Molecular Dynamics Simulations are a tool to study the behaviour
of atomic-scale systems. The simulations themselves solve the
equations of motion for hundreds to millions of particles over
thousands to billions of time steps. Due to the size of the
problems studied, such simulations are usually carried out on
large clusters or special-purpose hardware.
At a first glance, there is nothing much of interest for a
Numerical Analyst: the equations of motion are simple, the
integrators are of low order and the computational aspects seem
to focus on hardware or ever larger and faster computer
clusters.
The field, however, having been ploughed mainly by domain
scientists (e.g. Chemists, Biologists, Material Scientists) and
a few Computer Scientists, is a goldmine for interesting
computational problems which have been solved either badly or
not at all. These problems, although domain specific, require
sufficient mathematical and computational skill to make finding
a good solution potentially interesting for Numerical Analysts.
The proper solution of such problems can result in speed-ups
beyond what can be achieved by pushing the envelope on Moore's
Law.
In this talk I will present three examples where problems
interesting to Numerical Analysts arise. For the first two
problems, Constraint Resolution Algorithms and Interpolated
Potential Functions, I will present some of my own results. For
the third problem, using interpolations to efficiently compute
long-range potentials, I will only present some observations and
ideas, as this will be the main focus of my research in Oxford
and therefore no results are available yet.