王如云^1，， 吴俊香^2，*， 陈耀登^3，

（  1、河海大学水文水资源与水利工程科学国家重点实验室；       2、河海大学理学院；       3、河海大学水文水资源与水利工程科学国家重点实验室;河海大学海洋学院；  ）

摘要： 对于无结构网格的区域分裂问题，建立了以最小化最大执行时间为目标函数的区域分裂数学模型。推导出了邻接矩阵在发生行列交换前后模型中特征量新旧值的关系表达式，将之应用到模型的求解中去，并结合采用标记数组的方法使得求解该模型中特征量的计算量从原来的 减少至约为 。邻接矩阵的行列交换在执行时间最大子区域和执行时间最小子区域之间进行，交换方法是在各自区域选出一个单元，保证在交换后原执行时间最大子区域的执行时间有所减小的准则下进行。最后，以三角形无结构网格为例，通过计算给出了很好的并行加速比和并行效率的区域分裂方案，表明了该区域分裂数学模型的可行性和有效性。
关键词： 无结构网格，并行计算，区域分裂，并行效率

Wang Ruyun^1,， Wu Junxiang^2,*， Chen Yaodeng^3,4,

（  1、State Key Laboratory of Hydrology-water Resources and Hydraulic Engineering, HoHai University；       2、College of Science, HoHai University；       3、 State Key Laboratory of Hydrology-water Resources and Hydraulic Engineering, HoHai University；       4、College of Ocean, HoHai University；  ）

Abstract： About the decomposition of unstructured grids, a mathematical model（MMET） has been built, which minimizing maximum execution time of sub-domains was made as objective function. Then, the relationship expressions of the value of characteristic quantities between old and new were induced when the two ranks or columns of adjacency matrix changed each other. At the same time, a noted array was adapted to solve this model. Compared with the common method, the quantities of calculating on characteristic quantities decreased from to in this way. The two ranks, two columns of adjacency matrix changed each other between the maximum execution time sub-domain and the minimum execution time sub-domain. The method is choosing a cell each from the two sub-domains. However, it must be done on the condition that the execution time of the maximum execution time sub-domain decreased after two ranks, two columns changed each other. Finally, taking triangular unstructured grids as an example, according to the calculating, the speedup and efficiency are given. The feasibility and efficacy of the model are showed.

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