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

9504075在过去十年中，惠普自适应有限元和多处理器计算作为显著改进流体流动模拟的手段几乎同时发展，这使得将它们结合起来的可能性非常耐人寻味。潜在的回报非常高，但在实现这样的组合之前，还有许多挑战。在数据结构、自适应策略、问题分解和稳健的并行方程解算器方面有希望的新发展，尽管是在模型椭圆问题的背景下，使这个问题变得容易处理。在本项目中，将尝试将这些发展中的大部分扩展到求解复杂的三维粘性不可压缩流动。特别是，这个项目将开发一种新的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、用于生成最佳网格的自适应策略，以及定制的预条件共轭梯度型并行方程解算器。

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.