Multi-step variant of parareal algorithm

Katia Ait-Ameur (1, 2) , Yvon Maday (3, 1) , Marc Tajchman (2)

1 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
2 CEA - Commissariat à l'énergie atomique et aux énergies alternatives
3 IUF - Institut universitaire de France

In this paper, we propose a variant of the parareal algorithm for time-dependent problems involving a multi-step time scheme in the coarse and/or fine propagators. This choice can potentially bring higher approximation orders than plain one-step methods but the initialization of each time window needs to be appropriately chosen. In this work, we explore some possible initializations and demonstrate their relevance on a Dahlquist test equation, an advection-diffusion equation and an industrial application.

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Katia Ait-Ameur, Yvon Maday, Marc Tajchman. Multi-step variant of parareal algorithm. 2019. ⟨hal-02321882v2⟩