A Fast Potential and Self-Gravity Solver for Non-Axisymmetric Disks

Disk self-gravity could play an important role in the dynamic evolution of interaction between disks and embedded protoplanets. We have developed a fast and accurate solver to calculate the disk potential and disk self-gravity forces for disk systems on a uniform polar grid. Our method follows closely the method given by Chan et al. (2006), in which an FFT in the azimuthal direction is performed and a direct integral approach in the frequency domain in the radial direction is implemented on a uniform polar grid. This method can be very effective for disks with vertical structures that depend only on the disk radius, achieving the same computational efficiency as for zero-thickness disks. We describe how to parallelize the solver efficiently on distributed parallel computers. We propose a mode-cutoff procedure to reduce the parallel communication cost and achieve nearly linear scalability for a large number of processors. For comparison, we have also developed a particle-based fast tree-code to calculate the self-gravity of the disk system with vertical structure. The numerical results show that our direct integral method is at least two order of magnitudes faster than our optimized tree-code approach.