Wolfram Language

Differential Eigensystems

Obtain a Clamped Triangular Membrane's Symbolic Eigenfunctions

Specify a Laplacian operator.

In[1]:=
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\[ScriptCapitalL] = -Laplacian[u[x, y], {x, y}];

Specify homogeneous Dirichlet boundary conditions.

In[2]:=
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\[ScriptCapitalB] = DirichletCondition[u[x, y] == 0, True];

Find the four smallest eigenvalues and eigenfunctions of the operator in a triangle.

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{vals, funs} = DEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x, y], {x, y} \[Element] Triangle[], 4];
In[4]:=
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vals
Out[4]=

Visualize the eigenfunctions.

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Table[Plot3D[funs[[i]], {x, y} \[Element] Triangle[], Boxed -> False, Axes -> False, Method -> {"ShrinkWrap" -> True}], {i, 4}]
Out[5]=

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