基于保角映射的拉普拉斯方程降维法求解及场分布的可视化  

Solving Laplace equation by reduction dimension method based on conformal mapping andvisualization of electric field distribution

作　　者：姜宝钧[1] 王福谦 

机构地区：[1]电子科技大学物理电子学院,四川成都610051 [2]长治学院电子信息与物理系,山西长治046011

出　　处：《大学物理》2018年第1期37-41,共5页College Physics

摘　　要：通过保角映射将求解区域变换为上半平面或带形域,从而把二维电势降为一维,在此基础上方便地求解拉普拉斯方程的第一边值问题,给出其电势和场强分布,并利用软件MATLAB绘制出等势线和电场线图.With the help of the conformal mapping,we transform the domain of solution into the upper half plane or band domain,thus the dimensions of electric potential is reduced to 1 from 2,then the first boundary value problem of Laplace equation is solved easily. Meanwhile,the distributions of electric potential and electric field intensity are obtained,and the maps of both electric field land equipotential lines are plotted by using mathematical software MATLAB.

关 键 词：保角映射 拉普拉斯方程 第一边值问题 场强分布 电势分布 可视化 

分 类 号：O444.1[理学—电磁学]