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Mathematics > Numerical Analysis

arXiv:2203.08455 (math)
[Submitted on 16 Mar 2022 (v1), last revised 13 Sep 2022 (this version, v2)]

Title:Low-rank Parareal: a low-rank parallel-in-time integrator

Authors:Benjamin Carrel, Martin J. Gander, Bart Vandereycken
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Abstract:In this work, the Parareal algorithm is applied to evolution problems that admit good low-rank approximations and for which the dynamical low-rank approximation (DLRA) can be used as time stepper. Many discrete integrators for DLRA have recently been proposed, based on splitting the projected vector field or by applying projected Runge--Kutta methods. The cost and accuracy of these methods are mostly governed by the rank chosen for the approximation. These properties are used in a new method, called low-rank Parareal, in order to obtain a time-parallel DLRA solver for evolution problems. The algorithm is analyzed on affine linear problems and the results are illustrated numerically.
Subjects: Numerical Analysis (math.NA)
MSC classes: 65L05, 65L20, 65L70, 68W10, 65F45, 65F55
Cite as: arXiv:2203.08455 [math.NA]
  (or arXiv:2203.08455v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2203.08455

Submission history

From: Benjamin Carrel [view email]
[v1] Wed, 16 Mar 2022 08:25:14 UTC (2,873 KB)
[v2] Tue, 13 Sep 2022 07:36:34 UTC (2,340 KB)
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