三维拉普拉斯算子的特征函数
设定一个三维区域.
In[1]:=
![Click for copyable input](assets.zh/eigenfunctions-of-a-3d-laplacian/In_67.png)
\[CapitalOmega] =
ImplicitRegion[
x^6 - 5 x^4 y z + 3 x^4 y^2 + 10 x^2 y^3 z + 3 x^2 y^4 - y^5 z +
y^6 + z^6 <=
1, {{x, -1.25, 1.25}, {y, -1.25, 1.25}, {z, -1.25, 1.25}}];
计算拉普拉斯算子的特征值和特征函数.
In[2]:=
![Click for copyable input](assets.zh/eigenfunctions-of-a-3d-laplacian/In_68.png)
{vals, funs} =
NDEigensystem[Laplacian[u[x, y, z], {x, y, z}],
u, {x, y, z} \[Element] \[CapitalOmega], 4];
查看特征值.
In[3]:=
![Click for copyable input](assets.zh/eigenfunctions-of-a-3d-laplacian/In_69.png)
vals
Out[3]=
![](assets.zh/eigenfunctions-of-a-3d-laplacian/O_30.png)
将第四个特征函数可视化.
显示完整的 Wolfram 语言输入
Out[4]=
![](assets.zh/eigenfunctions-of-a-3d-laplacian/O_31.png)