Bakhvalov-Shishkin网格上求解边界层问题的差分进化算法  

Differential Evolution Algorithms for Boundary Layer Problems on Bakhvalov-Shishkin Mesh

作　　者：周琴[1] 程立正 Zhou Qin;Cheng Lizheng(School of Information,Mechanical and Electrical Engineering,Hunan International Economics University,Changsha 410205;MOE-LCSM,Hunan Normal University,Changsha 410081)

机构地区：[1]湖南涉外经济学院信息与机电工程学院,长沙410205 [2]湖南师范大学计算与随机数学教育部重点实验室,长沙410081

出　　处：《数学物理学报（A辑）》2021年第1期245-253,共9页Acta Mathematica Scientia

基　　金：国家自然科学基金(11771138);湖南省教育厅资助科研项目(18C1097,19B325);湖南省普通高校省级一流本科课程建设项目(2019)。

摘　　要：该文在Bakhvalov-Shishkin网格上求解具有左边界层或右边界层的对流扩散方程,并采用差分进化算法对Bakhvalov-Shishkin网格中的参数进行优化,获得了该网格上具有最优精度的数值解.对三个算例进行了数值模拟,数值结果表明:采用差分进化算法求解具有较高的计算精度和收敛性,特别是边界层的数值解精度明显优于选择固定网格参数时的结果.In this paper,the convection-diffusion equation with left boundary layer or right boundary layer is solved on Bakhvalov-Shishkin mesh.The parameter in Bakhvalov-Shishkin mesh is optimized by differential evolution algorithm,and we obtain numerical solution with optimal accuracy on Bakhvalov-Shishkin mesh.Three numerical examples are simulated,and the numerical results show that the differential evolution algorithm is accurate and convergence.Especially,the numerical solution accuracy of the boundary layer is obviously better than that of fixed mesh parameters.

关 键 词：边界层 Bakhvalov-Shishkin网格 差分进化算法 网格参数 

分 类 号：O241[理学—计算数学]