Postdoc: Parallel hp Adaptive Finite Elements for Viscous Incompressible 3D Flows

9504075 Oden在过去十年中，hp自适应有限元和多处理器计算几乎同时发展，作为显著改善流体流动模拟的手段，使得将它们结合起来的可能性非常有趣。潜在的回报非常高，但在实现这种组合之前存在许多挑战。在数据结构、自适应策略、问题分解和鲁棒并行方程求解器方面有前景的新发展，尽管是在模型椭圆问题的背景下，使这个问题易于处理。在这个项目中，将尝试将这些发展扩展到解决复杂的三维粘性不可压缩流动。特别是，该项目将开发一个新的hp自适应有限元代码，该代码建立在基于可扩展哈希表的数据结构之上，并配备了复杂的后验误差估计器、生成最佳网格的自适应策略和定制的预置共轭梯度型并行方程求解器。

9504075 Oden The almost simultaneous development, over the last decade, of hp adaptive finite elements and multi-processor computing as means of dramatically improving fluid flow simulations makes the possibility of combining them very intriguing. The potential payoffs are very high but there are many challenges before such a combination can be achieved. Promising new developments in data structures, adaptive strategies, problem decomposition and robust parallel equation solvers, albeit in the context of model elliptic problems, make this problem tractable. In this project an attempt will be made to extend most of these developments onto solving complex three dimensional viscous incompressible flows. In particular this project will develop a new hp adaptive finite element code built on top of an extendable hash table based data structure and equipped with sophisticated a posteriori error estimators, adaptive strategies for generating optimal meshes, and customized preconditioned conjugate gradient type parallel equation solvers.