siegman@sierra.Stanford.EDU (Anthony E. Siegman) (02/14/89)
I want to plot two-dimensional potential and flow lines, i.e.,
solutions of Laplace's equation such as equipotential contours and
E field lines in electrostatic problems, potential and flow fields
in fluid flow problems, or E and H fields in TEM transmission lines.
Relaxation methods for solving Laplace's equation on rectangular grids,
with specified boundary conditions are well known ("Computational
Physics" by Koonin for example); but then one has to run these results
through a contouring program.
I want an algorithm in which I can draw a set of (initially uncorrect)
potential and field lines, with the intersection points (x,y) stored in
arrays, and then have these _intersection points_ (the (,y) values) relax
toward correct values. In other words, instead of potential values on a
fixed grid relaxing toward the correct result, the grid itself relaxes.
Any pointers to references on how to do this? Not only should it speed up
the plotting of results as the problem converges, seems to me it would give
some physical insight also.