Metric and mesh: Definition and theoretical basics
Article REF: M3011 V1

Metric and mesh: Definition and theoretical basics

Authors : Abel CHEROUAT, Houman BOROUCHAKI, Florian BLACHERE

Publication date: September 10, 2023 | Lire en français

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Overview

ABSTRACT

This article gives the basics for finite element problems related to meshes. We are interested in the definition of a mesh. Thanks to the notion of metric, the geometric point of view is replaced by an algebraic and analytical point of view allowing to unify the notions of mesh, mesh adaptation and remeshing. In this new concept, a mesh is only a Riemannian space in which the metrics characterize the elements.

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AUTHORS

  • Abel CHEROUAT: University Professor - Unité de Recherche Génération Automatique de Maillage et Méthodes Avancées Troyes (GAMMA3) Université de Technologie de Troyes, France

  • Houman BOROUCHAKI: University Professor - Unité de Recherche Génération Automatique de Maillage et Méthodes Avancées Troyes (GAMMA3) Université de Technologie de Troyes, France

  • Florian BLACHERE: Senior Lecturer - Unité de Recherche Génération Automatique de Maillage et Méthodes Avancées Troyes (GAMMA3) Université de Technologie de Troyes, France

 INTRODUCTION

The finite element method is a powerful tool for numerically solving the partial differential equations involved in modeling most physical phenomena [BM 5 015] [M 3 185] . This method relies heavily on the spatial discretization of the computational domain, known as meshing. By adapting the mesh to the physics of the problem under consideration, it is also possible to achieve greater accuracy in the calculated solutions. For example, it is possible to capture geometric curvatures and rapid changes in the solution in areas of high variation, while maintaining an acceptable number of degrees of freedom

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KEYWORDS

finite elements   |   Metrics   |   Riemannian space   |   Mesh

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