图论在大气化学模式计算和灵敏度分析等中的应用

THE APPLICATION OF GRAPH THEORY IN ATMOSPHERIC CHEMICAL MODEL AND SENSITIVITY AN ALYSIS

若用吉尔型法求解大气化学模式、动力学模式和灵敏度分析时，预估矩阵是不对称矩阵。在图论中该矩阵对应于一有向图（ 一种类型的反应图） ，顶点代表反应物或产物，边表示反应。图论中将有向图划分成强成分可以用于ＬＵ 分解一系列小矩阵代替直接ＬＵ 分解预估矩阵本身，从而提高了效率。以大气化学模式的碳键机理和乙烷裂解动力学机理两例说明，给出了许多划分强成分前后动力学模型和灵敏度分析有关的有向图及其有关的矩阵，本法与间接法和其它方法的灵敏度分析的结果符合得很好，并评价了计算效率。

If Gear type method is employed to atmospheric chemical model, chemical kinetic model and sensitivity analysis, the prediction matrix is an unsymmetric matrix. The matrix is related to a directed graph (a kind of reactive graph) in graph theory. Vertices represent reactants or products, and edges for reactions. Partition of the directed graph to its strong components in graph theory can be used for LU decomposition of a series small dimension matrices instead of LU decomposition of the prediction matrix itself directly. The Carbon Bond Mechenism of atmospheric chemical model and the ethane pyrolysis mechanism are used as examples for illustration. Many directed graphes and related matrices before and after partition related to model equation and sensitivity analysis are given. The agreements of results of sensitivity analysis with indirect method and other methods are excellent. The computational efficiency is assessed.