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Wave propagation characteristics of Parareal
Publikationstyp
Journal Article
Date Issued
2018-05-29
Sprache
English
Author(s)
Volume
19
Issue
1-2
Start Page
1
End Page
17
Citation
Computing and Visualization in Science 19 (1-2): 1-17 (2018)
Publisher DOI
Scopus ID
Peer Reviewed
true
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.
Subjects
Advection-dominated problem
Convergence
Dispersion relation
Hyperbolic problem
Parareal
DDC Class
004: Informatik