Highly Parallel Direct Solvers for Sparse Linear Systems

求解稀疏线性系统的直接方法具有通用性和鲁棒性。对于某些应用中出现的线性系统，如线性规划和一些工程应用，它们是唯一可行的数值分解方法。该项目正在开发一个可扩展的并行直接求解器，用于求解线性方程的稀疏对称正定（SPD）系统，并正在研究其在线性规划问题和最小二乘问题中的效用和有效性。提出了SPD系统直接求解器分解相的高度并行式。这被扩展到一个完全可扩展并行直接求解器的其他三个阶段（排序、符号分解和三角系统求解）。并行公式正在各种硬件平台上进行研究，包括传统的mpp，如CM5和Cray T3D，以及DEC和IBM工作站的集群。并行算法正在使用支持集体通信的编程库以可移植的形式实现，并将提供给其他地方的研究人员和实践者。

Direct methods for solving sparse linear systems are because of their generality and robustness. For linear systems arising in certain applications, such as linear programming and some engineering applications, they are the only feasible methods for numerical factorization. This project is developing a scalable parallel direct solver for solving sparse symmetric-positive definite(SPD) systems of linear equations, and is investigating its utility and effectiveness in the context of linear programming problems and least square problems. A highly parallel formulation of the factorization phase of the direct solver for SPD systems has been developed. This is being extended to the other three phases (ordering, symbolic factorization and triangular system solving) of a complete scalable parallel direct solver. Parallel formulations are being investigated on a variety of hardware platforms, including traditional MPPs such as CM5 and Cray T3D, as well as clusters of DEC and IBM workstations. The parallel algorithms are being implemented in a portable form using a programming library that supports collective communication, and will be made available to researchers and practitioners elsewhere.