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A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation

Schmitt, Andreas and Schreiber, Martin and Peixoto, Pedro and Schäfer, Michael (2018):
A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation.
In: Computing and Visualization in Science, pp. 45-57, 19, (1), ISSN 1433-0369, DOI: 10.1007/s00791-018-0294-1, [Online-Edition: https://doi.org/10.1007/s00791-018-0294-1],
[Article]

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.

Item Type: Article
Erschienen: 2018
Creators: Schmitt, Andreas and Schreiber, Martin and Peixoto, Pedro and Schäfer, Michael
Title: A numerical study of a semi-Lagrangian Parareal method applied to the viscous Burgers equation
Language: English
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.

Journal or Publication Title: Computing and Visualization in Science
Volume: 19
Number: 1
Divisions: 16 Department of Mechanical Engineering
16 Department of Mechanical Engineering > Institute of Numerical Methods in Mechanical Engineering (FNB)
16 Department of Mechanical Engineering > Institute of Numerical Methods in Mechanical Engineering (FNB) > Numerics
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Date Deposited: 25 Jul 2018 11:48
DOI: 10.1007/s00791-018-0294-1
Official URL: https://doi.org/10.1007/s00791-018-0294-1
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