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

DMS奖摘要奖#：0207327 PI：Seshaiyer，PadmanabhanInstitution：德克萨斯理工大学项目：计算数学项目经理：Catherine Mavriplis标题：用于计算科学和工程问题建模的非协调惠普有限元方法大多数科学和工程问题通常需要在许多不相容的子离散化的集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使用。因此，为了支持灵活的网格划分过程，采用一种有效的方法来连接这些独立建模子网格是至关重要的。最近，首席研究员引入了一种非协调惠普有限元技术来实现这种耦合。这项研究将通过实现以下四个目标，系统地发展、改进和结合复杂的非协调惠普有限元方法和高性能计算。首先，这些非协调技术的稳定性和收敛将从理论上建立，并在更高的维度上进行计算验证。其次，研究了这些方法对连接不同维域的稳健性。第三，针对流体力学中的问题，分析了这些方法的性能。最后，我们将研究一种更一般的三场技术的稳定性和收敛问题。数值结果将从理论和计算上验证这些方法的指数收敛。这项研究的最终目标是开发一种灵活的问题解决方法，以适应高性能计算，允许不同物理过程、数学模型或模拟领域不同部分的离散化方法的严格耦合。拟议目标的成功结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。将要开发的解决方案方法论将提供高效和准确的解决方案，这些解决方案不仅将使航空航天、材料科学和生物工程等各种工程领域受益，还将有助于设计从飞机到假肢植入物的更好的工艺和产品。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