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

博士后助理将与伦斯勒（Rensselaer）科学计算研究中心（SCOREC）的研究人员合作，开发统一方法的平行自适应分区。这些方法代表了一种用于求解部分微分方程的新型离散技术，该方程不需要在典型有限元，有限差或有限体积方法中使用的传统脱节，非重叠单元格的传统网格。但是，它们确实需要对域的离散化，从而从中与自身和域边界相互作用。分区构建的关键是确定分区细胞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。拟议的研究计划将基于针对一般三维领域的自动自适应有限元分析的可扩展平行算法的专业知识，将考虑自动构造和自适应解决方案的替代方法，并同行，并行，分区的统一离散化的分区，用于根据实体模型定义的几何学域。特定的发展领域包括：（i）检查使用平行计算机上分布式的Octree结构来定义Octree域上的基本分区的替代方法，（ii）有效的技术来执行对统一细胞分配的必要集成，并特别关注那些与域相交的细胞，以及（IIII），以及（IIII），以及（iiii），（iiii III）