Pseudoparticle Multipole Method: A Simple Method to Implement High-Accuracy Treecode
نویسندگان
چکیده
In this letter we describe the pseudoparticle multipole method (PM), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of PM is that it works on GRAPE. GRAPE is a special-purpose hardware for the calculation of gravitational force between particles. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With PM, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using PM, we implemented an arbitrary-order treecode on GRAPE-4. Timing result shows GRAPE-4 accelerates the calculation by a factor between 10 (for low accuracy) to 150 (for high accuracy). Even on general-purpose programmable computers, our method offers the advantage that the mathematical formulae and therefore the actual program is much simpler than that of the direct implementation of multipole expansion. Subject headings: methods: n-body simulations — galaxies: kinematics and dynamics — large-scale structure of universe
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