Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

Loseille, Adrien; Dervieux, Alain; Alauzet, Frédéric

doi:10.1016/j.jcp.2009.12.021

Cited by 170 publications

(143 citation statements)

References 41 publications

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“…Alauzet et al introduced the notion of continuous metrics and continuous meshes to minimize interpolation error [3,26,2]. Loseille et al [27] applied this notion to a posteriori error estimates in order to minimize the approximation error during the solution process of some PDEs. Chen et al [11] considered anisotropic finite element approximation of functions in the L p norm.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Delaunay Mesh Generation

Boissonnat¹,

Wormser²,

Yvinec³

2015

SIAM J. Comput.

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Anisotropic meshes are triangulations of a given domain in the plane or in higher dimensions, with elements elongated along prescribed directions. Anisotropic triangulations are known to be well suited for interpolation of functions or solving PDEs. Assuming that the anisotropic shape requirements for mesh elements are given through a metric field varying over the domain, we propose a new approach to anisotropic mesh generation, relying on the notion of anisotropic Delaunay meshes. An anisotropic Delaunay mesh is defined as a mesh in which the star of each vertex v consists of simplices that are Delaunay for the metric associated to vertex v. This definition works in any dimension and allows to define a simple refinement algorithm. The algorithm takes as input a domain and a metric field and provides, after completion, an anisotropic mesh whose elements are shaped according to the metric field.

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Section: Introductionmentioning

confidence: 99%

Anisotropic Delaunay Mesh Generation

Boissonnat¹,

Wormser²,

Yvinec³

2015

SIAM J. Comput.

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“…Anisotropic adaptive algorithms are now widely used to solve complex systems based on partial differential equations, see for instance [5,6,11,16]. Our goal is to experiment such techniques for the 3D linear elasticity system, the computational domain being a thin 3D plate.…”

Section: The Linear Elasticity Model and The Numerical Methodsmentioning

confidence: 99%

“…The mesh generator fits the Riemannian metric framework of [4]. The goal is to generate a quasi-unit mesh with respect to the prescribed metric (11). The input of the mesh generator is the metric-a 3 3 symmetric positive definite matrix-thus we assume that, for each x 2˝, the metric M .x/ is known.…”

Section: Anisotropic Mesh Generationmentioning

confidence: 99%

Anisotropic, Adaptive Finite Elements for a Thin 3D Plate

Picasso

Loseille²

2015

New Challenges in Grid Generation and Adaptivity for Scientific Computing

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“…That happens for singular cases, and also for small number of nodes for which the same non-adaptive strategies do not show high order convergence. We refer to [12]. A general analysis of this favorable behavior is not yet available for the multi-dimensional case.…”

Section: Observed Convergencementioning

confidence: 99%

Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients,

Brèthes

2014

ESAIM: ProcS

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Abstract. In order to solve the linear partial differential equation Au = f , we combine two methods: FullMultigrid method and Hessian-based mesh adaptation. First, we define independently an Hessian-based mesh adaptation loop and a FMG algorithm where, at each phase, the equation is solved by a preconditioned GMRES with multigrid as preconditioner. Then we insert the adaptive loop between the FMG phases. We use this new algorithm and we compare its results with those obtained with non-adaptive FMG.Résumé. On se propose de résoudre uneéquation différentielle linéaire aux dérivées partielles Au = f en combinant deux méthodes : la méthode FMG et la méthode d'adaptation basée hessien. Tout d'abord, on définit, indépendamment l'un de l'autre, une boucle d'adaptation de maillage basée sur des hessiens et un algorithme FMG où dans chaque phase, l'équation est résolue par un GMRES préconditionné par les multigrilles. Puis, on insère la boucle adaptative entre les phases FMG. On utilise le nouvel algorithme ainsi obtenu et on compare ses résultats avec ceux obtenus avec le FMG non adaptatif.

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Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations

Cited by 170 publications

References 41 publications

Anisotropic Delaunay Mesh Generation

Anisotropic Delaunay Mesh Generation

Anisotropic, Adaptive Finite Elements for a Thin 3D Plate

Adaptive metric-based multigrid for a Poisson problem with discontinuous coefficients,

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