基于Krylov子空间及区域分解理论的二维矩阵特征线方法  

Two-Dimensional Matrix Characteristics Method Based on Krylov Subspace and Domain Decomposition Theories

作　　者：张宏博[1] 吴宏春[1] 曹良志[1] 郑友琦[1] 夏榜样[2] 

机构地区：[1]西安交通大学核科学与技术学院,西安710049 [2]中国核动力研究设计院核反应堆系统设计技术重点实验室,成都610041

出　　处：《核动力工程》2013年第4期1-6,15,共7页Nuclear Power Engineering

摘　　要：针对传统特征线方法(MOC)求解中子输运方程计算效率较低的缺陷,构造基于Krylov子空间及区域分解理论的矩阵特征线方法。该方法可得到与传统MOC的基本方程等价的线性代数方程组,并通过基于Krylov子空间理论的广义极小残余(GMRES)算法进行高效的矩阵求解;进而提出矩阵MOC的空间非重叠区域分解算法,充分利用成熟的CPU并行技术,提高大型矩阵计算效率。通过沿用二维任意几何传统MOC程序AutoMOC的几何处理框架,实现上述理论,并基于AutoCAD二次开发功能编制出直观方便的区域分解几何处理程序。相关数值计算结果表明,这种矩阵特征线方法较传统MOC具有相近的计算精度和更高的计算速度,并对复杂几何和高散射比问题具有很好的适应性。A matrix characteristics method is proposed based on Krylov subspace and domain decomposition theories to improve the efficiency of the conventional method of characteristics （MOC）. The new numerical method, with the form of linear algebraic equation systems, is derived from the MOC basic equations and solved efficiently by the generalized minimal residual （GMRES） method. The spatial non-overlapping domain decomposition method with multiprocessing parallel technology is then adopted to reduce the computational burden for large-scale problems. By inheriting the geometrical treatment manners of the conventional MOC solver AutoMOC, the theories mentioned above are implemented. Numerical results demonstrate that the matrix characteristics method with satisfactory accuracy is more efficient than the conventional MOC, and has good flexibility in complex geometry and strong scattering problems.

关 键 词：特征线方法(MOC) KRYLOV子空间 区域分解 并行计算 

分 类 号：TL323[核科学技术—核技术及应用]