A unified Analysis Framework for Iterative Parallel-in-Time algorithms(Thibaut Lunet, Hamburg University of Technology)

17.03.2022 16:00 – 17:00

Parallel-in-time (PinT) methods have received renewed attention in the last two decades, mainly motivated by the advent of new supercomputing resources that provide more and more concurrency. Four of the most widely studied methods are Parareal (Lions, Maday, Turinici), PFASST (Minion and Emmett), MGRIT (Falgout, Friedhoff, Kolev, MacLachlan, Schroder) and a specific form of Space-Time Multigrid (Gander and Neumueller). All those algorithms have a common aspect: they are iterative PinT "across-the-steps" methods, i.e they represent the time sequential solution process as a large linear or nonlinear system and solve it by iterating on all time steps simultaneously. While various convergence analyses exist for each algorithm separately, it is difficult to relate them and compare convergence of these iterative PinT methods when applied to various model problems, and in applications.

In this talk, we present a new approach that lets us analyze the convergence of these four iterative algorithms in a common framework. Following an idea of Hairer and Gander already used to analyze Parareal convergence, this framework is based on an abstract view of each iterative PinT algorithm and provides error bounds for the Dahlquist equation, the fundamental time-dependent test problem. Furthermore, it provides understanding of the different convergence mechanisms in each algorithm and its level of abstraction could eventually lead to novel PinT algorithms.

Lieu

Conseil Général 7-9, Room 1-07, Séminaire d'analyse numérique

entrée libre