块三对角矩阵的并行局部块分解预条件

Parallel Local Block Factorization to Block Tridiagonal Matrices

该文首先分析了并行局部块分解预条件的特征分布,分析表明其与串行局部块分解预条件的特征分布基本相当,从而从理论上保证了利用该预条件进行并行计算时的高效性.其次分析了利用该预条件进行并行计算时影响加速比的因素,由此说明了当问题规模不大而处理机台数增加时,计算效率必然逐渐下降的原因.最后在由 6台微机连成的机群系统上将该预条件与利用多分裂技术构造的多种预条件进行了比较,实验结果说明该预条件效率高于其它预条件方法.同时在某巨型机上进行的实验表明对处理机台数比较多时,该预条件也仍然很有效.

This paper first proves a theorem for the model matrix, that is, the distribution of the conditioned matrix with the parallel version of local block factorization is very close to the one with the serial version. This theorem assures the effectiveness of the parallel preconditioner. Second, it analyzes the factors of affecting the speedup of the iterative methods with this kind of preconditioner. The result shows that when the number of processors is not very large compared to the order of the coefficient matrix, the speedup will be very good. Finally, it compares the parallel preconditioner to many others based on multisplit technique in experiments. The result shows that the parallel preconditioner is much better.