Towards simultaneous meta-modeling for both the output and input spaces in the context of design shape optimization using asynchronous high-performance computing

ECCOMAS PhD Olympiads 2013International audience. In this paper, we propose a simultaneous meta-modeling protocol for both input and output spaces. We perform a reparametrization of the input space using constrained shape interpolation by introducing the concept of an α-manifold of admissible meshed shapes. The output space is reduced using constrained Proper Orthogonal Decomposition. By simultaneously using meta-modeling for both spaces, we facilitate interactive design space exploration for the purpose of design. The proposed approach is applied to several industrial problems

Estimation of the strain field from full-field displacement noisy data. Comparing finite elements global least squares and polynomial diffuse approximation

International audienceIn this study, the issue of reconstructing strain fields from corrupted full-field displacement data is addressed. Two approaches are proposed, a global one based on Finite Element Approximation (FEA) and a local one based on Diffuse Approximation (DA). Both approaches are compared on a case study which is supposed difficult (open-hole tensile test). DA provides more stable results, but is more CPU time consuming. Eventually, it is proposed to monitor locally the filtering effect of both approaches, the prospects being an impending improvement of the reconstruction for both approaches

La méthode PGD-BEM appliquée à l’équation de la chaleur nonlinéaire

National audienceDans [1] nous avons proposé une nouvelle méthode non incrémentale pour résoudre l’équation de la chaleur linéaire, la PGD-BEM. Nous proposons, une adaptation de cet algorithme dans le cas où le coefficient de conductivité thermique dépend de la température. Cette approche ne demande pas de connaître le noyau de Green de l’équation de la chaleur non-linéaire, seul le noyau de l’équation de Poisson en espace est nécessaire. Nous validons notre approche sur un exemple numérique

SLDLT: une technique de mise à jour de la décomposition LDLT pour l'accélération des simulations de Monte Carlo dans le cas de champs stochastiques non uniformes

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/29/54/ANNEX/r_79AK56I8.pd

Pseudo-divergence-free element free Galerkin method for incompressible fluid flow

Incompressible modeling in finite elements has been a major concern since its early developments and has been extensively studied. However, incompressibility in mesh-free methods is still an open topic. Thus, instabilities or locking can preclude the use of mesh-free approximations in such problems. Here, a novel mesh-free formulation is proposed for incompressible flow. It is based on defining a pseudo-divergence-free interpolation space. That is, the finite dimensional interpolation space approaches a divergence-free space when the discretization is refined. Note that such an interpolation does not include any overhead in the computations. The numerical evaluations are performed using the inf–sup numerical test and two well-known benchmark examples for Stokes flow

Résolution de l'équation des plaques minces de Kirchhoff par une approche sans maillage construite à l'aide d'une approximation moindres carrés mobiles

Nous présentons une méthode sans maillage de type EFG pour résoudre un problème de plaque mince de Kirchhoff. Nous utilisons une approximation Hermite moindres carrés mobiles, un schéma d'intégration HSCNI, et une méthode de pénalisation modifiée pour appliquer les conditions aux limites. De cette manière, nous obtenons des taux de convergence optimaux pour des bases d'approximations quadratique ou cubique

Surface remeshing by local hermite diffuse interpolation

International audienceWe propose a method to build a three-dimensional adapted surface mesh with respect to a mesh size map driven by surface curvature. The data needed to optimize the mesh have been reduced to an initial mesh. The building of a local geometrical model but continuous over the whole domain is based on a local Hermite diffuse interpolation calculated from the nodes of the initial mesh and from the normal vectors to the surface. The optimization procedures involve extracting from the surface mesh sets of triangles sharing the same node or the same edge and then remeshing the outer contour to a higher criterion (size or shape). These procedures may be used in order to refine or coarsen the mesh but also in a final step to enhance the shape quality of the elements. Examples demonstrate the ability of the method to create adapted meshes of complex surfaces while meeting high-quality standards and a good respect of the geometrical surface