Exponential Convergence of Online Enrichment in Localized Reduced Basis Methods

TL;DR

This paper proves that residual-based online enrichment in localized reduced basis methods converges exponentially and introduces an optimal enrichment strategy, supported by numerical experiments on high-contrast heat equations.

Contribution

It demonstrates exponential convergence of online enrichment on overlapping domains and proposes an optimal coupling strategy with a local fine space.

Findings

Residual-based online enrichment converges exponentially.

The optimal enrichment strategy improves the reduced space.

Numerical experiments confirm theoretical results.

Abstract

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.