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Understanding the effects of grid coarsening in space within the Parareal algorithm

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 (Unpublished)

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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 - INPT (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (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:
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Deposited By: Xavier Vasseur
Deposited On:28 Sep 2018 08:16

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