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

获奖摘要：获奖编号：0207327PI: Seshaiyer， PadmanabhanInstitution: Texas Tech University项目：Computational mathematics项目经理：Catherine mavriplis标题：非一致性hp有限元方法在科学和工程问题的计算建模科学和工程中的大多数问题通常需要在许多不兼容的子离散化的组合中进行有限元分析。通常，这些子离散化是独立建模的，或者可以从先前构建的网格中获得。因此，为了支持灵活的网格划分过程，采用一种有效的方法将这些独立建模的子网格连接起来至关重要。最近，首席研究员介绍了一种非一致性hp有限元技术来完成这种耦合。本研究将通过实现以下四个目标，系统地发展、改进复杂的非一致性hp有限元方法并将其与高性能计算相结合。首先，从理论上建立这些非一致性技术的稳定性和收敛性，并在更高的维度上进行计算验证。其次，将研究这些方法在连接不同维度域时的鲁棒性。第三，分析这些方法在流体力学问题中的性能。最后，我们将研究一种更一般的三场技术的稳定性和收敛性。数值结果将从理论上和计算上验证这些技术的指数收敛性。本研究的最终目标是开发一种灵活的问题解决方法，用于高性能计算，允许在模拟领域的不同部分严格耦合不同的物理过程，数学模型或离散方法。所提议的目标的成功整合将有助于建立一个共同的基础设施，为解决科学和工程中的各种问题提供有效的计算支持和并行数据管理。要开发的解决方案方法将提供高效和准确的解决方案，这不仅有利于各种工程领域，如航空航天，材料科学和生物工程，而且还有助于设计更好的工艺和产品，从飞机到假体植入物。日期：2002年6月6日

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