Solve PDEs with Complex-Valued Boundary Conditions over a Region
Solve a Laplace equation with a complex-valued boundary condition.
In[1]:=
![Click for copyable input](assets.en/solve-pdes-with-complex-valued-boundary-conditions/In_48.png)
ifun = NDSolveValue[{-\!\(
\*SubsuperscriptBox[\(\[Del]\), \({x, y}\), \(2\)]\(u[x, y]\)\) ==
1 + NeumannValue[I, x < 0],
DirichletCondition[u[x, y] == 0, x > -0]},
u, {x, y} \[Element] Disk[]]
Out[1]=
![](assets.en/solve-pdes-with-complex-valued-boundary-conditions/O_28.png)
Visualize the result.
In[2]:=
![Click for copyable input](assets.en/solve-pdes-with-complex-valued-boundary-conditions/In_49.png)
Plot3D[{Re[ifun[x, y]], Im[ifun[x, y]]}, {x, y} \[Element] Disk[],
PlotTheme -> "Detailed"]
Out[2]=
![](assets.en/solve-pdes-with-complex-valued-boundary-conditions/O_29.png)