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Publication . Conference object . 2019

Anisotropic Error Estimate for High-order Parametric Surface Mesh Generation

Feuillet, Rémi; Coulaud, Olivier; Loseille, Adrien;
Open Access
English
Published: 14 Oct 2019
Publisher: HAL CCSD
Country: France
Abstract

International audience; Parametric surface mesh generation is one of the crucial step of the computational pipeline. Standard techniques, that are now mature, control the deviation to the tangent plane by using intrinsic quantities as the minimum and maximum curvatures. However, for high-order meshes, deriving intrinsic quantities that have the ability to control the mesh generation process is much more challenging. Indeed, those provided by the first and second fundamental forms of a surface are not sufficient when high order curved meshes are employed. In this paper, we introduce a new set of error estimates for high-order surface mesh generation. It is based on performing a Taylor expansion of the underlying surface in the tangent plane. The independence to the parametric space is obtained by using an inversion formula. High-order terms of this expansion are then used to derive an optimal metric by using the log-simplex approach. Examples are shown to prove the efficiency of the method.

Subjects by Vocabulary

ACM Computing Classification System: ComputingMethodologies_COMPUTERGRAPHICS

Subjects

Surface mesh generation, High-order error estimates, High-order mesh generation, [MATH]Mathematics [math], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]

Funded by
ANR| IMPACTS
Project
IMPACTS
Ideal Mesh Generation for Modern Solvers and ComPuting ArchiteCTureS
  • Funder: French National Research Agency (ANR) (ANR)
  • Project Code: ANR-18-CE46-0003
,
ANR| LMH
Project
LMH
LabEx Mathématique Hadamard
  • Funder: French National Research Agency (ANR) (ANR)
  • Project Code: ANR-11-LABX-0056
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