Untangling and Smoothing of Quadrilateral and Hexahedral Meshes

Abstract

In this paper, we extend a simultaneous untangling and smoothing technique previously developed for triangular and tetrahedral meshes to quadrilateral and hexahedral ones. Specifically, we present a technique that iteratively untangles and smooths a given quadrilateral or hexahedral mesh by minimizing an objective function defined in terms of a modification of an algebraic quality measure. The proposed method optimizes the mesh quality by a local node relocation process. That is, without modifying the mesh connectivity. Finally, we present several examples to show that the proposed technique obtains valid meshes composed by high-quality quadrilaterals and hexahedra, even when we start from tangled meshes.

Robust moving-mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems

“…Following the conclusions of Wilson (2011), the best smoothing algorithm compromise is to use the GETMe smoothing algorithm designed for mixed elements mesh. However, we have decided to implement an untangler based on the GETMe method instead of one which optimises an objective function (Escobar et al (2003)).…”

“…Various modifications to the Laplacian smoothing operator and alternatives have been proposed, although we have decided to consider solely the most recent ones which are considered more promising according to the analysis done by Wilson (2011). First, an objective function (Bank and Smith (1997)) can be defined from elemental quality metrics (Knupp (2003)) and by minimizing it a better quality is expected through the mesh.…”

Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

“…In this section, we summarize the formulation of the algebraic framework for triangles and tetrahedra. Although it is already presented in [27], we include it here for completeness. Let t denote a triangle in the physical space, and t I denote the ideal triangle.…”

“…Finally, introducing Equations (26), (27) and (28) in Equation (25), we obtain the final expression for the second derivatives of the shape distortion measure …”

“…This paper is based in the work presented in [27]. However, in the current paper we include several new contributions that clearly improve the preliminary version of the simultaneous untangling and smoothing procedure for quadrilateral and hexahedral meshes.…”