A fast potential and self-gravity solver for nonaxisymmetric disks

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Abstract

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 closely follows the method given by Chan et al., in which a fast Fourier transform 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 a vertical structure. The numerical results show that our direct integral method is at least two orders of magnitude faster than our optimized tree-code approach. © 2009. The American Astronomical Society. All rights reserved.

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Shengtai, L., Buoni, M. J., & Hui, L. (2009). A fast potential and self-gravity solver for nonaxisymmetric disks. Astrophysical Journal, Supplement Series, 181(1), 244–254. https://doi.org/10.1088/0067-0049/181/1/244

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