Local training and enrichment based on a residual localization strategy

TL;DR

This paper introduces an adaptive localized model order reduction framework that combines local offline training and online enrichment with localized error control, improving efficiency for large-scale parametrized problems.

Contribution

It presents a novel combination of local training and enrichment strategies with a residual localization-based error estimator for improved model reduction.

Findings

Numerical experiments show effective local enrichment.

The approach achieves accurate solutions with reduced computational effort.

Localized error control guides adaptive enrichment effectively.

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.