Non-Conforming HP Finite Element Methods for Computational Modeling of Problems in Science and Engineering

用于科学与工程问题计算建模的非相容 HP 有限元方法

• 批准号: 0207327
• 负责人: Padmanabhan Seshaiyer
• 金额: $ 9万
• 依托单位: Texas Tech University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0207327&HistoricalAwards=false
• 关键词: Non; Conforming; HP; Finite; Element

DMS Award AbstractAward #: 0207327PI: Seshaiyer, PadmanabhanInstitution: Texas Tech University Program: Computational MathematicsProgram Manager: Catherine MavriplisTitle: Non-conforming hp finite element methods for computational modeling of problems in science and engineeringMost problems in science and engineering routinely require finite element analysis in the assembly of many incompatible sub-discretizations. Often, these sub-discretizations are independently modeled, or available from previously constructed meshes. Therefore, to support a flexible meshing procedure, it is crucial that an efficient method be employed to join these independently modeled sub-meshes. Recently, the principal investigator introduced, a non-conforming hp finite element technique to accomplish such coupling. The proposed research will systematically develop, improve and combine sophisticated non-conforming hp finite element methods with high performance computing, through the accomplishment of the following four objectives. First, the stability and convergence of these non-conforming techniques will be theoretically established and computationally validated in higher dimensions. Secondly, the robustness of such methods to concatenate domains of different dimensions will be investigated. Third, the performance of these methods will be analyzed for problems in fluid mechanics. Finally, the stability and convergence of a more general three-field technique will be investigated. Numerical results will be presented to validate the exponential convergence of these techniques both theoretically and computationally. An ultimate goal of this research is to develop a flexible problem solving methodology tuned to high performance computing that allows a rigorous coupling of different physical processes, mathematical models, or discretization methods in different parts of a simulation domain. The successful integration of the proposed objectives will contribute to a common infrastructure that provides efficient computational support and parallel data-management for solving a wide variety of problems in science and engineering. The solution methodology to be developed will provide efficient and accurate solutions that will not only benefit various engineering fields such as aerospace, materials science, and bioengineering, but also aid in the process of designing better processes and products from aircraft to prosthetic implants.Date: June 6, 2002

DMS奖Abstractaward＃：0207327PI：Seshaiyer，Padmanabhaninstitution：Texas Tech University计划：计算机数学学院计划经理：Catherine Mavriplistitle：不合格的HP有限元方法，用于科学和工程元素中问题和工程元素中问题的计算模型，需要有限的问题，需要有限的问题。许多不兼容的亚策略的组装。通常，这些亚挑剔是独立建模的，或者是从先前构造的网格中获得的。因此，为了支持灵活的网格划分程序，采用有效的方法来加入这些独立建模的子网格至关重要。最近，首席研究员介绍了一种不合格的HP有限元技术来完成此类耦合。拟议的研究将通过实现以下四个目标来系统地开发，改进和结合具有高性能计算的复杂的不合格HP有限元方法。首先，这些不合格技术的稳定性和收敛性将在理论上建立并在较高的维度上进行计算验证。其次，将研究此类方法对不同维度的联合域的鲁棒性。第三，将分析流体力学问题的这些方法的性能。最后，将研究更通用的三场技术的稳定性和收敛性。将提出数值结果，以验证这些技术在理论上和计算上的指数收敛性。这项研究的最终目的是开发一种调整到高性能计算的灵活问题解决方法，该方法可以在模拟域的不同部分中严格耦合不同的物理过程，数学模型或离散方法。所提出的目标的成功整合将有助于共同的基础架构，该基础架构提供有效的计算支持和并行数据管理，以解决科学和工程中的各种问题。要开发的解决方案方法将提供有效，准确的解决方案，不仅有益于航空航天，材料科学和生物工程等各个工程领域，而且还有助于设计从飞机到假体植入物的更好的过程和产品的过程。 2002年6月6日