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

DMS Award AbstractAward #： 0207327 PI： Seshaiyer，Padmanabhan 德州理工大学课程： 计算数学项目经理：Catherine Mavriplis标题：科学和工程问题计算建模的非协调hp有限元方法科学和工程中的大多数问题通常需要在许多不相容的子离散化的组装中进行有限元分析。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，关键是采用有效的方法来连接这些独立建模的子网格。最近，主要研究者介绍了一种非协调hp有限元技术来实现这种耦合。拟议的研究将系统地发展，改进和联合收割机复杂的非协调hp有限元方法与高性能计算相结合，通过以下四个目标的实现。首先，这些非协调技术的稳定性和收敛性将在理论上建立和计算验证在更高的维度。其次，这种方法的鲁棒性连接不同尺寸的域将被调查。第三，这些方法的性能将在流体力学的问题进行分析。最后，一个更一般的三场技术的稳定性和收敛性将进行调查。数值结果将被提出来验证这些技术的指数收敛的理论和计算。本研究的最终目标是开发一种灵活的问题解决方法，调整到高性能计算，允许严格耦合不同的物理过程，数学模型，或离散化方法在不同部分的仿真域。所提出的目标的成功整合将有助于一个共同的基础设施，提供有效的计算支持和并行数据管理，以解决各种各样的问题，在科学和工程。将开发的解决方案方法将提供有效和准确的解决方案，不仅有利于航空航天、材料科学和生物工程等各个工程领域，而且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