请给出基于MATLAB的BEM计算模型实例
时间: 2023-07-15 21:14:13 浏览: 56
以下是一个基于MATLAB的BEM计算模型实例,用于计算二维电场分布:
```matlab
% BEM计算模型实例
% 定义边界条件
V1 = 1; % 边界1电势值
V2 = 0; % 边界2电势值
n = 100; % 离散点个数
L = 1; % 区域长度
H = 1; % 区域宽度
% 计算离散点坐标
x = linspace(0, L, n);
y = linspace(0, H, n);
[X, Y] = meshgrid(x, y);
X = X(:);
Y = Y(:);
% 计算离散点所在边界
boundary = zeros(size(X));
boundary(X == 0) = 1;
boundary(Y == 0) = 1;
boundary(X == L) = 2;
boundary(Y == H) = 2;
% 计算边界上的电势值
V = zeros(size(X));
V(boundary == 1) = V1;
V(boundary == 2) = V2;
% 计算边界上的法向量
nx = zeros(size(X));
ny = zeros(size(Y));
nx(boundary == 1) = -1;
ny(boundary == 2) = 1;
% 计算矩阵A和向量b
A = zeros(n, n);
b = zeros(n, 1);
for i = 1:n
for j = 1:n
if boundary(i) == 0 % 内部离散点
if i > 1
A(i, i-1) = nx(i-1)*ny(i);
end
if i < n
A(i, i+1) = -nx(i)*ny(i+1);
end
if j > 1
A(i, i-n) = -ny(i-1)*nx(i);
end
if j < n
A(i, i+n) = ny(i)*nx(i+1);
end
elseif boundary(i) == 1 % 边界1离散点
A(i, i) = 1;
b(i) = V1;
elseif boundary(i) == 2 % 边界2离散点
A(i, i) = 1;
b(i) = V2;
end
end
end
% 求解矩阵方程
phi = A \ b;
% 绘制电势分布图
figure;
trisurf(delaunay(X, Y), X, Y, phi);
xlabel('X');
ylabel('Y');
zlabel('Potential');
```
该模型将区域离散为n个离散点,根据边界条件和离散点坐标计算出矩阵A和向量b,并求解矩阵方程得到离散点的电势分布。最后,使用MATLAB自带的三角剖分函数绘制电势分布图。