Exponential Convergence of Online Enrichment in Localized Reduced Basis Methods

Online enrichment is the extension of a reduced solution space based on the solution of the reduced model. Procedures for online enrichment were published for many localized model order reduction techniques. We show that residual based online enrichment on overlapping domains converges exponentially...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Buhr, Andreas
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.02.2018
Subjects
Convergence
Domains
Enrichment
Mathematical models
Mathematics - Numerical Analysis
Model reduction
Solution space
Thermodynamics
Online AccessGet full text

Cover

More Information
Summary:Online enrichment is the extension of a reduced solution space based on the solution of the reduced model. Procedures for online enrichment were published for many localized model order reduction techniques. We show that residual based online enrichment on overlapping domains converges exponentially. Furthermore, we present an optimal enrichment strategy which couples the global reduced space with a local fine space. Numerical experiments on the two dimensional stationary heat equation with high contrast and channels confirm and illustrate the results.
ISSN:2331-8422
DOI:10.48550/arxiv.1710.02104