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*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

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

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