结合多群耦合GMRES的Wielandt迭代用于加速矩阵MOC收敛

Wielandt Iteration Combined with Multi-Group GMRES for Accelerating Matrix MOC Convergence

矩阵特征线方法(MOC)通过构造并求解线性方程组,代替传统MOC方法中的反复特征线扫描。幂迭代法求解keff的收敛速度严重依赖于占优比,实际的较大规模的堆芯占优比接近于1,收敛很慢。本研究结合多群耦合GMRES算法直接求解多群问题,采用Wielandt迭代加速矩阵MOC临界问题的求解。对多个基准题的数值结果表明,与幂迭代法相比,结合多群耦合GMRES的Wielandt迭代具有良好的计算精度和更高的计算效率。

In the Matrix MOC, a linear algebraic equation system can be constructed by sweeping only once, and then solving the linear system takes the place of repeatedly characteristics sweeping. Traditionally, keff is computed by power iteration （PI）, whose convergence rate depends on the dominance ratio deeply. Large problems of practical interest often have dominance ratios close to 1, leading to slow convergence of PI. Combined with multi-group GMRES coupling all groups directly, Wielandt iteration is studied for accelerating Matrix MOC. Numerical results of several benchmarks demonstrate that Wielandt iteration combined with multi-group GMRES can obtain good accuracy and higher efficiency compared with PI.