  We present a cluster algorithm for resistively shunted Josephson junctions
and similar physical systems, which dramatically improves sampling efficiency.
The algorithm combines local updates in Fourier space with rejection-free
cluster updates which exploit the symmetries of the Josephson coupling energy.
As an application, we consider the localization transition of a single junction
at intermediate Josephson coupling and determine the temperature dependence of
the zero bias resistance as a function of dissipation strength.
