Measuring geometrical quality of different 3D linear element types

Abstract

In this article, we analyze how to measure quality on meshes composed of different types of 3D linear element. In particular, we focus on meshes composed of tetrahedra, pyramids, prisms and hexahedra. We propose a metric based on the scaled Jacobian that can be applied to all four element types and it is normalized in the range [−1,1]. We validated empirically its effectiveness to properly detect invalid and bad-quality elements using several test cases where our metric is contrasted with already existing ones. We also coded a simple mesh repair algorithm where the reallocation of the nodes was driven from different quality metrics. The results allow to compare the robustness of each metric and its effectiveness on improving overall mesh quality. Finally, it is known that Jacobian-based metrics fail to detect stretched and flat prisms and hexahedra, so we also propose a normalization of the aspect-ratio in those cases.

Claudio Lobos

Director of the Computer Science Department of the Universidad Técnica Federico Santa María

Director of the Computer Science Department of the Universidad Técnica Federico Santa María

Nancy Hitschfeld Kahler

+Lab founder | Full Professor Universidad de Chile

Full Professor at the Department of Computer Science, University of Chile. Her main research interests include geometric modeling, geometric meshes, and parallel algorithms (GPU computing), focused in computational science, and engineering applications.