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arXiv · 2203.08455

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

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.

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Benjamin Carrel, Martin J. Gander, Bart Vandereycken. 2022-03-16. Low-rank Parareal: a low-rank parallel-in-time integrator. https://arxiv.org/abs/2203.08455

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