Localized model reduction for parameterized problems

Andreas Buhr, Laura Iapichino, Mario Ohlberger, Stephan Rave, Felix Schindler, Kathrin Smetana

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

15 Scopus citations

Abstract

In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that have only support on part of the domain and compute a global approximation by a suitable coupling of the local spaces. In detail, we show how optimal local approximation spaces can be constructed and approximated by random sampling. An overview of possible conforming and nonconforming couplings of the local spaces is provided and corresponding localized a posteriori error estimates are derived. We introduce concepts of local basis enrichment, which includes a discussion of adaptivity. Implementational aspects of localized model reduction methods are addressed. Finally, we illustrate the presented concepts for multiscale, linear elasticity, and fluid-flow problems, providing several numerical experiments.

Original languageEnglish
Title of host publicationSnapshot-Based Methods and Algorithms
Pages245-305
Number of pages61
ISBN (Electronic)9783110671490
DOIs
StatePublished - 16 Dec 2020

Keywords

  • A posteriori error estimation
  • Basis enrichment
  • Localized model reduction
  • Multiscale problems
  • Online adaptivity
  • Parameterized systems
  • Randomized training
  • Reduced basis method

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