Discussion Forum

Your initial equation is called "Poisson's equation." I encourage you to not make your problem any more difficult or complicated than necessary. You can use Comsol's built-in/pre-configured tools. Start with Add Physics --> Mathematics --> Classical PDEs. Also, in the form you wrote it, it is recognizable as an electrostatics problem. So you could start there, alternatively, rather than have to define the meaning and units of your constants (among other things).

Robertt, thank you for your reply. If I use the built-in tool, I still have the same problem. The program set a zero flux boundary condition at top and bottom edge, but I do not want it.

Let's see. "Zero flux" seems to correspond to setting the electric field normal to the boundary as zero. So physics-wise, that is a requirement that the electric field be tangential to the boundary. But I take it that isn't what you want for a particular boundary, and you don't want to specify V there either? I don't know much about the weak formulation so i won't talk about that. But, I know if you are solving an electrostatics problem, you need to specify some kind of boundary condition on either the potential (V, in your notation), or the electric field (-grad V) on every boundary of the volume in which you are solving Poisson's equation. You say that your Poisson equation "has only two boundary conditions at the left and right edge. I do not have any boundary condition at the top and bottom edge." Well, any volume in which you use that equation has boundaries. You must specify boundary conditions on those boundaries. You can't simply say it "has only two boundary conditions at..." All that would mean is that you are failing to specify some of the required boundary conditions. I don't really know what your geometry looks like, but a fairly common error in electrostatics (and in preparing many EM models) is to fail to include enough computational space around the hardware of interest. For example, if you tried to model some random collection of charged objects in a small volume (say, of scale not much bigger than the distances between the charges), you could discover that it was impossible for you to correctly specify the boundary condition on the surfaces surrounding them! This is because you would literally not know either the fields or potentials there. And the reason you wouldn't know them would be that you need to calculate them in that space, i.e., the solution of the problem requires a larger computational space. With a sufficiently large space around a collection of charges, one can approximate the static field by a known (analytic) expression. If the charges add up to zero, you could approximate the field on any surface sufficiently far away as zero. If there is a net charge, you could approximate the fields by an analytic expression corresponding to a point charge (with that net charge). Or, you could perhaps do better approximations (such as accounting for the overall dipole moment), etc. But ultimately, you must specify a finite sized volume and you must specify boundary conditions on all the boundaries. There are other boundary condition-setting techniques for certain special cases, and accounting for symmetries, etc. But I'll leave that for others to speak about. Meanwhile, I suggest you post your model (.mph file) to the forum, perhaps along with some pictures of the geometry (and your computational space) annotated by arrows and text saying what boundary conditions you are seeking to specify on which surfaces, and identifying which surfaces are confusing you. Good luck.

Hello,

You must have boundary conditions on every edges and there is no way around that. This is the reason why COMSOL provides you with a default choice, that you should overwrite as necessary.

To understand what boundary conditions are appropriate, you must think about what will happen physically at those edges.

The zero-flux BC corresponds to a mirror symmetry. Hence in your situation, this is appropriate if your domain should be repeated an infinite number of times along the y-direction for instance. This occurs if you are modeling a semiconductor film. In order to help you further, you need to tell us what is physically happening at these top and bottom edges in the system that you are trying to model.