Wolfram Language

Differential Eigensystems

Compute Eigenfunctions for a Clamped Membrane

Compute the first six eigenfunctions for a circular membrane with the edges clamped.

Specify a Laplacian operator.

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

Specify a Dirichlet boundary condition.

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

Find the six smallest eigenvalues and eigenfunctions.

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{vals, funs} = NDEigensystem[{\[ScriptCapitalL], \[ScriptCapitalB]}, u[x, y], {x, y} \[Element] Disk[], 6];

Inspect the eigenvalues.

In[4]:=
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vals
Out[4]=

Visualize the eigenfunctions.

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Table[Plot3D[funs[[i]], {x, y} \[Element] Disk[], PlotRange -> All, PlotLabel -> vals[[i]], PlotTheme -> "Minimal"], {i, Length[vals]}]
Out[5]=

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