Mesh Smoothing Based on Riemannian Metric Non-Conformity Minimization

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.