通过迭代网格细化实现航空声学的双级正则化

arXiv - MATH - Optimization and Control Pub Date : 2024-09-10 DOI:arxiv-2409.06854

Christian Aarset, Tram Thi Ngoc Nguyen

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摘要

在这项工作中，我们阐述了自适应网格细化有限元离散 PDE 与最近开发的 \emph{bi-levelregularization algithm} 之间的联系。通过根据数据噪声进行自适应网格细化，正则化效果和收敛性是立竿见影的。此外，我们还以航空声学中的 Helmholtzequation 为例，在时间和重构质量方面证明了该算法在数值上优于经典的 Landweber 算法。

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Bi-level regularization via iterative mesh refinement for aeroacoustics

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.

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arXiv - MATH - Optimization and Control

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