Iterative Solvers on Parallel Architectures for Partial Differential Equations

所提议的工作涉及开发，评估和测试迭代算法和程序，用于求解线性代数方程的大型稀疏系统，这些系统通常出现在用有限差分方法或有限元方法求解偏微分方程的数值解中。主要的重点是有效地使用向量和并行计算机体系结构。研究的重点是针对不同类型的计算机体系结构设计并行迭代算法。还将对迭代算法的某些方面进行一般性研究，包括收敛速度、迭代算法的确定以及非对称系统的处理。这项工作的一个新特点是开发了混合迭代/直接方法，旨在结合两种方法的最佳特征。将为并行架构开发计算内核和研究型软件。算法和软件将使用一类测试问题进行评估，也使用从生物医学问题和其他物理应用中衍生的线性系统。这项工作的一个重要方面是与其他机构的研究人员合作。这对混合方法的研究尤其重要

The proposed work is concerned with the development, evaluation and testing of iterative algorithms and programs for solving large sparse systems of linear algebraic equations that typically arise in the numerical solution of partial differential equations by finite difference methods or by finite element methods. The main emphasis is on the efficient use of vector and parallel computer architectures. The research studies focus on parallel iterative algorithms designed for several types of computer architectures. General research studies on certain aspects of iterative algorithms including convergence rates, determination of iterative algorithms, and the treatment of nonsymmetric systems will also be made. A novel feature of the work is the development of hybrid iterative/direct methods designed to combine the best features of both types of methods. Computational kernels and research-oriented software will be developed for parallel architectures. The algorithms and software will be evaluated using a class of test problems and also using linear systems derived from biomedical problems and other physical applications. An important aspect of the work is the collaboration with researchers at other institutions. This will be especially important for the work on hybrid methods.//