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Scientific article
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English

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

Published inBIT, vol. 63, no. 13
Publication date2023-02-04
First online date2023-02-04
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.

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Citation (ISO format)
CARREL, Benjamin, GANDER, Martin Jakob, VANDEREYCKEN, Bart. Low-rank Parareal: a low-rank parallel-in-time integrator. In: BIT, 2023, vol. 63, n° 13. doi: 10.1007/s10543-023-00953-3
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ISSN of the journal0006-3835
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Creation04/03/2023 1:02:53 PM
First validation04/05/2023 2:28:04 PM
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