Possible to create global potential from local distribution?

[KFC]

Hi all,
I saw some figures about potential (contour) plot in some articles that has some beautiful gradient lines. The shape is quite weird but you can see clearly there are some strong concentration of potential at some places. For example, if you have 300x300 grids, there shows strong potential of 3V in region of radius 10 grids at somewhere close to bottom-left corner, 5V in region of radius 15 girds at top-right corner, -1V in region of radius 15 grids in middle. With this distribution is it possible to create all contour potential lines based on those 3 strong regions such that the potential line are gradually change to span whole space (grids)?

 

[mfb]

We discussed this a few weeks ago (mainly starting at post #10), does that thread help?

 

[KFC]

Thanks. After reading that post, base on my understanding, it is suggested to solve the spatial distribution of potential with Poisson equation. The excel file found there use the average of neighboring points to estimate the value of the current point (that's the idea of solving Poisson equation?) But after reading something about Poisson equation, it is about potential distribution if the charge distribution is known. I wonder if it is the same case since here I know some spatial distribution of potential, I am looking for how the other part of potential in space look like.

 

[mfb]

(that's the idea of solving Poisson equation?)

It is the discrete version of Poisson's equation in cartesian coordinates.
The charge distribution is known in every cell where you want to calculate the potential - it is zero (if it is not, the formulas need an additional term to account for that). You don't know the charge distribution at the electrodes, but there you know the potential.

 

[KFC]

Oh, so you mean we actually use the Laplace equation instead of Poisson equation to solve the problem since we know the potential in space already? So just average each point with its neighbor will do the work, is that correct?

 

[mfb]

If you have zero charge density where you want to calculate the potential (the usual case), both equations are identical.
You can fix the potential at some points, iterating the averages over neighbors will give an approximation for the potential elsewhere.

 

[KFC]

got it. Thanks mfb.