CGV: Large: Collaborative Research: Coupling Simulation and Mesh Generation using Computational Topology

许多模拟算法依赖于一个潜在的空间离散化-一个网格，它将域分解成一组有限的元素，可以通过计算机进行分析。 模拟的质量在一定程度上取决于网格的质量。 然而，在过去，网格生成和模拟是作为单独的过程来完成的。 通过将模拟与网格生成紧密结合可以获得更好的结果，而计算拓扑学的最新建议提供了这样做的关键。 计算拓扑允许分析数据的结构-在这种情况下是模拟变量。 通过理解模拟的结构，网格生成算法可以适应它，提供与实际模拟紧密相连的网格。由于模拟是整个计算科学中发现的强大工具，这项研究有可能在所有科学领域产生广泛的影响，并实现新的科学突破，可能产生巨大的社会影响。 这项研究还将围绕耦合模拟和网格化主题制作开源软件、短期课程和研讨会。该项目的跨学科性质将为研究生和本科生提供丰富的教育和研究环境。该项目网站提供研究成果、软件和教育材料（http：//sealab.cs.utah.edu/SimulationMeshingTopology）。

Many simulation algorithms depend on an underlying spatial discretization---a mesh that decomposes the domain into a finite set of elements that can be analyzed by a computer. The quality of the simulation is, in part, determined by the quality of the mesh. However, in the past, mesh generation and simulation were done as separate processes. Better results can be achieved by tightly integrating simulation with mesh generation and recent advices in computational topology provide the key to doing so. Computational topology allows for the analysis of the structure of data---in this case simulation variables. By understanding the structure of the simulation the mesh generation algorithms can adapt to it, providing meshes that are closely linked to the actual simulation.Because simulation is a powerful tool for discovery throughout computational science, this research has the potential to have broad impact across all fields of science and enable new scientific breakthroughs that could have tremendous societal impact. This research will also produce open-source software, short courses, and workshops around the topic of coupling simulation and meshing. The interdisciplinary nature of this project will lead to a rich educational and research environment for graduate and undergraduate students. The project web site provides access to research results, software and educational materials (http://sealab.cs.utah.edu/SimulationMeshingTopology).