Wave propagation characteristics of Parareal

The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareal’s wave propagation characteristics with the aim to better understand what causes the well documented stability problems for hyperbolic equations. The a...

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Bibliographic Details
Published inComputing and visualization in science Vol. 19; no. 1-2; pp. 1 - 17
Main Author Ruprecht, Daniel
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2018
Springer Nature B.V
Subjects
Algorithms
Calculus of Variations and Optimal Control; Optimization
Computational Mathematics and Numerical Analysis
Computer Applications in Chemistry
Mathematics
Mathematics and Statistics
Numerical Analysis
Propagation
S waves
Special Issue Parallel-in-Time Methods
Stability
Stability analysis
Time integration
Visualization
Wave dispersion
Wave propagation
Parareal
Dispersion relation
Hyperbolic problem
Advection-dominated problem
Convergence
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Summary:The paper derives and analyses the (semi-)discrete dispersion relation of the Parareal parallel-in-time integration method. It investigates Parareal’s wave propagation characteristics with the aim to better understand what causes the well documented stability problems for hyperbolic equations. The analysis shows that the instability is caused by convergence of the amplification factor to the exact value from above for medium to high wave numbers. Phase errors in the coarse propagator are identified as the culprit, which suggests that specifically tailored coarse level methods could provide a remedy.
Bibliography:ObjectType-Article-1
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ISSN:1432-9360
1433-0369
DOI:10.1007/s00791-018-0296-z