  We have two basic methods of modeling matter. We can treat matter as a
continuum and solve differential equations or we can treat it discretely and
solve massive N-body problems. The differential equations produced by
meaningful problems can be extremely difficult to formulate and much more
difficult to solve, if not impossible. Hence, in most cases, the resultant
differential equation is discretized and approximated numerically. We know that
matter is discrete, so why all the circular work of taking a discrete
phenomenon, putting a continuous model on it, and then discretizing this
continuous model into something that is solvable? We do this because the sheer
number of particles that make up any meaningful amount of matter is daunting
and impossible to handle even with todays largest supercomputer. One discrete
approach to deal with this problem is to group large numbers of particles
together and treat them as individual units called quasimolecules. Then pray
that the bulk behavior of this model behaves in a similar manner to the matter
being studied. The mathematical skills needed to set up such problems are much
more attainable than those needed to set up the differential equation, but the
N-body problem that ensues usually requires a supercomputer to propagate it
through time. Until recently the cost of such machines made this approach out
of the financial reach of all except the privileged few. But, thanks to the
gaming industry and recent advances in the ease to which one can program modern
graphics processing units (GPUs), this is no longer true. Supercomputing has
finally reached the masses. Here we use a simple example of a vibrating string
to compare the continuous and discrete approaches to modeling and show how GPUs
can enhance an undergraduate modeling experience.
