大学物理 ›› 2018, Vol. 37 ›› Issue (7): 15-18.doi: 10. 16854 /j. cnki. 1000-0712. 170442

• 教学讨论 • 上一篇    下一篇

基于保角映射的格林函数法及其应用

王福谦,殷勇,刘伟歧   

  1. 西南交通大学希望学院基础部,四川成都610400
  • 出版日期:2018-07-20 发布日期:2018-07-20
  • 作者简介:王福谦( 1957—) ,男,山西运城人,西南交通大学希望学院教授. 主要从事通电磁场边值问题及场结
  • 基金资助:
    西南交通大学希望学院校级课题( “基于数值模拟的大学物理研究性教学”) 资助

The Green's function method based on conformal mapping and its pplication

WANG Fu-qian,YIN Yong,LIU Wei-qi   

  1. Department of Basic Courses,Hope College,Southwest Jiaotong University,Chengdu,Sichuan 610400,China
  • Online:2018-07-20 Published:2018-07-20

摘要: 将格林函数法与保角映射相结合,求解复杂形状边界的二维静电场边值问题,得出电场分布规律,并通过MATLAB数据处理软件的数值计算功能进行数值模拟,绘制出其电场线与等势线( 面) 分布图,验证了所得结论的正确性. 此方法拓展了格林函数法的应用范围,为求解边界形状复杂的二维静电场的边值问题提供了一种新的思路和途径.

关键词: 格林函数法, 保角映射, 边值问题

Abstract: The two - dimensional ( 2D) boundary value problem of the complex shape boundary is solved by combing the Green's function method and conformal mapping. Meanwhile the distribution of electric field is got.Both the electric field line and equipotential line maps are plotted by using mathematical software MATLAB,thus the validity of the method in the paper is presented. The application range for the Green's function method is expanded,and a novel idea and way is provided for solving the complex shape boundary 2D electrostatic field boundary value problem.

Key words: Green's function method, conformal mapping, boundary value problem