Hybrid mesh smoothing based on Riemannian metric non-conformity minimization

A smoothing method specifically designed to treat hybrid meshes is presented in this paper. This method, based on Riemannian metric comparison, minimizes a cost function constructed from a measure of metric non-conformity that compares two metrics: the metric that transforms a given element into its reference element and a specified Riemannian metric that contains the desired target size and shape of each element. This combination of metrics allows the proposed mesh smoothing method to be cast 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 in terms of orthogonality at the boundary and overall smoothness, when compared to other known methods.