Introduction to the GRAPE

• N-body : direct integration of the equations of motion• Fokker-Planck : direct integration of the Fokker-Planck equation• Monte-Carlo : particle-based method which uses Monte-Carlo to apply relaxation in the Fokker-Planck approximation• Gas model : cluster modeled as conducting gas• Hybrid methods : gas+MC, FP+N-body

Numerical Methods for Dense Stellar Systems

The GRAPE project

• GOAL : Design and build specialized hardware for simulation of stellar systems.

• Rationale : You can do larger simulations (better resolution) for the same amount of money.

History of the GRAPE

TABLE-1 Low-Precision machines Machine Year Peak speedGRAPE-1 1989 240 Mflop/s,GRAPE-3 1991 15 Gflop/sGRAPE-5 1998/9 ~ 1Tflop/s

TABLE-2 High-Precision machines Machine Year Peak speed GRAPE-2 1990 40Mflop/sHARP-1 1993 180 Mflop/sGRAPE-4 1995 1 Tflop/sGRAPE-6 2002 64 Tflop/s

10n Prefix Symbol

10+24 yotta Y10+21 zetta Z10+18 exa E10+15 peta P10+12 tera T10+9 giga G10+6 mega M10+3 kilo k10+2 hecto h10+1 deca, deka da

1 (none) (none)10−1 deci d10−2 centi c10−3 milli m10−6 micro µ (u)10−9 nano n10−12 pico p10−15 femto f10−18 atto a10−21 zepto z10−24 yocto y

Sciences with the GRAPE• Solar system / Planetary formation

• Star-forming region / Open clusters

• Globular clusters

• Galactic dynamics/ Galactic nuclei

• Galaxy formation

• Star formation

• Clusters of Galaxies / Cosmology (CDM halo)

More than just N-body

• SPH “GRAPE-SPH” - Nakasato & Nomoto , Matthias Steinmetz & Klaus Dolag , Volker Springe “Tree-GRAPE-SPH”

• MHD “Grape-MSPH” - Dolag et al. (1991, 2002) SPH simulations of magnetic fiels in galaxy clusters. K. Dolag. (A&A 348, 351, 1999)

• PM “Grape + PM” - Andreas Huss

Constructing a GRAPE Cluster

• 6,900,000 Yen for each GRAPE6-BLX64 board– Each BLX64 has 4 GRAPE chips– Total 132 Gflops

• 3,000,000 Won for each host PC– Two 2.0GHz dual-core Xeons, 1 GB memory

• 3,800,000 Won for one server PC– Two 2.0GHz dual-core Xeons, 1 GB memory

The Korean GRAPE Consortium

• 이형목 교수님 : 구매 진행 중– 2007 : 4 BLX64’s– 2008 : 4 BLX64’s or DR ?

• SRC 멤버 : 3 월 구매 예정– 2007 : 4 BLX64’s – 2008 : 4 BLX64’s or DR ?

• 공동연구 과제 신청 ?– 학진 기초과학 공동연구 : 1 억 / 년 , 최대 3 년 (3 월 신청 )– 과학재단 특정기초 :1 억 / 년 , 최대 5 년 (5 월 신청 )

Proposed Research Topics

• Galactic Dynamics– Galactic warps : triaxial live halo– Galaxy interaction and evolution

• Galactic Center Hydrodynamics– 200-pc molecular ring (the Central Molecular Zone)– 5-pc molecular ring (the Circumnuclear Ring)

• Stellar Dynamics– Evolution of the globular cluster mass function– The Arches cluster

• Future Plans– Development of new codes (Monte Carlo simulations +

GRAPE)– Planetary dynamics