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

arXiv (Cornell University)

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

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

2. Henrik Eisenmann Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen

3. André Uschmajew