Finite element solving of Laplace's equation doesn't converge

[crum]

Homework Statement

I'm trying to solve Laplace's equation numerically in 3d for a charged sphere in a big box. I'm using Comsol, which solves using the finite elements method. I used neumann BC on the surface of the sphere, and flux=0 BC on the box in which I have the sphere. The result does not converge.

Homework Equations

Laplace's equation \[\nabla^2 \phi=0\]

The Attempt at a Solution

I've tried using derichlet BC instead of neumann, and a fixed potential at the box (instead of flux=0), but the result still doesn't converge. Convergance errors usually appears when the mesh is not fine enough or I'm missing a boundary condition, but I don't see how using neumann at the surface and flux=0 at the box wouldn't be enough boundary conditions. I have used the same BCs using the Poisson-Boltzmann eq and it worked fine there.

 

[Chestermiller]

Is it being solved iteratively?

 

[DrClaude]

Is it being solved iteratively?

Yes, that's how COMSOL works.

@crum: can you give more details about how you are setting up the problem in COMSOL?

 

[crum]

Yes, that's how COMSOL works.

@crum: can you give more details about how you are setting up the problem in COMSOL?

I make a small sphere inside of a big simulation box (100times the size of the sphere). I set the laplace to hold inside of the simulation box and inside the sphere. I set neumann conditions on the surface of the sphere, and flux=0 BC on the edge of the box. I don't know what other info i could give you.

I tried making a small-scale 1d model and it still didn't work, so I'm guessing it has to do with some more basic error. I set Laplace's equation to hold on an interval, with neumann BC on one side of the interval, and flux=0 BC on the other side. The result still didn't converge.

 

[Orodruin]

I set neumann conditions on the surface of the sphere, and flux=0 BC on the edge of the box. I don't know what other info i could give you.

When you say you set Neumann conditions on the surface of the sphere, are you implying that you have non-homogenous Neumann conditions? If so, this would imply a non-zero flux into (or out of) your volume and no sources inside the volume. Thus, your boundary conditions would be incompatible with your differential equation.