A methodology for user-oriented scalability analysis

Scalability analysis provides information about the effectiveness of increasing the number of resources of a parallel system. Several methods have been proposed which use different approaches to provide this information. This paper presents a family of analysis methods oriented to the user. The methods in this family should assist the user in estimating the benefits when increasing the system size. The key issue in the proposal is the appropriate combination of a scaling model, which reflects the way the users utilize an increasing number of resources, and a figure of merit that the user wants to improve with the larger system. Another important element in the proposal is the approach to characterize the scalability, which enables quick visual analyses and comparisons. Finally, three concrete examples of methods belonging to the proposed family are introduced in this paper.Peer ReviewedPostprint (published version

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.Comment: 8 figures, accepted to ApJ