  Simple toy models are often not sufficient to cover the complexity of the
dust coagulation process, and a number of numerical approaches are therefore
used, among which integration of the Smoluchowski equation and various versions
of Monte Carlo algorithm are the most popular. In this paper, we directly
compare the Smoluchowski and Monte Carlo approaches and we find a general
agreement for most of the coagulation problems. However, for the sweep-up
growth driven by the "lucky" breakthrough mechanism, the methods exhibit very
different resolution dependencies. With too few mass bins, the Smoluchowski
algorithm tends to overestimate the growth rate and the probability of
breakthrough. The Monte Carlo method is less resolution dependent in the growth
timescale aspect but it tends to underestimate the breakthrough chance due to
its limited dynamic mass range. We discuss the features and drawbacks of both
the approaches, which may limit their astrophysical applications.
