子通道分析矩阵算法的无向图分区方法

Undirected Graph Partitioning Method of Matrix Algorithm in Reactor Sub-Channel Analysis

子通道分析软件CORTH在全堆芯栅元级别的粒度下采用结构化网格矩阵算法对总焓守恒控制方程和动量守恒控制方程进行求解,现阶段引入并行增强其计算效率。由于系数矩阵具备稀疏对称性,可以转换为无向图下的分区算法进行研究,取得最小化通信体积、计算量和负载均衡的目标。通常该问题为非线性问题(NP问题),在子通道分析应用场景下对比讨论了几种典型的无向图分区方法及其效果。数值实验表明,基于多层次的k-way无向图分区方法能够取得该应用场景下几种分区算法中矩阵系数并行计算的次优解,且对压水堆全堆芯栅元子通道的分析计算进行了集群计算机性能测试,其并行能力表现良好。

In scale of fuel element level in the reactor core, the enthalpy conservation equation and momentum conservation equation are solved by using the structured mesh manner of according matrix algorithm in the sub-channel analysis code named CORTH. At present, parallel computing is introduced to enhance the calculation efficiency of CORTH. The coefficient matrix is with sparse symmetry which can be studied by converting to the undirected graph and using partitioning algorithms to achieve the goal of minimizing the communication volume, computation and load balance. Usually the problem is related to the non-linear polynomial(NP) algorithm. Several typical undirected graph partitioning methods and their effects are compared and discussed under sub-channel analysis scenario. Numerical experiments show that the sub-optimal solution of according matrices could be obtained by multi-level k-way undirected graph partitioning method in the application scenarios based on these algorithms. Furthermore, the computing performance of cluster is carried out for the test of pressure water reactor(PWR) full core sub-channel problem, and the parallel capability is well.