show various drag force schemes – NGP corresponding to Nearest Grid Point and TSC to Triangular Shaped Cloud [@HockneyEastwood1981]. We achieve near perfect scaling up to 4096 cores. Including self-gravity by a Fast Fourier Transform (FFT) method the code slows down by approximately a factor of two, but the scaling is only marginally worse than optimal, with less than 50% slowdown at 4096 cores. This must be seen in the light of the fact that 3-D FFTs involve several transpositions of the global density array, each transposition requiring the majority of grid points to be communicated to another processor (see online supplement of J07).

Particle parallelisation
------------------------

At high resolution it becomes increasingly more important to parallelise efficiently along at least two directions. In earlier publications we had run $256^3$ simulations at 64 processors, with the domain decomposition [nprocy=32]{} and [nprocz=2]{} (J07). Using two processors along the $z$-direction exploits the intrinsic mid-plane symmetry of the particle distribution, while the Keplerian shear suppresses most particle density variation in the azimuthal direction, so that any processor has approximately the same number of particles.

However, at higher resolution we need to either have [nprocz&gt;2]{} or [nprocx&gt;1]{}, both of which is subject to particle 