求解二维粒子输运方程的CGS算法

CGS Algorithm for Solving 2D Particle Transport Equation

本文采用CGS算法来求解二维粒子输运方程。首先通过离散纵标法将输运方程离散为线性方程组的形式,同时引进预条件矩阵来改善系数矩阵的谱性质。通过数值试验,将预处理后的CGS算法与传统的源迭代方法进行对比,并对预处理前后特征值的分布做了比较。结果表明预处理后的矩阵特征值分布较为集中,且CGS算法收敛速度较快。

In this paper,CGS algorithm is used to solve two-dimensional particle transport equation.First,the dispersion equation is used to discretize the transport equation in the form of a linear system of equations.At the same time,the preconditioned matrix is introduced to improve the spectral properties of the coefficient matrix.Through numerical experiments,the preprocessed CGS algorithm is compared with the traditional source iterative method,and the distribution of eigenvalues before and after pretreatment is compared.The results show that the distribution of matrix eigenvalues after preprocessing is more concentrated and the CGS algorithm converges faster.