Bi-level regularization via iterative mesh refinement for aeroacoustics

TL;DR

This paper introduces a novel bi-level regularization method that leverages iterative mesh refinement for solving PDEs in aeroacoustics, demonstrating improved efficiency and accuracy over classical algorithms.

Contribution

It establishes a connection between adaptive mesh refinement and bi-level regularization, showing how mesh refinement enhances regularization effects and convergence in PDE solutions.

Findings

Adaptive mesh refinement improves reconstruction quality.

The proposed method outperforms Landweber algorithm in speed and accuracy.

Numerical experiments confirm the effectiveness in aeroacoustic Helmholtz problems.

Abstract

In this work, we illustrate the connection between adaptive mesh refinement for finite element discretized PDEs and the recently developed \emph{bi-level regularization algorithm}. By adaptive mesh refinement according to data noise, regularization effect and convergence are immediate consequences. We moreover demonstrate its numerical advantages to the classical Landweber algorithm in term of time and reconstruction quality for the example of the Helmholtz equation in an aeroacoustic setting.