The paper focuses on developing efficient model order reduction techniques for parametric PDEs. The key insights are:
Classical linear subspace-based model reduction methods are limited in their applicability, especially for transport-dominated or weakly coercive PDEs.
The authors propose a tree-based library approach that can use both linear and nonlinear approximation spaces to represent the solution manifold. This allows handling a broader class of PDEs.
Two tree-based library construction algorithms are presented:
The tree-based representation of the library allows for a compressed storage and efficient evaluation of the reduced model, compared to a flat library approach.
Numerical experiments demonstrate the effectiveness of the proposed tree-based strategies in approximating the solution manifold for various types of PDEs, including diffusion, convection-diffusion, and transport-dominated problems.
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by Diane Guigna... at arxiv.org 04-19-2024
https://arxiv.org/pdf/2404.12262.pdfDeeper Inquiries