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

从地球物理到生物医学的各种应用领域都使用某种形式的哈密顿-雅可比(H-J)数学模型。这些模型是表达守恒性质的一种自然方式，文献中最常用的两个H-J模型是Eikonal方程(基于确定最小路径的Fermat原理的静态H-J模型)和Level-Set方程(用于解决运动界面问题的依赖于时间的H-J模型)。这项工作的目标是开发、测试、记录和分发一组软件工具，用于在使用商用流架构的非结构化(三角形和四面体)网格上有效地求解几类H-J型方程--特别是Eikonal(最小路径)方程和水平集方程。PI以前已经证明了在GPU上高效求解H-J方程的可行性；这一努力既寻求对先前工作的科学扩展，也寻求将软件固化为公开可用的工具套件。这项工作的智能优点是开发了有效的算法策略，用于将非结构网格上求解H-J方程的数值方法映射到商用流体系结构。拟议的工作将解决几个重要的技术挑战。一个挑战是在并行计算单元(块)上保持足够的计算密度，特别是在我们转向3D非结构网格的时候。第二个技术挑战是块之间的通信带来的效率损失。这些挑战的解决方案将允许我们利用目前可用的商用流媒体架构，这些架构有望在桌面上提供teraflop性能，这将对依赖于计算成本高昂的基于模拟的实验的各种社区有利。通过克服使用商品流体系结构在非结构网格上开发和分发求解H-J方程的软件的繁琐和不平凡的步骤，这项工作的影响在基础科学、医学和工程等不同领域的广泛应用中具有持久性和普遍性。

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.