固定された三角形の膜の記号的固有関数を得る
ラプラス演算子を指定する.
In[1]:=
![Click for copyable input](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/In_119.png)
\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];
同次ディリクレ境界条件を指定する.
In[2]:=
![Click for copyable input](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/In_120.png)
\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];
三角形中の演算子の固有値と固有関数を小さい方から4個求める.
In[3]:=
![Click for copyable input](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/In_121.png)
{vals, funs} =
DEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]},
u[x, y], {x, y} \[Element] Triangle[], 4];
In[4]:=
![Click for copyable input](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/In_122.png)
vals
Out[4]=
![](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/O_59.png)
固有関数を可視化する.
In[5]:=
![Click for copyable input](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/In_123.png)
Table[Plot3D[funs[[i]], {x, y} \[Element] Triangle[], Boxed -> False,
Axes -> False, Method -> {"ShrinkWrap" -> True}], {i, 4}]
Out[5]=
![](assets.ja/obtain-a-clamped-triangular-membranes-symbolic-eig/O_60.png)