CAREER: Geometric Methods for Numerical Computing: Graph Partitioning, Mesh Generation and Parallel Computation

本研究的重点是几何方法的发展及其数值应用。该项目涉及为并行几何和数值计算中的各种基本问题设计高效算法，并在现代超级计算机和工作站集群上实现这些算法。这项研究有两个主要方向。非结构化网格划分和生成的几何方法：主要的理论和软件问题是如何利用底层几何结构和数值条件生成非结构化有限元网格并对其进行划分以进行后续的并行数值模拟。并行数值和应用：主要目标是将几何网格技术应用于大型稀疏线性系统的并行解决方案，自适应和分层计算，分布式COSMOS电路仿真以及并行n体仿真的动态负载平衡。配套的教育计划是设计和教授计算机科学课程，在明尼苏达大学新引入的科学计算项目中，以及在连接这两者的领域。它包括为对跨学科研究感兴趣的研究生和本科生制定研究计划和项目。它还包括为来自工业公司、政府研究实验室和其他大学的专业人员开发夏季专业课程，以启动大学与工业之间的合作。

This research focuses on the development of geometric methods and their numerical applications. The project involves the design of efficient algorithms for a variety of fundamental problems in parallel geometric and numerical computing and the implementation of these algorithms on both modern supercomputers and workstation clusters. The research has two principal directions. Geometric Methods for Unstructured Mesh Partitioning and Generation: The main theoretical and software question is how to make use of underlying geometric structures and numerical conditions to generate an unstructured finite element mesh and partition it for subsequent parallel numerical simulations. Parallel Numerical and Applications: The primary goal is to apply geometric mesh techniques to the parallel solution of large sparse linear systems, to adaptive and hierarchical computations, to distributed COSMOS circuit simulation, and to dynamic load balancing for parallel N-body simulations. The companion education plan is to design and teach courses in computer science, in the newly introduced Scientific Computation Program at the University of Minnesota, and in the areas that bridge the two. It involves the development of research programs and projects for graduate and undergraduate students who are interested in interdisciplinary research. It also involves the development of summer professional programs for professionals from industry companies, government research labs, and other universities, to initiate the collaboration between universities and industry.