  We investigate the classical ground state of a large number of charges
confined inside a disk and interacting via the Coulomb potential. By realizing
the important role that the peripheral charges play in determining the lowest
energy solutions, we have successfully implemented an algorithm that allows us
to work with configurations with a desired number of border charges. This
feature brings a consistent reduction in the computational complexity of the
problem, thus simplifying the search of global minima of the energy.
Additionally, we have implemented a divide and conquer approach which has
allowed us to study configurations of size never reached before (the largest
one corresponding to $N=40886$ charges). These last configurations, in
particular, are seen to display an increasingly rich structure of topological
defects as $N$ gets larger.
