How I can solve the equation in 3D domain? According to the following post, I encounter an error when I run the program. Any help would be graet!

This section should be considered as a continuous program to avoid any possible errors

  • $\begingroup$ "ImplicitRegion[surf, {{x, -1, 1}, {y, -1, 1}, {z, -1, 1}}]" incorrectly defined. "surf" should be a condition. $\endgroup$ – Daniel Huber Sep 16 '20 at 20:25
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    $\begingroup$ "surf" is a vector function of u and v. However, Implicite Region needs a condition, e.g.ImplicitRegion[x^2 + y^2 <= 1, {x, y}] $\endgroup$ – Daniel Huber Sep 17 '20 at 10:57
  • $\begingroup$ Can you please specify explicitly the error that you get? Thank you! $\endgroup$ – CA Trevillian Sep 17 '20 at 19:28

I assume "tours structure" means "torus surface". For this I would use a parameterized torus in cart. coord. Toroidal coordinates make this unnecessary complicated. E.g.

r1 = 1; r2 = 2;
reg = ParametricRegion[{(r2 + r1 Cos[phi]) Cos[
      tau], (r2 + r1 Cos[phi]) Sin[tau], 
    r1 Sin[phi]}, {{phi, -Pi, Pi}, {tau, -Pi, Pi}}];

enter image description here

  • $\begingroup$ Very nice! Does this solve the OP’s issue? Is it possible to show this? Thank you :) $\endgroup$ – CA Trevillian Sep 17 '20 at 19:29
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    $\begingroup$ There are syntax errors: "Module[{u, x, y, z, t, pde, dirichletCondition,..." has no closing bracket. "{eigenValues, evIF, mesh}];" has no opening bracket, where does it belong? $\endgroup$ – Daniel Huber Sep 18 '20 at 8:22
  • $\begingroup$ Still syntax errors. Please copy it back to your machine and check. $\endgroup$ – Daniel Huber Sep 19 '20 at 10:54
  • $\begingroup$ I now executes. But it aborts because a lack of memory. I have 32 GB. $\endgroup$ – Daniel Huber Sep 21 '20 at 9:03
  • $\begingroup$ The size of the problem makes it difficult. I think it will help to first solve a 2D problem or even a 1D problem and learn from this how to do it $\endgroup$ – Daniel Huber Sep 24 '20 at 8:45

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