What type of study is this?

This is a Quantitative Study study.

October 2, 2025Open Access

A Generalized Framework for Higher-Order Localized Orthogonal Decomposition Methods

MHMoritz HauckNumerical Method (China)ALAlexei LozinskiCentre National de la Recherche Scientifique RMRoland MaierNumerical Method (China)

Puntos clave

The framework analyzes localization strategies for linear elliptic problems, enhancing problem-solving techniques.
Numerical examples reveal important differences between conforming and nonconforming constraints in problem construction.
Extensions are proposed for both the Helmholtz equation and the Gross-Pitaevskii eigenvalue problem, broadening applicability.
The generalized approach accommodates various constraints, potentially improving the robustness of multiscale solutions.

Resumen

We introduce a generalized framework for studying higher-order versions of the multiscale method known as Localized Orthogonal Decomposition. Through a suitable reformulation, we are able to accommodate both conforming and nonconforming constraints in the construction process. In particular, we offer a new perspective on localization strategies. We fully analyze the strategy for linear elliptic problems and discuss extensions to the Helmholtz equation and the Gross--Pitaevskii eigenvalue problem. Numerical examples are presented that particularly provide valuable comparisons between conforming and nonconforming constraints.

Preguntar a la IA

Me gusta

Guardar

Ver artículo completo