Mesh Smoothing Based on Riemannian Metric Non-Conformity Minimization

Abstract

Summary.A mesh smoothing method based on Riemannian metric comparison is presented in this paper. This method minimizes a cost function constructed from a measure of metric non-conformity that compares two metrics: the metric that transforms the element into a reference element and a specified Riemannian metric, that contains the target size and shape of the elements. This combination of metrics allows to cast the proposed mesh smoothing method in a very general frame, valid for any dimension and type of element. Numerical examples show that the proposed method generates high quality meshes as measured both in terms of element characteristics and also in terms of orthogonality at the boundary and overall smoothness, when compared to other known methods.

Robust and accurate optimal transportation map by self-adaptive sampling

“…The mesh adaption methods include centroidal Voronoi tessellation (CVT) (Du and Wang, 2005;Liu et al, 2009;Rong et al, 2011;Yan et al, 2011), interpolation error minimization (Kunert, 2002;Alauzet et al, 2006), optimal Delaunay triangulations (ODTs) (Chen and Xu, 2004), mesh refinement (Apel and Lube, 1996;Bossen and Heckbert, 1996;Löhner and Cebral, 2000;Berndt and Shashkov, 2003;Apel et al, 2004), monitor functions (Huang, 2006), mesh smoothing (Sirois, et al, 2006), and a branch of other methods (Bottasso, 2004;Dobrzynski and Frey, 2008). Many of these methods were generalized to produce anisotropic meshes by incorporating a metric tensor into the functional.…”