Comparison of the mass distribution evolution obtained using our Smoluchowski and Monte Carlo codes. In a standard case when an insurmountable fragmentation barrier is present, the two methods perfectly agree (three upper panels); however, we encounter some differences between the results obtained with the two approaches (three bottom panels) with the possibility of breakthrough. For the Smoluchowski code, the presented results were obtained with a resolution of 30 mass bins per decade. For the Monte Carlo code, the results are averaged from the simulations using 120 000 particles. The “check points”, m₁ and m₂, which are indicated with the dotted lines, are used to quantitatively compare dust growth timescales in Sect. 4.1.