Pebble accretion efficiency ε_2D vs τ_s and M_p. Three planetmasses (M_p = 10⁻³ M_⊕, 10⁻¹ M_⊕ and 10 M_⊕) and nine dimensionless stopping times (τ_s ranging from10⁻³ to 10) are considered. Three different simulations are conducted for each case, the local method (magenta square), global direct method (blue triangle) and global hybrid method (orange circle), respectively. The errorbar represents the Poission error. Different total number of pebbles are used for different planet mass cases, N_tot = 3 × 10⁴ for M_p = 10⁻³ M_⊕, N_tot = 3000 for M_p = 10⁻¹ M_⊕ and N_tot = 300 for M_p = 10 M_⊕, respectively. The solid line corresponds to the analytical fit described in Sect. 3.3. The vertical dashed line gives the boundary where our fit can be applied. For the global approach, the hybrid method matches the direct method well when τ_s ≲ 0.1. Local simulations are consistent with global simulations in the settling regime (τ_s < 1) except when the planet is very massive (e.g., M_p = 10 M_⊕).