区域分裂并行计算中预条件迭代若干性质

For-condition Iteration Characters in the Domain Decomposition Parallel Computation

对网格方程组作区域分裂并行计算 ,讨论了预条件迭代的相关性质及其对算法收敛性的影响 ,给出两层分块预条件迭代收敛的充要条件 ,指出消元预条件迭代在谱条件意义下具最优收敛率 .在对称正定情形下 ,通过消元预条件揭示了预处理的内在结构 ,为构造预处理方法提供了理论依据 .对于区域分裂 D-N算法 ,讨论了构造较优预处理的方法 .

The paper considers domain decompose parallel computation of the net equation system,discusses the characters of the for condition iteration,and the algorithm convergence.It gives the it erative convergence necessary condition of the two levels decomposition,and obtains the optimum convergence efficiency under spectrum condition.The article reveals the innerconstruction of the for condition,by using Gauss for condition method,which constructs a theoretic base of the for condition methods,the optimum constructing for condition method is discussed in the case of the domain decomposition D N algorithm.