大型稀疏代数方程组的分解

大型稀疏代数方程组是稳态过程模拟与过程设计数学模型的典型形式.与联立求解法相比,迭代求解的长处在于可解算包括非线性在内的方程,而且即使中途停顿也会得到解算过程的信息.此外,占内存少,计算时间短.在迭代之前,须预先确定设计变量(如果变量数多于方程数)、迭代变量、输出集和迭代次序.本文提出一种将给定方程组的关联矩阵重新排序的简便方法,根据重排后的关联矩阵优先决定迭代变量,然后决定输出集和设计变量.这种方法可以确保可行迭代顺序的产生,也比现有的方法简便.

Decomposition of Large Systems of Sparse Algebraic Equations

A large system of sparse linear and nonlinear algebraic equations is the typical form of mathematical models of process design and steady state process simulation. Successive substitution is an efficient solution strategy for this type ot models in that the equations can be nonlinear and an output is available at any step of calculation. Besides, it needs less storage space and shorter CPU time. However, the design variables(if the number of variables is larger than that of equations), iteration variables, output set and the substitution sequence must be first determined before iteration begins. A simple and convenient method of rearranging the occurrence matrix of the system is proposed in the paper. After rearrangement, the iteration variables are firsty determined, and subsequently the output set and design variables are determined, so that a feasibie solution routine of the system ot equations is established.