucial component of Parareal is the coarse time stepping scheme, which strongly impacts the convergence of the parallel-in-time method. Three choices of coarse time stepping schemes are investigated in this work: explicit Runge--Kutta, implicit--explicit Runge--Kutta, and implicit Runge--Kutta with semi-Lagrangian advection. Manufactured solutions are used to conduct studies, which provide insight into the viability of each considered time stepping method for the coarse time step of Parareal. One of our main findings is the advantageous convergence behavior of the semi-Lagrangian scheme for advective flows. |
| Fachbereich(e)/-gebiet(e): | 16 Fachbereich Maschinenbau 16 Fachbereich Maschinenbau > Fachgebiet für Numerische Berechnungsverfahren im Maschinenbau (FNB) 16 Fachbereich Maschinenbau > Fachgebiet für Numerische Berechnungsverfahren im Maschinenbau (FNB) > Numerische Berechnungsverfahren Exzellenzinitiative Exzellenzinitiative > Graduiertenschulen Exzellenzinitiative > Graduiertenschulen > Graduate School of Computational Engineering (CE) |
| Hinterlegungsdatum: | 25 Jul 2018 11:48 |
| Letzte Änderung: | 12 Mär 2019 09:36 |
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