An Adaptive Parareal Algorithm
Maday, Yvon; Mula, Olga (2018), An Adaptive Parareal Algorithm. https://basepub.dauphine.fr/handle/123456789/17973
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-01781257v2
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
Institut Universitaire de France [IUF]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an obstacle for the solution of large scale and high dimensional problems. Our main contribution is the significant improvement of the parallel efficiency of the parareal in time method, an iterative predictor-corrector algorithm. This is achieved by first reformulating the algorithm in a rigorous infinite dimensional functional space setting. We then formulate implementable versions where time dependent subproblems are solved at increasing accuracy across the parareal iterations (in opposition to the classical version where the subproblems are solved at a fixed high accuracy). Aside from the important improvement in parallel efficiency and as a natural by product, the new approach provides a rigourous online stopping criterion with a posteriori error estimators and the numerical cost to achieve a certain final accuracy is designed to be near-minimal. We illustrate the gain in efficiency of the new approach on simple numerical experiments. In addition to this, we discuss the potential benefits of reusing information from previous parareal iterations to enhance efficiency even more.
Subjects / Keywordsdomain decomposition; parareal in time algorithm; parallel efficiency; convergence rates; inexact fine solver; a posteriori estimators
Showing items related by title and author.
Argaud, J. P.; Bouriquet, B.; Gong, Helin; Maday, Yvon; Mula, Olga (2018) Article accepté pour publication ou publié