Dynamical low-rank approximation for parabolic problems

André Uschmajew (MPI MiS Leipzig)

May 09. 2022, 11:20 — 12:10

Dynamical low-rank approximation is a framework for time integration of matrix valued ODEs on a fixed-rank manifold based on a time dependent variational principle. Several applications arise from PDEs on product domains, but setting up a corresponding well-posed problem in function space (before discretization) may not be straightforward. Here we present a weak formulation of dynamical low-rank approximation for parabolic PDEs in two spatial dimensions. The existence and uniqueness of weak solutions is shown using a variational time-stepping scheme on the low-rank manifold which is related to practical methods for low-rank integration.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)