Iterative Substructuring Methods for Elliptic Problems & Related Algorithms

本项目继续研究迭代子结构方法 和其他区域分解算法的偏微分 方程 这些算法都是并行的迭代方法 解非常大的代数方程组，出现在 石油储层的有限元/差分建模， 计算流体动力学、弹性等。在每次迭代中， 解决了给定问题对许多子区域中的每个子区域的限制 近似地，并且数据在相邻子域之间交换。 一 全局问题，每个子域的自由度很少，也是 当使用许多子域时，需要获得快速收敛。 研究将集中在分析，改进和实施 几类区域分解算法，具体地， 适合于新兴的大规模并行系统。 的 最终目标是解决非常大的病态问题， 连续介质力学，传统的迭代方法 直接方法太慢， 太多的记忆。 这一基本理论已被证明是 这些快速算法最新发展将进一步 发展和系统的数值实验测试的想法。

This project continues research on iterative substructuring methods and other domain decomposition algorithms for partial differential equations. These algorithms are iterative methods for the parallel solution of very large systems of algebraic equations that arise in finite element/difference modeling of petroleum reservoirs, computational fluid dynamics, elasticity, etc. In each iteration, the restriction of the given problem to each of many subregions is solved approximately and data is exchanged between neighboring subdomains. A global problem, with few degrees of freedom per subdomain, is also required to obtain fast convergence when many subdomains are used. The research will focus on analyzing, improving and implementing several classes of domain decomposition algorithms, in particular, those which are suitable for emerging massively parallel systems. The ultimate goal is to solve very large, ill-conditioned problems of continuum mechanics for which traditional iterative methods are unsatisfactory and for which direct methods are too slow and require too much memory. The underlying theory, which has proven central in the recent development of these fast algorithms, will be further developed and the ideas tested in systematic numerical experiments.