A Linear Algebra Approach to Time Parallelization: Parareal, ParaExp, ParaDiag, ParaOpt and ParaStieltjes

Abstract: Time parallelization has been a very active research area over the past decade. This is due to so massively parallel computer architectures that parallelization in the spatial direction rarely suffices to take full advantage of such systems when solving evolution problems. Time parallelization is however quite different from spatial parallelization, since information only propagates forward in time, never backward. Time parallelization algorithms are often derived at the PDE level, but whenever they are used, they take the form of solvers for linear algebra problems. I will give in my presentation an introduction to such algorithms at the linear algebra level, starting with two simple but typical model problems, namely a heat equation and a transport equation. At the linear algebra level, these two problems look deceivingly similar, but time parallel algorithms need different features when solving one or the other in parallel. I will explain the reason for this at the linear algebra level, and then show how Parareal, ParaExp and ParaDiag address them. If time permits, I will also briefly explain the newer classes of ParaOpt and ParaStieltjes algorithms.

computational engineering, finance, and sciencenumerical analysis

Audience: researchers in the topic

E-NLA - Online seminar series on numerical linear algebra

Series comments: E-NLA is an online seminar series dedicated to topics in Numerical Linear Algebra. Talks take place on Wednesdays at 4pm (Central European Time) via Zoom and are initially scheduled on a weekly basis.

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