Randomized POD-Beyn algorithm for nonlinear eigenvalue problems – analysis and perspectives

Next Monday December 11, 2023:

Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
Title: Randomized POD-Beyn algorithm for nonlinear eigenvalue problems – analysis and perspectives
Speaker: Luka Grubišić
Affiliation: University of Zagreb (Croatia)

Abstract. We present a method to accelerate the solution of nonlinear eigenvalue problems in engineering by utilizing a reduced order model (ROM) of a resolvent via a randomized projection onto a suitable subspace. The projected problem can be proved to have eigenpairs identical to the full problem in a selected region of the complex plane (Beyn approach). The POD subspace is automatically constructed by solving (using a finite element approximation) the full problem at few random points inside the region of interest and is then updated using an a posteriori error estimator. The obtained method is suitable for any nonlinear eigenvalue problem given in the separable (affine like dependence on the spectral parameter) form. We also present residual error estimators to validate the results. We test our theory on a family of thermoacoustic application, and show how to generalize the method to applications dealing with other problems of vibrational stability.

WHEN

Mon. December 11, 2023 at 16:15H

WHERE

On-site: Room 03.323
Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstraße 11, 91058 Erlangen
GPS-Koord. Raum: 49.573764N, 11.030028E

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