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    $\begingroup$ I think PeriodicBoundaryCondition might do what you want here. $\endgroup$ Commented May 16, 2019 at 3:59
  • $\begingroup$ What do you want to express with DirichletCondition[u[x, y] == u[-x, y], x^2 + y^2 == 1]? $\endgroup$ Commented May 16, 2019 at 5:04
  • $\begingroup$ @sr101studios Read the tutorial: Eigensystems with inhomogeneous Dirichlet conditions cannot be solved. $\endgroup$ Commented May 16, 2019 at 14:36
  • $\begingroup$ @user21 I used PeriodicBoundaryCondition and I got the code to work. For example, when I specify keyhole = ImplicitRegion[x^2 + y^2 >= 1, {{x, -1/2, 1/2}, {y, 0.0001, ymax}}] with ymax <= 100, it works. However, I encounter a problem for ymax > 100. I keep getting the error Eigensystem::herm: The matrix SparseArray[Automatic,<<2>>,{1,{{<<1>>},{<<1>>}},{(lots of numbers here)}] is not Hermitian or real and symmetric. Do you know what might be going on and how I can resolve this? I've edited my original post with the new code. $\endgroup$ Commented May 17, 2019 at 23:18
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    $\begingroup$ @ThiesHeidecke, thank you for your help. I have slightly new issue now which I was wondering if you could help with. It's in my above comment and I've edited my initial post to describe it. Thank you again for your help. $\endgroup$ Commented May 17, 2019 at 23:20