Levelsets and anisotropic mesh adaptation

Ducrot, Vincent; Frey, Pascal; Claisse, Alexandra

doi:10.3934/dcds.2009.23.165

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…This approach was proposed in the work of Coupez and depends on a so‐called length distribution tensor, which is derived from a statistical concept introduced in polymer science . The originality lies in the construction of the metric, and the associated edge‐based error estimator, which avoids complex Hessian reconstructions like those proposed in the works of Abgrall et al and Claisse et al In the case of level sets, the target region for the adaptation process is not the whole domain but the zone near the isozero. This is achieved here by working with the regularized Heaviside function of the level set

u_{ϵ} false(normalx false) = ϵ \tanh ((), \frac{φ false(normalx false)}{ϵ}) .

…”

Section: Fictitious Domain Strategies Based On Anisotropic Mesh Adaptmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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Summary A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh that is refined near the geometrical interface and elongated in the direction of a small curvature. This strategy allows to decrease the integration cost, which can be problematic for high‐order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behavior with respect to locking.

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u_{ϵ} false(normalx false) = ϵ \tanh ((), \frac{φ false(normalx false)}{ϵ}) .

…”

Section: Fictitious Domain Strategies Based On Anisotropic Mesh Adaptmentioning

confidence: 99%

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Legrain

Moës

2018

Numerical Meth Engineering

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“…We refer to the book of Sethian [16] for a description of level set methods. We also refer to [1] and therein references for the construction of anisotropic adapted mesh from a given set of points.…”

Section: 3c High Frequency Approximationmentioning

confidence: 99%

About the transmembrane voltage potential of a biological cell in time-harmonic regime.

Poignard¹

2009

ESAIM: Proc.

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Abstract. The paper presents heuristics to reduce several difficulties related to the determination of the transmembrane voltage potential (TMP) on cells with arbitrary smooth shape. We show how the thin weakly conducting membrane can be replaced by asymptotically equivalent transmission conditions at the interface between the cell interior (the cytoplasm) and the extracellular medium. We describe our formal asymptotic method for constructing precise models of cells. This method is based on an appropriate change of variables in the thin membrane. Our frequency dependent models is helpfull to determine the TMP on cells on which experiment measurements are prohibited. We end the paper by presenting briefly the sketch of the proofs of the asymptotics and the a priori error estimates.Résumé. Dans cet artice, nous présentons une méthode de développement asymptotique de milieuà couche mince en dimension 3 permettant de réduire les difficultés numériques liées au calcul du potentiel transmembranaire d'une cellule biologique. Nous montrons comment la fine membrane faiblement conductrice de la cellule peutêtre remplacée par des conditions de transmission appropriées sur le bord du cytoplasme. Notre méthode est basée sur un changement de variables adéquat dans la couche mince. Nous obtenons trois différents modèles permettant de décrire le comportement du potentiel quasi-élecrostatique d'un cellule suivant trois types de fréquences: basse, moyenne ou haute fréquences. Ces modèles permettent le calcul du potentiel transmembranaire dans des cellules sur lesquelles des mesures expérimentales sont difficilesà réaliser. Nous concluons en présentant brièvement les principes de démonstration des résultats.

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“…Adaptive Mesh Refinement (AMR) techniques have been used [2,3] as well as level set methods coupled with anisotropic mesh adaptation [4,5].…”

Section: Introductionmentioning

confidence: 99%

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

Menier

2015

ESAIM: Proc.

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Abstract. Anisotropic unsteady mesh adaptation is applied to the high-fidelity prediction of bubble motion, which has applications in the framework of safety evaluations for nuclear reactors. A prescribed advection of the bubble is performed, which lacks any physical sense but is representative of the reality and makes it possible to precisely measure the diffusion caused by the numerical model. The model is described, and results are presented in 2D and 3D, with comparisons in terms of mesh convergence, CPU time, and propagation of the interface.Résumé. L'adaptation de maillage instationnaire anisotropique est appliquéeà la prédiction hautefidélité de la propagation de l'interface d'une bulle, dont les applications existent notamment dans le cadre desévaluations de sureté des réacteurs nucléaires. Une advection de la bulle est prescrite, qui n'est pas physique mais représente bien la réalité tout en permettant une mesure précise de la diffusion causée par le modéle numérique. Ce dernier est décrit et des résultats sont présentés en 2D et 3D avec comparaisons des convergences en maillage, des temps CPU et de la propagation de l'interface de la bulle.

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Levelsets and anisotropic mesh adaptation

Cited by 6 publications

References 18 publications

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

Adaptive anisotropic integration scheme for high‐order fictitious domain methods: Application to thin structures

About the transmembrane voltage potential of a biological cell in time-harmonic regime.

3D Parallel Anisotropic Unsteady Mesh Adaptation for the High-Fidelity Prediction of Bubble Motion

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