Parallelized Solution Method of the Three-dimensional Gravitational Potential on the Yin-Yang Grid

We present a new method for solving the three-dimensional gravitational potential of a density field on the Yin-Yang grid. Our algorithm is based on a multipole decomposition and completely symmetric with respect to the two Yin-Yang grid patches. It is particularly efficient on distributed-memory machines with a large number of compute tasks, because the amount of data being explicitly communicated is minimized. All operations are performed on the original grid without the need for interpolating data onto an auxiliary spherical mesh.