Improving Mixed Methods by Hybridization and Multigrid Techniques

通过混合和多重网格技术改进混合方法

• 批准号: 0410030
• 负责人: Jay Gopalakrishnan
• 金额: $ 13.97万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0410030&HistoricalAwards=false
• 关键词: Improving; Mixed; Methods; Hybridization; Multigrid

This proposal considers innovative numerical methods using hybridization and multigrid techniques. While hybridization was thought of as an implementation technique in its inception, the investigator argues that it is much more. It is shown to be a computational technique that has the potential of achieving goals difficult to achieve by conventional techniques in applications ranging from computational fluid mechanics to electromagnetics. E.g., a new technique using hybridization to solve a long standing research problem, namely computing exactly incompressible approximations to fluid flow, is proposed. Other proposed uses of hybridization include construction and analysis of variable degree mixed methods and design of local post-processing techniques to enhance accuracy. A different category of proposed activities involve accelerated solution techniques by multigrid methods. Powerful multigrid techniques are proposed for various systems arising from computational electromagnetics and hybridization. The aim is to make solution techniques efficient. This goal, while often achieved by multigrid methods, can also be achieved by utilizing symmetries such as axisymmetry occurring in practical problems. E.g., investigation of methods for the axisymmetric Maxwell equations form a part of the proposed activities. While the proposed research has significant theoretical impact, equally important is the fact that parts of the research are motivated by the needs of industrial applications such as clinical ablation. Use of the proposed new methods in these applications is an integral part of the proposal. Broader impacts of the proposed activities result not only from the applications to the industrial problems, but also from educational activities and broad dissemination of results.

该提案考虑使用混合和多重网格技术的创新数值方法。 虽然杂交一开始就被认为是一种实现技术，但研究人员认为它的含义远不止于此。 它被证明是一种计算技术，有可能实现从计算流体力学到电磁学等应用中传统技术难以实现的目标。例如，提出了一种使用杂交来解决长期存在的研究问题的新技术，即精确计算流体流动的不可压缩近似值。杂交的其他用途包括构建和分析可变程度混合方法以及设计局部后处理技术以提高准确性。提议的活动的不同类别涉及多重网格方法的加速求解技术。 针对计算电磁学和混合产生的各种系统提出了强大的多重网格技术。 目的是使解决方案技术更加高效。这一目标虽然通常通过多重网格方法来实现，但也可以通过利用实际问题中出现的轴对称等对称性来实现。例如，对轴对称麦克斯韦方程方法的研究构成了拟议活动的一部分。 虽然拟议的研究具有重大的理论影响，但同样重要的是，部分研究是由临床消融等工业应用的需求推动的。 在这些应用中使用所提出的新方法是该提案的一个组成部分。 拟议活动的更广泛影响不仅来自于对工业问题的应用，还来自于教育活动和成果的广泛传播。