全六面体边界层网格的鲁棒拓扑构造

IF 2.7 1区 数学 Q2 COMPUTER SCIENCE, SOFTWARE ENGINEERING
Maxence Reberol, Kilian Verhetsel, François Henrotte, David Bommes, Jean-François Remacle
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引用次数: 0

摘要

我们提出了一种鲁棒技术,在具有任意复杂脊和角的模型边界上构建拓扑最优的全六面体层。生成的边界层网格严格尊重输入曲面网格的几何形状,边界边缘的六面体价尽可能接近其理想值(局部二面角除以90°)是最优的。从一个有效的水密曲面网格(实际为全四边形)出发,构建了一个全局优化整数规划问题,以最小化边界边的六面体价与其理想值之间的不匹配。整数规划问题的公式依赖于磁盘的边界六面体构型和三角形之间的对偶性,我们根据整数约束对其进行重构。由于六面体网格的固有约束,局部网格拓扑结构必然是不规则的,通过在复杂脊/角附近定义的一系列子问题上进行组合分支定界搜索,有效地求解了全局问题。从整数解出发,构建了全六面体层的拓扑结构,并通过解缠/平滑计算网格几何形状。我们的方法是完全自动化的、拓扑健壮的、快速的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Robust Topological Construction of All-hexahedral Boundary Layer Meshes

We present a robust technique to build a topologically optimal all-hexahedral layer on the boundary of a model with arbitrarily complex ridges and corners. The generated boundary layer mesh strictly respects the geometry of the input surface mesh, and it is optimal in the sense that the hexahedral valences of the boundary edges are as close as possible to their ideal values (local dihedral angle divided by 90°). Starting from a valid watertight surface mesh (all-quad in practice), we build a global optimization integer programming problem to minimize the mismatch between the hexahedral valences of the boundary edges and their ideal values. The formulation of the integer programming problem relies on the duality between boundary hexahedral configurations and triangulations of the disk, which we reframe in terms of integer constraints. The global problem is solved efficiently by performing combinatorial branch-and-bound searches on a series of sub-problems defined in the vicinity of complicated ridges/corners, where the local mesh topology is necessarily irregular because of the inherent constraints in hexahedral meshes. From the integer solution, we build the topology of the all-hexahedral layer, and the mesh geometry is computed by untangling/smoothing. Our approach is fully automated, topologically robust, and fast.

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来源期刊
ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software 工程技术-计算机:软件工程
CiteScore
5.00
自引率
3.70%
发文量
50
审稿时长
>12 weeks
期刊介绍: As a scientific journal, ACM Transactions on Mathematical Software (TOMS) documents the theoretical underpinnings of numeric, symbolic, algebraic, and geometric computing applications. It focuses on analysis and construction of algorithms and programs, and the interaction of programs and architecture. Algorithms documented in TOMS are available as the Collected Algorithms of the ACM at calgo.acm.org.
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