Work

Multilevel Parareal Algorithm with Averaging for Oscillatory Problems

Year: 2024

Type: article

Abstract: . The present study is an extension of the work done by Peddle, Haut, and Wingate [ SIAM J. Sci. Comput., 41 (2019), pp. A3476–A3497] and Haut and Wingate [ SIAM J. Sci. Comput., 36 (2014), pp. A693–A713], where a two-level Parareal method with mapping and averaging is examined. The method proposed in this paper is a multilevel Parareal method with arbitrarily many levels, which is not restricted to the two-level case. We give an asymptotic error estimate which reduces to the two-level estimate for the case when only two levels are considered. Introducing more than two levels has important consequences for the averaging procedure, as we choose separate averaging windows for each of the different levels, which is an additional new feature of the present study. The different averaging windows make the proposed method especially appropriate for nonlinear multiscale problems, because we can introduce a level for each intrinsic scale of the problem and adapt the averaging procedure such that we reproduce the behavior of the model on the particular scale resolved by the level. The method is applied to nonlinear differential equations. The nonlinearities can generate a range of frequencies in the problem. The computational cost of the new method is investigated and studied on several examples.

Source: SIAM Journal on Scientific Computing

DOI: 10.1137/23m1547123

Authors: Juliane Rosemeier, Terry Haut, Beth Wingate

Institutions: Lawrence Livermore National Laboratory, University of Exeter, Freie Universität Berlin

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid