Dynamical low-rank tensor approximations to high-dimensional parabolic problems: existence and convergence of spatial discretizations

Numerische Mathematik, vol. 157, pp. 781–822

Abstract

Abstract We consider dynamical low-rank approximations to parabolic problems on higher-order tensor manifolds in Hilbert spaces. In addition to existence of solutions and their stability with respect to perturbations to the problem data, we show convergence of spatial discretizations. Our framework accommodates various standard low-rank tensor formats for multivariate functions, including tensor train and hierarchical tensors.

Authors 3

1. Markus Bachmayr Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

2. Henrik Eisenmann corresponding Aachen Institut für Geometrie und Praktische Mathematik

   RWTH Aachen University

   Affiliation as printed

   Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Templergraben 55, 52062, Aachen, Germany

3. André Uschmajew

   University of Augsburg

   Affiliation as printed

   Institute of Mathematics & Centre for Advanced Analytics and Predictive Sciences, University of Augsburg, 86159, Augsburg, Germany