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MiS Preprint
33/2020

Existence of dynamical low-rank approximations to parabolic problems

Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew

Abstract

The existence and uniqueness of weak solutions to dynamical low-rank evolution problems for parabolic partial differential equations in two spatial dimensions is shown, covering also non-diagonal diffusion in the elliptic part. The proof is based on a variational time-stepping scheme on the low-rank manifold. Moreover, this scheme is shown to be closely related to practical methods for computing such low-rank evolutions.

Received:
Feb 27, 2020
Published:
Feb 27, 2020

Related publications

inJournal
2021 Repository Open Access
Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew

Existence of dynamical low-rank approximations to parabolic problems

In: Mathematics of computation, 90 (2021) 330, pp. 1799-1830