???

1
???Performance Tuning of a CFD Code on the
Earth Simulator

• ???????
• ????

2
Intorduction

• ??????????Navier-Stokes??????????(DNS)????????????
  ?????????????????????????????????????????????????
  ???????
• ??????????????????????Itakura?????????

3
?????????
???????? ??????????
?????????? ?????????????!
????????????? 8Gflops ??????? 5120
??????????? 64Gflops ??????? 640
??????????? 16GB ????? 40Tflops
????? 10TB
4
??????
Navier-stokes???
???????? ?????????????? ????4????????
??????
??????????????????????????!
???FFT????
4
4
5
???

• ????????????(????Nn3)
• ?????4????????O(N)
• ?????????O(N)
• FFT???FFTO(NlogN)

?????????FFT????? ?????????????!
6
???(??)
z
3D-FFT??????????
XFFT
???????????
2D-FFT?????????????????
x
y
ZFFT
7
???(??)
y??x??????y????z??? (????????????)
YFFT
??????????x???????1D-FFT????
3D-FFT???
8
???
9
???
XFFT
?????????????
10
???
?????????????
ZFFT
11
???
YFFT
?????????????
12
???
2????????????????1??????????????????????????????
??
13
????
???????????????
?????????????? ???
nd????????N????????????????N????????nd?????????
?????????
??????????????????????
14
????
?????????????
????????
15
????
????????
?????????????????!
16
???

• ???DNS??????????????????????????3D-FFT????????????
  ?????????????
• ??16.4TFLOPS?????????????

17
????

• 16.4-TFLOPS Direct Numerical Simulation of
  turbulence by a Fourier Spectral Method on the
  Earth Simulator(2002)
• M.Yokokawa,K,Itakura et al
• Performance Tuning of a CFD Code on the Earth
  Simulator(2003)
• K.Itakura A.Uno,M.Yokokawa,M.Saito,Ishihara.T,Ka
  neda.Y

18
????
19
??(??????)
u 3??????????? 3??????????u?
3?????????alias error??? 24???????
41????????72??FFT???!
?FFT
FFT