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

姜宝钧，王福谦

doi:10.16854 /j.cnki.1000-0712.160065

大学物理 >

2018 , Vol. 37 >Issue 1: 37 - 41

DOI: https://doi.org/10.16854 /j.cnki.1000-0712.160065

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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

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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

姜宝钧( 1969—) ，男，山西太原人，电子科技大学物理电子学院讲师.主要从事通信技术及电磁场结构

收稿日期: 2016-02-17

修回日期: 2017-05-26

网络出版日期: 2018-01-20

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

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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 date: 2016-02-17

Revised date: 2017-05-26

Online published: 2018-01-20

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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.

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

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姜宝钧，王福谦 . 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[J]. 大学物理, 2018 , 37(1) : 37 -41 . DOI: 10.16854 /j.cnki.1000-0712.160065

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

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