We critically review the fast algorithms for the numerical study of tw
o-dimensional Josephson junction arrays and develop the analogy of suc
h systems with electrostatics. We extend these procedures to arrays wi
th busbars and defects in the form of missing bonds. The role of bound
aries and of the gauge choice in determining the Green's function of t
he system is clarified. The extension of the Green's-function approach
to other situations is also discussed.