Stiff- One-Dimensional Poisson Equation in Plasma

aditya.p

Hey Guys,

So I am trying to model the development of a collisional plasma in time. Now the problem I face is at the sheath boundary the changes in the charge densities is very large.

I use the charge densities to evaluate the electric potential at different points in the plasma. I have the charge densities as a number available at all points.

Now comes the problem. When I use a regular solver like Gauss Siedel or Successive Over relaxation, the changes in charge density in space is still too rapid for these methods to give me a solution within respectable error tolerances. (at least 1e-2).

The in built poisson solver in matlab requires a two dimensional case. I was curious if anyone know of a robust poisson solver for a one-d case which can handle stiff cases.

Its is a dirichlet problem. I know the potential at both boundaries (one is the electrode and the other is the wall).

Would be great if I can get some insight.

Thanks

Aditya