X-SFEM, a computational technique based on X-FEM to deal with random shapes

Anthony Nouy (1) , Franck Schoefs (1) , Nicolas Moes (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

We propose a new method to deal with random geometries. It is an extension to the stochastic context of the eXtended Finite Element Method. This method lies on two majors points: the implicit description of geometry by the level set technique and the use of the partition of unity method for the enrichment of the finite element approximation space. This new technique leads by a direct calculus on a fixed finite element mesh to a solution which is explicit in terms of the basic random variables describing the geometry. We present here the basis of this approach and several examples to illustrate its performances.

Mots clés: computational stochastic mechanics; X-FEM; level set; stochastic finite element; random geometry

Domaines: Analyse numérique [math.NA]; Mécanique [physics.med-ph]

Anthony Nouy, Franck Schoefs, Nicolas Moes. X-SFEM, a computational technique based on X-FEM to deal with random shapes. Revue Européenne de Mécanique Numérique/European Journal of Computational Mechanics, 2007, 16 (2), pp.277-293. ⟨10.3166/remn.16.277-293⟩. ⟨hal-00368060⟩