Existence of dynamical low-rank approximations to parabolic problems

Bachmayr, Markus; Eisenmann, Henrik; Kieri, Emil; Uschmajew, André

doi:10.1090/mcom/3626

Existence of dynamical low-rank approximations to parabolic problems
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by Markus Bachmayr, Henrik Eisenmann, Emil Kieri and André Uschmajew HTML | PDF

Math. Comp. 90 (2021), 1799-1830 Request permission

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.

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