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# Re: visualizing fields near charged objects

• From: Leigh Palmer <palmer@SFU.CA>
• Date: Fri, 9 Feb 2001 11:51:42 -0800

At 6:02 AM -0800 2/9/01, John Mallinckrodt wrote:
On Fri, 9 Feb 2001, John S. Denker wrote

At 08:12 AM 2/9/01 -0500, Ludwik Kowalski wrote:

>1) Is it appropriate to perform simple averaging for usual
>cylindrical cells (dr=const)?

No.

and went on to give the essential theory. To put it into practice
here's what I did (and, I assume, what others are doing as well.)

The key difference is the first derivative term in the cylindrical
Laplacian which involves r itself. This means that we need a
radial coordinate which can be simply generated as an index along
the side of the "universe."

27 ^ (+ r direction)
26 |
25 c
24 d a b -> (+z direction
23 e
22

Using John's drawing above, in my implementation:

23 25
a <- (2a + d + b + ---- e + ---- c)/6
24 24

where the numerical factors come from the radial index.

This form follows directly from the Laplacian. I also generate a
row (in my case) with radial coordinates. My cells on axis have
a different formula; the surrounding cells are unweighted for
these cells.

Leigh