An Efficient Velocity Update for the Method of Benítez-Llambay et al. (2019)

We present a fast velocity update for the drag-force solver described in Benítez-Llambay et al. for N species. This velocity update is valid when drag forces between N - 1 species are negligible, a regime of particular relevance to dust dynamics in gaseous protoplanetary disks. The complexity of the solution is ${ \mathcal O }(N)$ , that is ${ \mathcal O }({N}^{2})$ faster than standard matrix inversion, enabling efficient calculations of multi-species protoplanetary disks.