SI2-SSE: A GPU-Enabled Toolbox for Solving Hamilton-Jacobi and Level Set Equations on Unstructured Meshes

SI2-SSE：用于求解非结构化网格上的 Hamilton-Jacobi 和水平集方程的 GPU 工具箱

• 批准号: 1148291
• 负责人: Robert Kirby
• 金额: $ 50万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1148291&HistoricalAwards=false
• 关键词: SI2; SSE; GPU; Enabled; Toolbox

A variety of application domains from geophysics to biomedicine employ some form of Hamilton-Jacobi (H-J) mathematical models. These models are a natural way to express conservation properties, and the two most prevalent H-J models seen in the literature are the Eikonal equation (a static H-J model based upon Fermat's Principle for determining minimal paths) and the Level-Set equations (a time-dependent H-J model used for addressing moving interface problems). The goal of thiseffort is to develop, test, document and distribute a collection of software tools for efficiently solving several classes of equations of H-J type -- in particular, Eikonal (minimal path) equations and Level-set equations -- on unstructured (triangular and tetrahedral) meshes using commodity streaming architectures. The PIs have previously demonstrated the feasibility of efficiently solving H-J equations on GPUs; this effort seeks to both scientific extend previous work as well as solidify the software into a publicly available tool suite. The intellectual merit of this effort is the development of efficient algorithmic strategies for mapping numerical methods for solving H-J equations on unstructured meshes to commodity streaming architectures. The proposed work will tackle several important technical challenges. One challenge is maintaining sufficient computational density on the parallel computational units (blocks), especially as we move to 3D unstructured meshes. A second technical challenge is the loss in efficiency that comes with communication between blocks. The solutions to these challenges will allow us to exploit currently available commodity streaming architectures that promising to provide teraflop performance on the desktop, which will be a boon for a variety of communities that rely on computationally expensive, simulation-based experiments. By overcoming the tedious and non-trivial step of developing and distributing software for solving H-J equations on unstructured meshes using commodity streaming architectures, the impact of this work has both longevity and ubiquity in a wide range of applications in diverse fields such as basic science, medicine, and engineering.

从地球物理学到生物医学的各种应用领域采用某种形式的汉密尔顿 - 雅各比（H-J）数学模型。这些模型是表达保护特性的自然方法，文献中看到的两个最普遍的H-J模型是Eikonal方程（基于Fermat的静态H-J模型，基于Fermat用于确定最小路径的原理）和级别集合方程（用于解决移动接口问题的时间依赖性H-J模型）。 ThisFort的目的是开发，测试，记录和分发一系列软件工具，用于在非结构（三角形和四面体）网格上使用商品流体系结构架上有效地解决几类H-J类型方程（特别是Eikonal（最小路径）方程式和级别的方程式）。 PI先前已经证明了在GPU上有效求解H-J方程的可行性。这项努力既试图将科学扩展到先前的工作，又要将软件巩固到公开可用的工具套件中。这项工作的智力优点是开发有效的算法策略，用于绘制用于求解非结构化网格的H-J方程为商品流架构的数值方法。拟议的工作将面临一些重要的技术挑战。一个挑战是在平行计算单元（块）上保持足够的计算密度，尤其是当我们移动到3D非结构化网格时。第二个技术挑战是效率的损失随块之间的通信带来的。解决这些挑战的解决方案将使我们能够利用当前可用的商品流式体系结构，该体系结构有望在桌面上提供TERAFLOP性能，这对于依靠基于计算昂贵的，基于模拟的实验的各种社区来说将是一个福音。通过克服开发和分发软件的繁琐和非平凡的步骤，用于使用商品流体系结构来解决非结构性网格的H-J方程，这项工作的影响既可以在基础科学，医学和工程等各种领域的广泛应用中延长寿命和无处不在。