A Posteriori Error Analysis of Component Mode Synthesis for the Frequency Response Problem

TL;DR

This paper develops a posteriori error estimates for component mode synthesis reduced models in frequency response problems, enabling adaptive algorithms to optimize subspace dimensions based on error contributions.

Contribution

It introduces a posteriori error estimates for CMS in frequency response analysis, facilitating adaptive model reduction with error control.

Findings

Error estimates accurately reflect subspace influence on overall error.

Adaptive algorithms can automatically determine optimal subspace sizes.

Numerical examples validate the effectiveness of the error estimates.

Abstract

We consider the frequency response problem and derive a posteriori error estimates for the discrete error in a reduced finite element model obtained using the component mode synthesis (CMS) method. We provide estimates in a linear quantity of interest and the energy norm. The estimates reflect to what degree each CMS subspace influence the overall error in the reduced solution. This enables automatic error control through adaptive algorithms that determine suitable dimensions of each subspace. We illustrate the theoretical results by including several numerical examples.