基于矩阵分解的周期块三对角线性方程组的并行直接解法

A parallel direct algorithm based on matrix decomposition for solving periodical block-tridiagonal linear equations

提出了分布式环境下求解周期块三对角线性方程组的一种并行算法.该算法充分利用系数矩阵结构的特殊性,通过对系数矩阵进行适当分解及近似处理,使算法只在相邻处理机间通信2次,并从理论上给出了算法有效的一个充分条件.最后,在HP rx2600集群上进行了数值试验,结果表明,实算与理论是一致的,并行性也很好.

A parallel algorithm for periodical block-tridiagonal linear equations on distributed-memory multi-computers is presented. Making full use of the special structure of the coefficient matrix, the algorithm is based on decomposing the coefficient matrix properly and approximately disposing the matrix. The communication only needs twice between the adjacent processors. Theoretically, a sufficient condition about effectivity of this algorithm is given. Finally, some numerical results on HP rx2600 cluster demonstrate that practice computing is consistent with theory. The algorithm＇s parallelism is preferable.