大型稀疏方程组的MIMD分布式异步并行求解

A Asynchronous and Distributed Parallel Numerical Solution about Large-scale and Sparse Equations

采用MIMD(多数据流多指令流)分布式异步并行迭代软计算法,分析了大型稀疏方程Au=B的M×M阶系数矩阵A=(a_(ij))的性态数值计算任务ψ:u=Du+R迭代格式收敛的相互关系,在分布式并行方式下,对数值计算任务ψ:M=Du+R的各子任务t_i∈T,引入了时间步τ_i∈τ和多处理机pi∈P,实现了异步进程迭代运算,并当稀疏迭代矩阵D满足不可约弱对角占优阵的条件时,构造了分布式MIMD下数值解迭代矩阵软计算的异步并行迭代格式u_i((n_i+ 1)r_i)=d_(il)u_i(t)+d_(i2u2)(t)+Λ+d_(in)u_n(t)+r_i(i=1,2,Λ,n),给出了该迭代格式的收敛证明及类Jacobi法稀疏矩阵分块有关异步并行收敛的一个有效推论。

on the basis of soft computing with asynchronous and distributed parallel and iterative method for the MIMD （ Multi - Instruction and Multi - Data） compuer, analyze a correlation that property of matrix A = （ aij ） of M ×M -level of large-scale and sparse equations as Au = B and that convergence on iterative format about the task of nu- meric arithmetic ψ： u = Du ＋ R. On parallel, for the sub-task ti ∈ T of the task of numeric arithmetic ψ： u = Du ＋ R, this introduce time-step Ti ∈T and multi-processor pi∈ P in order to realize iterative account by asynchronous process, and make that an asynchronous parallel and herative format ui （ （ ni ＋ 1 ）Ti） dijoi （t） ＋ di2u2 （t） ＋ Λ ＋ dinun （t） ri （i=1,2 ,Λ, n）while sparse and iterative matrix D with irreducible and ascendent diagonally, and prove this format is convergent, show a effective conclusion by asynchronous parallel about a distributing to sparse matrix that resemble Jacobi iterative method at end.