Re: The relaxation method

[Bernard Cleyet <anngeorg@PACBELL.NET>]

Ludwik!

You already know how to do it ( sent the 24th).  I post for the benefit
for those who wish to read it from a book instead of a monitor.


"  ........ I've just read the section of Eisberg's text where he
describes how to solve
Laplace's eq. numerically with a calculator and works the problem of a
semi-infinite rectangular parallelepiped sides of potential 0. 1. 2. 1.
This is
what you've been doing?

bc"

P.s. Bob calls it an iterative soln. for Laplace's eq.  It's on page
985 ff.  1981  (Remember this is for 1981 freshmen, so very crude.)

P.p.s.  Bernard is wrong:  I've now read more carefully Eisber's text
and the several problems at the end of the chapter -- He avoids the
problem of the boundary condix by having conductors there, so you must
read JD's page.  Maybe an even more careful reading would reveal that he
does indeed show how to deal with the boundary.  Eisberg published a
numerical supplement, which includes a field lines and equipotentials
program for the TI 99/4, inter alia.

kowalskil wrote:

> JohnD reminded us that the distribution of potential on a
> flat sheet can be predicted by the so-called "relaxation"
> method. Suppose the area is a grid of 1000 by 1000
> square cells and that constant potentials 0 and 100 volts
> are assigned to two cells. Find potentials in all other cells.
> We discussed this last year.
>
> I do not know how to deal with marginal cells. An
> interior cell always has four neighbors  but a marginal
> cell has only three neighbors. How to deal with marginal
> cells when it comes to averaging? The only boundary
> condition I want to impose is 0 and 100 volts on two cells
> representing the electrodes. Margins must adjust to the
> existence of the imposed DOP. I want to predict what
> happens at the margins. Is this possible?
> Ludwik Kowalski