# Solving equation in 3D

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

• "ImplicitRegion[surf, {{x, -1, 1}, {y, -1, 1}, {z, -1, 1}}]" incorrectly defined. "surf" should be a condition. – Daniel Huber Sep 16 '20 at 20:25
• "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}] – Daniel Huber Sep 17 '20 at 10:57
• Can you please specify explicitly the error that you get? Thank you! – 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}}];
Region@reg • Very nice! Does this solve the OP’s issue? Is it possible to show this? Thank you :) – CA Trevillian Sep 17 '20 at 19:29
• 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? – Daniel Huber Sep 18 '20 at 8:22
• Still syntax errors. Please copy it back to your machine and check. – Daniel Huber Sep 19 '20 at 10:54
• I now executes. But it aborts because a lack of memory. I have 32 GB. – Daniel Huber Sep 21 '20 at 9:03
• 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 – Daniel Huber Sep 24 '20 at 8:45