Zhang Yongjie, Hughes Thomas J R, Bajaj Chandrajit L
Department of Mechanical Engineering, Carnegie Mellon University.
Comput Methods Appl Mech Eng. 2010 Jan 1;199(5-8):405-415. doi: 10.1016/j.cma.2009.06.007.
This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.
本文描述了一种自动且高效的方法，用于为由异质材料组成的复合域构建非结构化四面体和六面体网格。这些材料区域的边界形成非流形表面。在早期的论文中，我们开发了一种基于八叉树的等值面绘制方法，用于为具有流形边界的单材料（均匀）域构建非结构化三维网格。在本文中，我们引入了材料变化边的概念，并使用它来识别两种或多种不同材料之间的界面。提供了一种新颖的方法来计算由两种以上材料共享的单元的最小化点，该点在边界上形成一个非流形节点。然后，我们直接从体数据同时自动对所有材料区域进行网格划分，并使其符合它们的边界。分析材料变化边和内部边以构建四面体网格，并分析内部网格点以进行适当的六面体网格构建。最后，使用边收缩和平滑方法来提高四面体网格的质量，并使用枕形、几何流和优化技术的组合来提高六面体网格的质量。枕形方案的收缩集自动定义为每个材料区域的边界。还提供了我们的多材料网格生成方法的几个应用结果。
