One problem with the accuracy of calculating C numerically,
is the size of each cell. Suppose sigmas were calculated and
one needs E (=dV/dl) for the corresponding locations. What
should one use for dl? So far I am using dl=one half of the
cell size. This is based on the assumption that V assigned to
a cell, at the end of iterations, really belongs to the center of
the cell (as far as the r,z projections are concerned). Right?
If so then the value of E=dV/dl belongs to the distance
of dl/4 from the surface. I need E at the surface, not at
dl/4 from the surface. What is a good algorithm for
extrapolations?
I know that E at zero distance from the surface would be
the same as E at the distance dl/4 from it, if dl/4 were
sufficiently small to make E(l)=const. But this is not true
when cells are large, especially at locations close to rims.
So the issue of extrapolating correctly, in my case for a
cylindrical disk, positioned at the center of a cylindrical
universe, is very real. Any suggestions? Iterations in space
made from millions of cells would take too much of
computer time, even if memory were available.
Ludwik Kowalski