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

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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