density not just to the nearest grid point, but also to the neighbouring grid points.

6.  In the beginning of each sub-time-step the gas density and gas velocity field is communicated from the main grid to the adopted particle blocks.

7.  Drag forces are added to particles and back to the gas grid points in the adopted blocks. This partition aims at load balancing the calculation of drag forces.

8.  At the end of each sub-time-step the drag force contribution to the gas velocity field is communicated from the adopted blocks back to the main grid.

To illustrate the advantage of this scheme we show in [Fig. \[f:speed\_t\]]{} the instantaneous code speed for a problem where the particles have sedimented to the mid-plane of the disc. The grid resolution is $256^3$ and we run on 2048 cores, with 64 cores in the $y$-direction $32$ cores in the $z$-direction. The blue (black) line shows the results of running with standard domain decomposition, while the orange (grey) line shows the speed with the improved Particle Block Domain Decomposition scheme. Due to the concentration of particles in the mid-plane the standard domain decomposition leaves many cores with few or no particles, giving poor 