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

doi:10.16854 /j.cnki.1000-0712.160065

College Physics ›› 2018, Vol. 37 ›› Issue (1): 37-41.doi: 10.16854 /j.cnki.1000-0712.160065

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

JIANG Bao-jun1，WANG Fu-qian1，2

1. School of Physical Electronics，University of Electronic Science and Technology of China，Chengdu，Sichuan 610051，China; 2. Department of Electronic Information and Physics，Changzhi University，Changzhi，Shanxi 046011，China

Received:2016-02-17 Revised:2017-05-26 Online:2018-01-20 Published:2018-01-20

Abstract

Abstract: 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.

Key words: conformal mapping, Laplace equation, first boundary value problem, distribution of electric potential, distribution of electric field intensity, visualization

JIANG Bao-jun1，WANG Fu-qian1，2. Solving Laplace equation by reduction dimension method based on conformal mapping andvisualization of electric field distribution[J].College Physics, 2018, 37(1): 37-41.

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

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