# Computing electrostatic field using FDM, trouble with end results, related to mesh

1. Jun 14, 2010

### Aiggy

1. The problem statement, all variables and given/known data
I am trying to solve the electrostatic field (2D) for a microstrip laid on a dielectric with a ground plane on the other side. I am also calculating the capacitance of the microstrip by evaluating a closed surface integral to get the charge on the conductors. I am using FDM, coding in matlab.

2. Relevant equations

Field:

$$\nabla$$V = 0

Charge:

eps*eps0*length*$$\oint$$E*dl) = charge

Capacitance:

C=Q/U

3. The attempt at a solution

a. The geometry of the problem is always the same. If I compute the field and then compute the capacitance for a 100x100 mesh I get say 10.2pF. However if I make the mesh finer, say 200x200 I get a different result, 10.75pF. I let the iterations reach 50k (jacobi iteration) in both cases. Why is there such a big difference between the results?

b. I also calculate the charge on the ground plane, for a sanity check. The value I get is too small by 30%. What is wrong?

c. I am always using dirichlet boundary condition for the ground plane, for the other sides of the space I tried using both dirichlet and neumann conditions, difference in the final results for the charge (capacitance) is around 0.6%, which is good, but leads me to the conclusion that for my chosen space size (5x5mm) and the microstrip size - it doesn't really matter which boundary condition do I choose. Do you agree?

Last edited: Jun 14, 2010