Numerical Calculation of Electric Potentials

The Laplace's Equation governs the electric potential in a vacumme when all the boundaries' electric potential are pre-determined. The example to the left is an animation of a program calculating the electric potential numerically by iteration using the following simple formula:

p(x,y) = {p (x-1, y) + p (x+1,y) + p(x, y-1) + p (x,y+1) } / 4

Laplace's equation works in 3 dimensions as well. Notice how the calculation takes many iterations despite the simple calculation. This is certainly a problem as the grid size becomes enormous in 3-D calculations. Higher dimension calculations and higher resolution calculation require, therefore, better update methods, or some initial approximations to speed up calculations. Can you think of any way to speed up the calculation?

NOTE: To view the movie, click on the triangular "play" button. If you cannot see it (may happen on UNIX machines), try clicking on the picture. or pressing return.

Last Updated: 6/30/98 by Hide Oki

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