Re: visualizing fields near charged objects

[Leigh Palmer <palmer@SFU.CA>]

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
>  21 <-(radial index)

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