﻿ 不规则区域上Laplace方程基本解方法的MATLAB实现 The Method of Fundamental Solutions for Laplace Equation on Irregular Domain by Using MATLAB

Vol.06 No.04(2017), Article ID:21282,6 pages
10.12677/AAM.2017.64055

The Method of Fundamental Solutions for Laplace Equation on Irregular Domain by Using MATLAB

Kang Shan, Huantian Xie*, Wenxiang Wang, Yongkang Duan, Hongyue Lao

School of Mathematics and Statistics, Linyi University, Linyi Shandong

Received: Jun. 14th, 2017; accepted: Jul. 3rd, 2017; published: Jul. 6th, 2017

ABSTRACT

In this paper, Laplace equation on irregular domain is solved by MATLAB programming, which is the method of fundamental solutions. The result of numerical experiment shows the feasibility and accuracy of the meshless method.

Keywords:Irregular Domain, Laplace Equation, The Method of Fundamental Solutions, Meshless Method

1. 引言

2. 基本解方法

1) 选取中心点，其中是包含求解区域的封闭曲面(线)；

2) 构造用于近似原问题的解

3) 选择边界点，并令

4) 求解上述方程组得到数值解。

3. Laplace方程的基本解无网格方法

4. 数值实验

Figure 1. Chosen points, numerical solution and absolute error for scheme I

Figure 2. Chosen points, numerical solution and absolute error for scheme II

Table 1. Comparison of ABE for scheme I

Table 2. Comparison of ABE for scheme II

5. 结论

The Method of Fundamental Solutions for Laplace Equation on Irregular Domain by Using MATLAB[J]. 应用数学进展, 2017, 06(04): 468-473. http://dx.doi.org/10.12677/AAM.2017.64055

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for s=1:M

for t=1:M

q(s,t)=sqrt((node1(s,1)-node(t,1))^2+(node1(s,2)-node(t,2))^2);

A(s,t)=log(1/q(s,t));

end

end

alfa=A\f;

for t=1:M

qq=((X-node(t,1)).^2+(Y-node(t,2)).^2).^(1/2);

u=u+alfa(t).*log(1./qq);

end

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NOTES

*通讯作者。