Error Estimation and Stopping Criteria for Krylov-Based Model Order Reduction in Acoustics

TL;DR

This paper investigates an error estimator based on Krylov subspace methods to determine the optimal reduced model order in acoustic simulations, supported by mathematical analysis and numerical experiments.

Contribution

It provides a mathematical validation of a heuristic error estimator for Krylov-based model order reduction in acoustics.

Findings

The difference between consecutive Krylov models accurately estimates the true error.

Numerical experiments confirm the estimator's effectiveness in acoustic models.

The estimator can serve as a stopping criterion for model reduction.

Abstract

Depending on the frequency range of interest, finite element-based modeling of acoustic problems leads to dynamical systems with very high dimensional state spaces. As these models can mostly be described with second order linear dynamical system with sparse matrices, mathematical model order reduction provides an interesting possibility to speed up the simulation process. In this work, we tackle the question of finding an optimal order for the reduced system, given a desired accuracy. To do so, we revisit a heuristic error estimator based on the difference of two reduced models from two consecutive Krylov iterations. We perform a mathematical analysis of the estimator and show that the difference of two consecutive reduced models does provide a sufficiently accurate estimation for the true model reduction error. This claim is supported by numerical experiments on two acoustic models. We briefly discuss its feasibility as a stopping criterion for Krylov-based model order reduction.