Authors : Ciaramella, Gabriele (Author of the conference)
CIRM (Publisher )
Abstract :
The parallel-in-time integration of wave-type equations is well known to be a difficult task. When applying classical waveform-relaxation (WR) and parareal type methods, one generally experiences rapid error growth before reaching convergence in a finite number of iterations. This negative behavior prevents, in general, the successful application of these domain decomposition methods. In this talk, the focus is on WR-type methods. Classical WR convergence analyses use classical Laplace/Fourier techniques. However, these approaches provide analyses for unbounded time intervals, and do not allow one to describe precisely the WR converge behavior on finite time intervals. In this talk, we present a novel analysis based on the methods of characteristics, which allows us, on the one hand, to obtain a detailed characterization of the error growth along with the iterations and, on the other hand, to introduce a new parallel-in-time computational strategy. Numerical experiments support our new theoretical and numerical findings. This is a joint work with Martin J. Gander and Ilario Mazzieri.
Keywords : waveform relaxation methods; wave equation; space-time domain decomposition methods
MSC Codes :
35L05
- Wave equation (hyperbolic PDE)
65F10
- Iterative methods for linear systems
65M55
- Multigrid methods; domain decomposition (IVP of PDE)
Additional resources :
https://www.cirm-math.fr/RepOrga/2642/Slides/Ciaramella.pdf
Film maker : Hennenfent, Guillaume
Language : English
Available date : 29/07/2022
Conference Date : 12/07/2022
Subseries : Research talks
arXiv category : Numerical Analysis
Mathematical Area(s) : Numerical Analysis & Scientific Computing ; PDE
Format : MP4 (.mp4) - HD
Video Time : 00:27:18
Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students
Download : https://videos.cirm-math.fr/2022-07-12_Ciaramella.mp4
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Event Title : Jean-Morlet Chair - PinT 2022: 11th Conference on Parallel-in-Time Integration / Chaire Jean-Morlet 2022 - 11ème conférence PinT - Parallel-in-Time Integration Event Organizers : Gander, Martin ; Hubert, Florence Dates : 11/07/2022 - 15/07/2022
Event Year : 2022
Event URL : https://www.chairejeanmorlet.com/2642.html
DOI : 10.24350/CIRM.V.19938503
Cite this video as:
Ciaramella, Gabriele (2022). On waveform-relaxation type methods for wave-type equation. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19938503
URI : http://dx.doi.org/10.24350/CIRM.V.19938503
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