The Helmholtz-Hodge Decomposition-A Survey
The Helmholtz-Hodge Decomposition-A Survey
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DOI：
10.1109/tvcg.2012.316
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发表时间：
2013-08-01
影响因子：
5.2
通讯作者：
Bremer, Peer-Timo
中科院分区：
文献类型：
--
作者：
Bhatia, Harsh;Norgard, Gregory;Bremer, Peer-Timo
亥姆霍兹-霍奇分解 (HHD) 描述了流场分解为其无散度和无旋度分量。天气建模、海洋学、地球物理学和计算机图形学等各个领域的许多研究人员都有兴趣了解代表不可压缩性和涡度等物理现象的流动特性。 HHD 已被证明是流体分析的重要工具，使其成为流体动力学的基本定理之一。流分析领域的最新进展导致 HHD 在流可视化、拓扑分析、成像和机器人等许多研究领域中得到应用。然而，由于最初的工作主要是在物理学界，因此该主题的研究已经变得支离破碎，不同的社区基本上孤立地工作，经常重复甚至有时相互矛盾的结果。此外，不同的术语已经演变，这进一步模糊了领域之间的基本联系，使得知识的转移变得困难。本调查试图通过收集相关参考文献的综合列表并使用通用术语对其进行检查来解决这些问题。特别关注的是计算 HHD 时边界条件的讨论。其目标是通过创建计算 HHD 的通用技术存储库以及广泛领域的大量示例应用程序集合来促进该领域的进一步研究。
The Helmholtz-Hodge Decomposition (HHD) describes the decomposition of a flow field into its divergence-free and curl-free components. Many researchers in various communities like weather modeling, oceanology, geophysics, and computer graphics are interested in understanding the properties of flow representing physical phenomena such as incompressibility and vorticity. The HHD has proven to be an important tool in the analysis of fluids, making it one of the fundamental theorems in fluid dynamics. The recent advances in the area of flow analysis have led to the application of the HHD in a number of research communities such as flow visualization, topological analysis, imaging, and robotics. However, because the initial body of work, primarily in the physics communities, research on the topic has become fragmented with different communities working largely in isolation often repeating and sometimes contradicting each others results. Additionally, different nomenclature has evolved which further obscures the fundamental connections between fields making the transfer of knowledge difficult. This survey attempts to address these problems by collecting a comprehensive list of relevant references and examining them using a common terminology. A particular focus is the discussion of boundary conditions when computing the HHD. The goal is to promote further research in the field by creating a common repository of techniques to compute the HHD as well as a large collection of example applications in a broad range of areas.