MINIMAL VARIATIONAL SURFACES AND QUALITY MESHES

Houman Borouchaki (1, 2) , Pascal Lafon (3) , P Laug (1) , P George (1)

1 Gamma3 - Automatic mesh generation and advanced methods
2 UTT - Université de Technologie de Troyes
3 LASMIS - Laboratoire des Systèmes Mécaniques et d'Ingénierie Simultanée

Many physical phenomena in science and engineering can be modelled by partial di erential equations (PDEs) and solved using the nite element method (FEM). Such a method uses as computational spatial support a mesh of the domain where the equations are formulated. The mesh quality i s a k ey-point for the accuracy of the numerical solution. This paper describes a methodology to construct a quality mesh of the domain from a given discretization of its boundary. W e show that the size map related to such a mesh constitutes a minimal variational surface supported by a given contour. This surface can be constructed, from its boundary, using the nite element method or by the resolution of a simple discrete optimization problem. The quality mesh of the domain is then a mesh conforming to the size map given by this surface. A numerical example is given to demonstrate the method.

Mots clés: minimal variational surfaces; quality meshes; equilateral meshes; regular meshes; adaptative meshing; nite elements; convex quadratic optimization

Domaines: Sciences de l'ingénieur [physics]

Houman Borouchaki, Pascal Lafon, P Laug, P George. MINIMAL VARIATIONAL SURFACES AND QUALITY MESHES. 9th International Meshing Roundtable Conference, Oct 2000, New Orleans, United States. ⟨hal-03620917⟩