- 16 - Vol. 15, No. Special Issue 1, 2013 · C 2 2 T k n p (15) iii) p kn TS 3 1 3 3 ( 1) 3 2 1 C 3...

99%

(bow shock)

( )

( )

100 150 km/s

[1]

“

スーパーコンピューティングニュース� Vol.�15,�No.�Special�Issue�1,��2013- 15 -

”

2

CME

GPS

GPS


:

CME

Voyager 1 2 Pioneer 10 11 Ulysses Galileo Cassini New

Horizon Galileo

Galileo

[2][3][4]


Voyager 1 Pioneer 10 11 Cassini

Cassini Cassini

Galileo

[5][6]

Cassini

:

5 9.5

[nT] [hr] [km] [A.U.]

31,000 N 24 6,378 1

420,000 N 10 71,492 5.2

21,000 N 10.65 60,268 9.55

3 : [NASA ]


: [7]


: [6]

MagnetoHydroDynamics MHD

MHD

MHD

0.01

RE (1 RE = 6,380 km) 15,0003

FX10

10,000×8,000×8,000


Vlasov

Boltzmann

0)(vf

BvEmq

rf

vtf s

s

sss (1)

E B r v ),,( tvrf ss -

s sq sm

Maxwell

0

1

0

20

B

E

tBE

tE

cJB

(2)

J 0 0 c

J

vdvfqJ ss

s (3)

J

0Jt

(4)

MHD MHD Vlasov (1)

Vlasov

Vlasov (1)

0)( sss untn

(5)

su Vlasov (1) vm

0)()( BJEPuunmunmt ssssssssss (6)

sP2

21 vm Vlasov (1)

0)23

21()

23

21( 22

ssssssssssssss JEhuPupuunmpunmt

(7)


sp3~1

,,31

isiis Pp

sh

ss

snm Um

um

ss

ss

s

0s

s JJs

s (8)

0)( Ut

(9)

0)( BJpUUtU (10)

0)( UppUtp

(11)

35 pIP

ss I

0BUE (12)

Darwin

JB 0 (13)

(9) (13) MHD [9]

MHDMHD Ogino et al. [10] Modified Leap

Frog 1 two step Lax-Wendroff l 1

leap-frog l

1

l = 8 Modified leap frog two step Lax-Wendroff

leap frog


:

1 2 3 n3 p

p 2 p1/2 3 x, y, z p1/3

[11]

MPI 3

(TS1, TS2, TS3) (TC1, TC2, TC3)

i)

pnkTS

31

1 )1(221 pnkTC (14)

ii)

pnkTS

31

2 )1(2 212

22 pnkTC (15)

iii)

pnkTS

31

3 )1(3 312

23 pnkTC (16)

k1 k2 n p

x, y, z n

TS1 TS2 TS3 p TC1, TC2, TC3 p

TC1, TC2, TC3

7

k2


KB

CPU

MHD

8 u(i,j,k,m)

Type A m = 8

u(m,i,j,k,) Type

B

: [11]

(14) (16)

TS TC k1=1 k2=0.01

kn

MHDMHD 1 GB/node weak

scaling MHD Modified Leap Frog 5 GB/node


do

Flat MPI

OpenMP

VPP5000 NEC SX-6

do

HPC2500 FX1

RS200S6 SR16000/L2 HA8000

[12]

core

Flat MPI 4,800 76,800

Type B 210 TFlops

180 TFlops TypeA

110 TFlops

19 %

SPARC POWER

CPU CPU

Xeon Opteron

[12] SSE

/ MPI TypeB

25% MPI /

22 % 2 %


/ 21 %

230 TFlops 10,000×8,000×8,000

:

:


FX10 Tofu

5

C MPI

1 1200 20x15x4

16x15x5 8x15x10 16x12x10

2MB 2KB Allgather Allreduce Alltoall

Tofu Tofu

Tofu

Bruck Recursive Doubling

: Allgather 2MB


: Allgather 2KB

: Allreduce 2MB


: Allreduce 2KB

: Alltoall 2MB


: Alltoall 2KB

FX10 4800

MHD Tofu

MHD 3

/ /

230 TFlops 21 %

OpenMP MPI 22%

4800 17 % /

FX10 1PFlops

/ 2% 20TFlops

x86

SPARC


[1] Margaret G. Kivelson Christopher T. Russell Introduction to space physics Cambridge

University Press 1995.

[2] Ogino, T., R. J. Walker, and M. G. Kivelson, A global magnetohydrodynamic simulation of the

Jovian magnetosphere, J. Geophys. Res., 103, 225, 1998.

[3] Fukazawa, K., T. Ogino, and R.J. Walker, “Dynamics of the Jovian magnetosphere for

northward interplanetary magnetic field (IMF)”, Geophys. Res. Lett., 32,

doi:10.1029/2004GL021392, 2005.

[4] Fukazawa, K., T. Ogino, and R.J. Walker, "The Configuration and Dynamics of the Jovian

Magnetosphere", J. Geophys. Res., 111, A10207, 2006.

[5] Fukazawa, K., T. Ogino, and R.J. Walker, "Magnetospheric Convection at Saturn as a Function

of IMF BZ", Geophys. Res. Lett., 34, L01105, 2007a.

[6] Fukazawa, K., T. Ogino, and R.J. Walker, "Vortex-associated reconnection for northward IMF

in the Kronian magnetosphere", Geophys. Res. Lett., 34, L23201, 2007b.

[7] Khurana, K. K., M. G. Kivelson, V. M. Vasyliunas, N. Krupp, J. Woch, A. Lagg, B. H. Mauk

and W. S. Kurth, The Configuration of Jupiter's Magnetosphere, In:Bagenal, F., T. Dowling and

W. McKinnon (Ed.), Jupiter, Cambridge University Press, New York, 2004.

[8] MHD .

http://center.stelab.nagoya-u.ac.jp/web1/simulation/hpfja/comput04.html

[9] R. O. Dendy Plasma Dynamics Oxford University Press 1990.

[10]T. Ogino, R. J. Walker, M. Ashour-Abdalla, A global magnetohydrodynamic simulation of the

magnetopause when the interplanetary magnetic field is northward, IEEE Trans. Plasma Sci.20,

817.828, 1992.

[11]Fukazawa, K., T. Umeda, T. Miyoshi, N. Terada, Y. Matsumoto, and T. Ogino, Performance

measurement of magneto-hydro-dynamic code for space plasma on the various scalar type

supercomputer systems, IEEE Transactions on Plasma Science, Vol. 38, No. 9, pp2254, 2010.

[12]Fukazawa, K., T. Umeda, Performance measurement of magnetohydrodynamic code for space

plasma on the typical scalar type supercomputer systems with the large number of cores,

International Journal of High Performance Computing, doi:10.1177/1094342011434813, 2012.


- 16 - Vol. 15, No. Special Issue 1, 2013 · C 2 2 T k n p (15) iii) p kn TS 3 1 3 3 ( 1) 3 2 1 C 3...

Documents

Transcript of - 16 - Vol. 15, No. Special Issue 1, 2013 · C 2 2 T k n p (15) iii) p kn TS 3 1 3 3 ( 1) 3 2 1 C 3...