10–13 Jun 2024
Inria Center at the University of Lille
Europe/Paris timezone

Global space-time low-rank methods for the time-dependent Schrödinger equations

11 Jun 2024, 15:15
Amphitheater, Building B (Inria Center at the University of Lille)

Amphitheater, Building B

Inria Center at the University of Lille

Parc scientifique de la Haute-Borne, 40 avenue Halley, 59650 Villeneuve d'Ascq – France


Virginie Ehrlacher (Ecole des Ponts ParisTech and Inria Paris Centre)


The aim of this talk is to present novel global space-time methods for the approximation of the time-dependent Schrödinger equation, using Kato theory. The latter can be used in conjunction with low-rank tensor formats (such as Tensor Trains for instance) to derive new variational principles to compute dynamical low-rank approximations of the solution, which are different from the Dirac-Frenkel principle. One significant advantage of this new variational formulation is that the existence of a dynamical low-rank approximation for any finite-time horizon can be proved, whereas dynamical low-rank approximations constructed with the Dirac-Frenkel principle can usually be porved to exist only locally in time. Illustrative numerical results will be presented to highlight the differences between the dynamical low-rank approximations obtained with these different approaches. This is joint work with Clément Guillot and Mi-Song Dupuy.

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