Mathematical Sciences: Algorithms and Tools for Parallel Unsymmetric Sparse Matrix Factorization

9223088 Davis首席研究员将致力于开发并行算法、工具和数据结构，以解决计算科学中出现的大型不规则问题。大型、稀疏、非对称方程组的解就是这类问题的一个例子。它构成了许多科学问题解决方案的关键组成部分，但它的不规则性质限制了它在当前高性能计算机上的性能：并行矢量共享内存计算机（即Cray）、分布式内存计算机（即Ncube、Intl）和基于risc的流水线工作站（即IBM RS/6000、SUN SParc/10）。所有这些计算机都有一个复杂的内存层次结构，以利用许多科学代码中存在的常规内存寻址模式。这种规则模式在非对称稀疏矩阵的典型分解算法中并不存在。要解决这个问题，需要使用具有常规内存寻址行为的密集矩阵内核，以及高性能的并发数据结构，以尽可能有效地执行剩余的不规则行为。* * *

9223088 Davis The principal investigator will work on the development of parallel alllgorithms, tools, and data structures for large irregular problems arising in computational science. The solution of large, sparse, unsymmetric systems of equations is an an example of one such problem. It forms a critical componment of many solutions to scientific problems, and yet has an irregular nature that limits its performance on a wide range of current high performance computers: parallel-vector shared- memory computers (i.e., Cray), distributed-memory computers (i.e., Ncube, Intl), and pipelined, RISC-based workstations (i.e., IBM RS/6000, SUN SParc/10). All of these computers have a complexx memory hierarchy to take advantage of the regular memory addressing patterns that are present in many scientific codes. This regular pattern is not presentin typical factorization algorithms for unsymmatic sparse matrices. Addressing this problem will require the use of dense matrix kernels with regular memory addressing behavior, and high- performamce cocurrent data structures that allow the remaining irregular behavior to be carried out in as an efficient manner as possible. ***