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.