Seminar by Maxim Olshanskii

Speaker

Maxim Olshanskii (University of Houston)

Title

A tensor POD-ROM for parameter dependent dynamical systems

Date

  • December 05, 2023 16:00 CET+0100 (Europe/Rome)

  • December 05, 2023 10:00 EST-0500 (US/Eastern)

  • December 05, 2023 09:00 CST-0600 (US/Central)

  • December 05, 2023 07:00 PST-0800 (US/Pacific)

Abstract

A space-time-parameters structure of the parametric dynamical systems encourages the application of tensor methods for defining reduced-order models. Within a tensor-based ROM framework, traditional dimension reduction techniques like the matrix SVD yield to a low-rank tensor decomposition (LRTD). This extension of the Galerkin proper orthogonal decomposition ROMs using tensors enhances both the practical efficiency of the ROM and its suitability for rigorous error analysis when applied to parametric PDEs. I intend to present the new LRTD-ROM framework and explain an error analysis for an abstract linear parabolic problem. Through this analysis, we will observe that the error estimation relies more on the smoothness of the parameterized manifold of solutions rather than on the Kolmogorov n-widths.

Recording

Watch the recording on our YouTube channel.