Contrôle de l'approximation géométrique d'une interface par une métrique anisotrope

Ducrot, Vincent; Frey, Pascal

doi:10.1016/j.crma.2007.10.008

Cited by 8 publications

(11 citation statements)

References 2 publications

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“…An interesting potentiality of local anisotropic mesh adaptation is related to the accuracte tracking and aproximation of a dynamically evolving interface [16]. In this approach, the metric tensor field is related to the intrinsic properties of the manifold of codimension one that correspond to the interface.…”

Section: Capture Of An Interfacementioning

confidence: 99%

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Anisotropic Delaunay Mesh Adaptation for Unsteady Simulations

Dobrzynski

Frey

2008

Proceedings of the 17th International Meshing Roundtable

121

123

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Summary. Anisotropic mesh adaptation is a key feature in many numerical simulations to capture the physical behavior of a complex phenomenon at a reasonable computational cost. It is a challenging problem, especially when dealing with time dependent and interface capturing or tracking problems. Here, we describe an extension of the Delaunay kernel for creating anisotropic mesh elements based on adequate metric tensors. The accuracy and efficiency of the method is assessed on various numerical examples of complex three-dimensional simulations.

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Section: Capture Of An Interfacementioning

confidence: 99%

“…In this respect, it can be considered as an extension of previous works on anisotropic meshing for planar domains. Second, it explains how to build an anisotropic metric tensor for level set interface tracking, following the ideas of [16]. Then, we show how this method can be efficiently used to resolve a moving mesh problem.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Delaunay Mesh Adaptation for Unsteady Simulations

Dobrzynski

Frey

2008

Proceedings of the 17th International Meshing Roundtable

121

123

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“…In [20,21], we proposed a method for defining the metric tensor to control the generation of anisotropic elements in the vicinity of an interface defined with a level set function. Here, we adapted this approach as follows.…”

Section: Anisotropic Mesh Generationmentioning

confidence: 99%

“…(1) initialization stage: at first, a scalar value d(x, V ) corresponding to its distance to the point set V is assigned to each mesh vertex x of a quasi-uniform anisotropic triangulation T h , that is highly refined in the vicinity of the point cloud using the technique described in [20]; (2) evolutionary stage: an initial regular implicit curve Γ(t = 0) is progressively deformed by solving a level set based advection equation until it fits at best through the data set; (3) discretization stage: in the third phase, a piecewise affine approximation of the regular final curve is obtained that allows for the fast visualization of the numerical solution.…”

Section: Our Approachmentioning

confidence: 99%

Level set driven smooth curve approximation from unorganized or noisy point set

Claisse

Frey

2009

ESAIM: Proc.

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Abstract. In this paper, we propose a curve construction method for a non uniform point data set based on a minimal curve approximation model. Numerically, the level set method is used for curve reconstruction. We represent the shape of the curve through its distance function and formulate curve reconstruction as a constrained minimization problem. We solve the minimization problem on a highly anisotropic triangulation to improve the accuracy of the numerical scheme. This method can handle complex geometries and deal with arbitrary topologies as well as with noisy data sets. Several numerical examples are provided to show the efficiency of the proposed approach.Résumé. Dans ce papier, on propose un modèle de courbe d'approximation minimale pour construire une courbeà partir d'un nuage de points. Numériquement, la reconstruction de la courbe s'appuie sur une formulation de type ligne de niveau. On représente la forme de la courbe par sa fonction distance aux points et on exprime ce problème comme un problème de minimisation. Ce dernier est résolu sur une triangulation anisotrope qui permet d'améliorer la précision du schéma numérique. Cette méthode permet de traiter des géométries complexes et des topologies quelconques ainsi que des données bruitées. Des exemples de reconstruction sont proposés pour montrer l'éfficacité de cette approche.

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“…In order to improve the accuracy of the numerical approximation, it is desirable to increase the local mesh density in the vicinity of the point cloud. To this end, we start from a quasi-uniform unstructured simplicial mesh with respect to an anisotropic metric tensor field, [5]. The latter is defined based on the local mean curvature of the zero levelset, here d(x, V ) = 0.…”

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confidence: 99%