CAREER: Robust Preconditioners for Sparse Linear Systems

本计画将发展一类新的强健且可平行化的预条件子，以解由偏微分方程式所产生的稀疏线性系统。该方法是基于与线性系统相关联的矩阵的hierarchicaldecomposition，并被设计为提高预处理器的有效性，而不损害计算中固有的并行性。一个正式的方法将开发的建设，应用和分析这些预条件。 这些技术的有效性将在不可压缩流体模拟问题上进行测试。这些预处理器的可编程实现将被开发，并在各种多处理器平台上对其性能进行评估。图书馆也将被开发并通过互联网提供给其他人。作为教育计划的一部分，创新技术将被用于计算科学和工程的课程开发，大学范围的讲习班和研讨会将为研究界组织。

This project will develop a new class of robust and parallelizablepreconditioners for the solution of sparse linear systems arising frompartial differential equations. The approach is based on a hierarchicaldecomposition of the matrices associated with the linear system, and isdesigned to improve the effectiveness of the preconditioner withoutcompromising the parallelism inherent in the computation. A formalmethodology will be developed for construction, application, andanalysis of these preconditioners. Effectiveness of these techniqueswill be tested on problems in incompressible fluid simulations. Parallelimplementations of these preconditioners will be developed and theirperformance evaluated for various multiprocessor platforms. Parallellibraries will also be developed and made available to others via theinternet. As part of the educational plan innovative techniques will beemployed for curriculum development in computational science andengineering, and university wide workshops and seminars will beorganized for the research community.