Postdoc: Parallel Adaptive Partition of Unity Methods

博士后：Unity方法的并行自适应划分

基本信息

批准号：
9704696
负责人：
Mark Shephard
金额：
$ 4.62万
依托单位：
Rensselaer Polytechnic Institute
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
1997
资助国家：
美国
起止时间：
1997-04-15 至 1999-03-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704696&HistoricalAwards=false
关键词：
Postdoc Parallel Adaptive Partition Unity

项目摘要

The postdoctoral associate will work with researchers in Rensselaer's Scientific Computation Research Center (SCOREC) on the development of parallel adaptive partition of unity methods. These methods represent a new class of discretization techniques for solving partial differential equations, which do not require the traditional grids of disjoint, non-overlapping cells, as used in typical finite element, finite difference or finite volume methods. However, they do require a discretization of the domain from which an appropriate set of partition cells interact with themselves and the domain boundary. Key to the construction of the partitions is determining how the partition cells interact with themselves and the domain boundary. The ultimate effectiveness of these methods will depend on efficient construction and control of the partitions. Building on expertise on the development of scalable parallel algorithms for automated adaptive finite element analysis over general three-dimensional domains, the proposed research program will consider alternative methodologies for the automatic construction and adaptive solution, in parallel, of partition of unity discretizations for geometric domains defined in terms of solid models. Specific areas of development include: (i) examination of alternative methods to use distributed octree structures on parallel computers to define basic partitions over the domain of the octree, (ii) effective techniques to perform the required integrations over partition of unity cells, with particular concern for integrating those cells that intersect boundaries of the domain, and (iii) develop parallel adaptive partition of unity solution methodologies

这位博士后助理将与伦斯勒科学计算研究中心 (SCOREC) 的研究人员合作，开发统一方法的并行自适应划分。这些方法代表了一类用于求解偏微分方程的新型离散化技术，不需要传统的有限元、有限差分或有限体积方法中使用的不相交、不重叠单元的传统网格。然而，它们确实需要域的离散化，其中一组适当的分区单元与其自身和域边界相互作用。构建分区的关键是确定分区单元如何与自身和域边界相互作用。这些方法的最终有效性将取决于分区的有效构造和控制。基于开发通用三维域自动自适应有限元分析的可扩展并行算法的专业知识，拟议的研究计划将考虑几何域单位离散化分区的并行自动构造和自适应解决方案的替代方法根据实体模型定义。具体的开发领域包括：（i）检查在并行计算机上使用分布式八叉树结构的替代方法来定义八叉树域上的基本分区，（ii）在单位单元分区上执行所需集成的有效技术，特别是关注整合那些与域边界相交的单元，以及（iii）开发统一解决方法的并行自适应划分