Mathematical Sciences: Theory and Applications of Multigrid Methods

数学科学：多重网格方法的理论与应用

• 批准号: 9209332
• 负责人: Susanne Brenner
• 金额: $ 6.45万
• 依托单位: Clarkson University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-09-01 至 1995-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9209332&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Theory; Applications; Multigrid

In this project, the investigator will study nonconforming multigrid methods. Robust multigrid algorithms for various finite element methods in elasticity will be developed, the performance of which will not deteriorate as the material becomes nearly incompressible. A nonconforming multigrid method for a fluid flow free-boundary problem will also be studied. Numerical experiments will be performed for these problems. In addition, some theoretical topics (conforming and nonconforming) such as pointwise convergence of multigrid methods, and multigrid methods that can overcome the pollution effects of singular solutions, will also be investigated. The results of this research will lead to efficient algorithms for the solution of large-scale computational problems in fluid mechanics and elasticity. They will find many applications in various fields of engineering and physics.

在这个项目中，研究人员将研究非相容多重网格方法。 将开发用于弹性中各种有限元方法的鲁棒多重网格算法，其性能不会随着材料变得几乎不可压缩而恶化。 还将研究流体流动自由边界问题的非相容多重网格方法。 针对这些问题将进行数值实验。 此外，还将研究一些理论主题（一致和非一致），例如多重网格方法的点收敛，以及可以克服奇异解污染效应的多重网格方法。 这项研究的结果将带来解决流体力学和弹性领域大规模计算问题的有效算法。 他们将在工程和物理的各个领域找到许多应用。