Lunet, Thibaut and Bodart, Julien and Gratton, Serge
and Vasseur, Xavier
Understanding the effects of grid coarsening in space within the Parareal algorithm.
(2018)
In: 25th International Domain Decomposition Conference (DDXXV), 23 July 2018 - 27 July 2018 (St John, Canada).
(Unpublished)
Full text not available from this repository.
Official URL: https://dd25.math.mun.ca/Masterfile_abstract.pdf
Abstract
Among all Parallel-in-Time solutions that are available today, Parareal has the great advantage of not requiring heavy implementation work to be used within any already existent time-stepping solver. In the particular case of an explicit solver, space coarsening can be used to define a coarse solver, that provides interesting properties in terms of accuracy and time-parallel speedup. However, a major drawback of Parareal is that numerical instabilities can be expected for advection dominated problems, if some simulation parameters are not chosen wisely, hence a loss of parallel speedup. In this talk, we study the use of Parareal with space coarsening to solve the linear advection equation, by the mean of a Fourier analysis. The latter combines concepts from both Von Neuman analysis for space-time discretizations and Local Fourier Analysis for multi-grid methods. We identify the main effects of the grid coarsening on the convergence of Parareal, in order to bring some answers on the following questions: • Can Parareal with space-coarsening be stable when used on the advection problem ? • What is the influence of the chosen interpolation methods, and its order ? • Does the initial solution play a role in the convergence of the parallel-in-time algorithm ? Finally, a comparison to a bigger and more complex problem (Navier-Stokes equations) will be done to assess the generality of this analysis.
Item Type: | Conference or Workshop Item (Other) |
---|---|
Additional Information: | No full-text document attached to this repository. |
Audience (conference): | International conference proceedings |
Uncontrolled Keywords: | |
Institution: | French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE) Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE) Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE) Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE) Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE) Other partners > Université de Genève (SWITZERLAND) |
Laboratory name: | |
Statistics: | download |
Deposited On: | 28 Sep 2018 08:16 |
Repository Staff Only: item control page