GRAPE-5: A Special-Purpose Computer for N-Body Simulations

Abstract

We have developed a special-purpose computer for gravitational many-body simulations, GRAPE-5. GRAPE-5 accelerates the force calculation which dominates the calculation cost of the simulation. All other calculations, such as the time integration of orbits, are performed on a general-purpose computer (host computer) connected to GRAPE-5. A GRAPE-5 board consists of eight custom pipeline chips (G5 chip) and its peak performance is 38.4 Gflops. GRAPE-5 is the successor of GRAPE-3. The differences between GRAPE-5 and GRAPE-3 are: (1) The newly developed G5 chip contains two pipelines operating at 80 MHz, while the GRAPE chip, which was used for GRAPE-3, had one at 20 MHz. The calculation speed of GRAPE-5 is 8-times faster than that of GRAPE-3. (2) The GRAPE-5 board adopted a PCI bus as the interface to the host computer instead of VME of GRAPE-3, resulting in a communication speed one order of magnitude faster. (3) In addition to the pure 1/r potential, the G5 chip can calculate forces with arbitrary cutoff functions, so that it can be applied to the Ewald or P3M methods. (4) The pairwise force calculated on GRAPE-5 is about 10-times more accurate than that on GRAPE-3. On one GRAPE-5 board, one timestep with a direct summation algorithm takes 14 (N/128 k)2 seconds. With the Barnes-Hut tree algorithm (θ = 0.75), one timestep can be done in 15 (N/106) seconds.

GADGET: a code for collisionless and gasdynamical cosmological simulations

“…For our current set-up at MPA this break-even point is about at 300000 particles. However, it is also possible to combine GRAPE with a tree algorithm (Fukushige et al 1991;Makino 1991a;Athanassoula et al 1998;Kawai et al 2000), for example by exporting tree nodes instead of particles in an appropriate way. Such a combination of tree+GRAPE scales as O(N log N ) and is able to outperform pure software solutions even for large N .…”

“…Yet another approach to the N-body problem is provided by special-purpose hardware like the GRAPE board (Makino 1990;Ito et al 1991;Fukushige et al 1991;Makino & Funato 1993;Ebisuzaki et al 1993;Okumura et al 1993;Fukushige et al 1996;Makino et al 1997;Kawai et al 2000). It consists of custom chips that compute gravitational forces by the direct summation technique.…”

A natural symmetrization for the plummer potential

“…those that run on typical CPUs without special hardware, can easily include our calculation model. Phantom-GRAPE (Nitadori et al, in preparation) is an optimized library that utilizes the SIMD instructions of X86 CPUs and has application interfaces comparable with GRAPE-5 (Kawai et al, 2000). For this software, we can easily modify the gravity kernel in the library.…”

“…The increase in the calculation cost due to this modification of the potential is quite small. Thus, it is widely used in simulations of self-gravitating systems and the GRAPE (GRAvity PipE) series also adopts this form of the gravitational potential (Sugimoto et al, 1990;Ito et al, 1991;Okumura et al, 1993;Makino et al, 1997;Kawai et al, 2000;Makino et al, 2003;Kawai & Fukushige, 2006;Makino, 2005. Due to the wide adoption of the Plummer potential, there have been several studies on the choice of the optimal gravitational softening length (Merritt, 1996;Athanassoula et al, 2000;Dehnen, 2001).…”

Simulation Techniques for Cosmological Simulations

“…Furthermore, the communication time between the host computer and the GRAPE system can be an issue in certain circumstances. However, newer versions of the GRAPE chips circumvent this problem, and can also be combined with the tree algorithms (which are described in detail in the next section), see Fukushige et al (1991), Makino (1991), Athanassoula et al (1998), Kawai et al (2000).…”