Anisotropic Tetrahedral Mesh Adaptation with Improved Metric Alignment and Orthogonality

Abstract

An enhanced mesh adaptation method aiming at generating elements that align the metric is proposed. Well-proven and robust local operators are tailored to modify an existing mesh to satisfy the underlying metric field while enhancing the metric-alignment and orthogonality of the mesh elements. The metric field defines a target element size, shape, and orientation at each point, and a corresponding transformation from a reference element to the target element. A quality criterion based on this transformation is used for selecting edges for splitting and deciding local mesh connectivity after edge collapse, which helps to improve metric alignment and orthogonality of the adapted mesh. Finally, a workflow is organized by combining the local operations and the new techniques to adapt a mesh according to a metric field. Numerical experiments on anisotropic meshes are presented to demonstrate the effectiveness of the proposed method.