并行计算中一种非结构网格分割方法

A Method of Non-structured Mesh Partition for Parallel Computation

将递归谱对剖分方法应用于流体力学并行计算中的非结构网格分割,以解决负载平衡和最小切割问题。为使用这种方法,计算了网格伴随图的离散Laplacian矩阵的第二特征矢,然后从该特征矢的分量引入网格的对剖分。特征矢计算中应用了Rayleigh商迭代,并进行了一些修正以使收敛强烈地偏向于第二特征矢及考虑逆迭代步中线性方程组的迭代求解。最后,通过非结构自适应网格上Euler方程分区计算的数值结果验证了所发展的网格分割方法。

A recursive spectral bisection method is applied to partition non-structured triangular meshes in parallel CFD for the treatment of load balance and minimum cut graph bisection. To use this method, the second eigenvector of the discrete Laplacian matrix of the dual graph of a mesh is computed and the bisection is obtained from components of this eigenvector. A classical Rayleigh quotient iteration is applied in the computation of the second eigenvector, and some modifications are made both to bias convergence to the second eigenvector and to account for the solution of the linear system in the inverse iteration step by an iterative process. Finally, the mesh partition approach is validated in the numerical experiments for solving Euler equations in parallel on the adaptive non-structured meshes.