Local training and enrichment based on a residual localization strategy

Tim Keil, Mario Ohlberger, Felix Schindler, Julia Schleuß

Research article in edited proceedings (conference) | Peer reviewed

Abstract

To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and local online enrichment with localized error control. For the latter, we adapt the residual localization strategy introduced in [Buhr, Engwer, Ohlberger, Rave, SIAM J. Sci. Comput., 2017] which allows to derive a localized a posteriori error estimator that can be employed to adaptively enrich the reduced solution space locally where needed. Numerical experiments demonstrate the potential of the proposed approach.

Details about the publication

PublisherFrolkovič, P; Mikula, K; Ševčovič, D
Book titleProceedings of the Conference Algoritmy 2024
Page range76-84
Publishing companyJednota slovenských matematikov a fyzikov
Place of publicationBratislava
Title of seriesProceedings of the Conference Algoritmy
Volume of series8
StatusPublished
Release year2024
ConferenceAlgoritmy 2024, Podbanske, Slovakia
ISBN978-80-89829-33-0
Link to the full texthttp://www.iam.fmph.uniba.sk/amuc/ojs/index.php/algoritmy/article/view/2157
Keywordslocalized model reduction; randomized training; online enrichment; residual localization

Authors from the University of Münster

Keil, Tim
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Ohlberger, Mario
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Center for Nonlinear Science
Center for Multiscale Theory and Computation
Schindler, Felix Tobias
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)
Schleuß, Julia
Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)