Comparison of the azimuthally averaged column density of solids as a function of radial position and time. The column density of solids ﹩{{\rm{\Sigma }}}_{p}﹩ is normalized by the initial gas column density ﹩{{\rm{\Sigma }}}_{g,0}﹩, while the radial position x and the time t are normalized by the gas scale height H and the local orbital period P, respectively. The left panel shows the simulation with the original explicit integration in Yang & Johansen (2014), while the right panel shows our algorithm in this work. The models are otherwise the same, with a computational domain of 1.6H × 1.6H × 0.2H and a resolution of 160 points per H.