Re: visualizing fields near charged objects

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

I also started to do this but in True Basic and in rectangular
coordinates. It would be beneficial if we all worked on
the same disk in the position with respect to the finite size
universe.

My universe (outer shield where V=0, no matter what)
is a cylinder whose diameter is 201 cells and whose
height is 201 cells. The center of my cylindrical disk is
in the center of this universe. The axis of the disk is
is parallel to the axis of the universe. The diameter of
the disk is 21 cells and its height is 7 cells.

It takes 10 seconds to perform one iteration on my
Mac (180 Mhz is no longer the state of the arts). My
last try was 500 iterations (stopping when the biggest
correction at the end of an iteration was 0.2%) but
the result was still different from the one which had
only 300 iterations (stopping at 0.3%). I will start
another tun to stop at 0.05%.

The best way to compare the results would be at the
level of the total charge Q or the corresponding disk
capacity (with respect to the artificial infinity). That
is only one number to compare. The anisotropy along
the surface will be a little larger than 2; so far it keeps
increasing slowly with the number of iterations. The
anisotropy along the height was about 1.3 in the last
run. The moral of the story is "do not stop too early,
make sure that a longer run gives nearly the same
anisotropies as the shorter run. I will share my results
when I am satisfied.

I would be happy to compare my C and my anisotropies
with somebody else whose geometry is similar. I can
easily change the disk diameter (odd number of cells)
or its height (also odd number) but not the size and
shape of my universe. I assume that cells are cubes
of 1 cm but any other scaling factor can be set (giving
a different capacity). Time to go to school.

Ludwik Kowalski

PS
I would appreciate help from somebody who remembers
how to allocate more memory to True Basic. (The size of
my universe is limited by what True Basis allows. The
300 by 300 was not acceptable. My computer has 64 Mb
of memory plus ten time more of virtual memory. I did
not undersatand the "not enough memory" message
which appears at once when I try to run the code.

Leigh Palmer wrote:

> I have set up a relaxation calculation in Excel based on the Laplace
> equation in cylindrical coordinates. Even on this old, slow Mac it is
> converging, and tomorrow I ought to have a nice spreadsheet representing
> the potential field around a disc of diameter 40 and thickness 10, in a
> concentric cylindrical conducting box of diameter 254 and height 254. I
> made the cells square to represent the geometry more accurately, but I
> don't know how to do colors like John's nice plot. Each cell has in it a
> two digit number representing the potential at a point. The plot is an
> axial cross-section because the solution is azimuthally invariant.
> I will make the plot and the cylindrical Laplace template available to
> anyone who wants it (by ftp). They are very large files (3.3 Mb each).
>
> The charge density on the surface of the disc must now be inferred by
> looking at the difference between numbers at the surface. The electric
> field intensity is proportional to the surface charge density, and the
> gradient of the potential field is the relevant parameter here. When I
> have a converged result I can make another spreadsheet (not iterative)
> which will show the charge density on the surface. It won't be great
> right on the sharp edges (my disc has edges with radius of curvature of
> about ten percent of its thickness) but it should be a pretty good
> picture.
>
> I haven't done a large relaxation calculation since I got my Power Mac
> 7500/100 in 1995, using Excel 3.0. I wish I were an Excel guru. I am
> using Excel 98 for the calculation I'm doing now on my office 7600/132.
> It is my impression that the calculation is running much faster on it
> than it did on my home machine. Is Excel 98 somehow faster? I can't wait
> to get my titanium PowerBook G4 to try this sort of stuff. I agree with
> Ludwik; while it is easier to do this in Fortran, it is neat that one
> can do it in Excel. I'm a big fan of using Excel for teaching.
>
> Leigh