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JAERI-Data/Code—97-032
JAERI-Data Code97-032
KBSHOOTCDfJiJib
1997*P7E
Japan Atomic Energy Research Institute
it- Hi,
(T319-11
(T319-11
*5 f) t to
This report is issued irregularly.
Inquiries about availability of the reports should be addressed to Research
Information Division, Department of Intellectual Resources, Japan Atomic Energy
Research Institute, Tokai-mura, Naka-gun, Ibaraki-ken 319-11, Japan.
© Japan Atomic Energy Research Institute, 1997
JAERI- Data/Code 97-032
~ KKBSHOOT
* • J£* # ** • Mike ELIA**
(1997^7^ 1
f i 7
v JL - r -f > ^ ^ - K KBSHOOT C o i ^ t , VPP500fo]§ H
: o t ' J y'-f ; i / 3 - KO1PE (Processing Element)!: X Z>&*Uit LT,4PE -eft 3 f§, 16PE
T 3ii-oi ^^miRiBrgBswirrisiiij soi-oi* m±a (ft**
JAERI- Data/Code 97-032
Parallelization of Kinetic Ballooning Shooting Code KBSHOOT
Mitsuru YAMAGIWA, Toshiyuki NEMOTO*. Akira HIROSE**
and Mike ELIA**
Department of Fusion Plasma Research
Naka Fusion Research Establishment
Japan Atomic Energy Research Institute
Naka-machi, Naka-gun, Ibaraki-ken
(Received July 1, 1997)
This report describes parallelization of the kinetic ballooning shooting code,
KBSHOOT, developed at the Plasma Physics Laboratory, University of
Saskatchewan, Canada, for running on the VPP500 machine. The speed of the
code, which was highly vectorized, has been further enhanced by parallelization.
The CPU time has been reduced by three times for the 4PE (Processing
Element) mode and eight times for the 16PE mode, as compared to that of the
original code with the 1PE mode.
Keywords: Kinetic Ballooning Mode, Tokamak, Plasma, Shooting Code,
Parallelization, VPP500, NEXT
* On leave from Fujitsu Ltd.**Plasma Physics Laboratory, University of Saskatchewan, Canada
JAERI-Data/Code 97-032
e
1. It D#>\Z 1
2. a»»w^^--^^*- K*SS 23. KBSHOOT O^yiJ-ft 3
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Contents
1. Introduction ; 1
2. Kinetic Ballooning Mode Equation 2
3. Parallelization of KBSHOOT 3
3.1 Code Analysis 3
3.2 Guideline for Parallelization 3
3.3 Tuning for Parallelization 4
3.4 Effect of Parallelization 5
4. Summary 6
Acknowledgement 6
References 6
JAERI- Data/Code 97-032
K (KBM) J
K KBSHOOT O
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(NEXT)
KBSHOOT
, KBSHOOT
- 1 -
JAERI- Data/Code 97-032
KBSHOOT
, 5, 7] :
dd L l v ' J d6 J 2 ( l + x ) e n ( l + rj)
x [ (1 - 0 . 6 / F ) { ( O - l ) ( O - / ( 0 ) ) + T7c/(6>) }-Ii2 82lx
6 } x { (1 - 0 . 6 / e ) ( Q - l ) -
u 7
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f/fdd
5F ioT Q + 1 + rj;(*2 + y2 - 1 )
' 2
(1)
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(3)
(4)
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- 2 -
JAERI-Data/Code 97-032
3. KBSHOOT
3. 1 U-KttW
KBSHOOT T'
i>tx\ is*—( 1 )
FUNCTION Y
FUNCTION Y2
FUNCTION BESJO
SUBROUTINE ZROOT
, ^ | = 0 at 0 = 0 £ «t Tfdo
<j)(d),
5$ ( 1 )
Bessel Hl
ft)^ (Root Finder)
3 - v^z& y-^ANALYZER [8 ]
KBSHOOT <7) '7
3. 2
t
IU2 HDO 10*3
t2 E ^ ~ •/<D
XI2, JO,
- 3 -
JAERI-Data/Code 97-032
AIO> AIK AI2, (M 2f^ AKK A l l , AI2
T200 i -1=51, 100> 1=101,150, 1=151,
=l, 50>
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(2)
PROCESSORS^MAINfc R
(D^SPREADo - t U i ©(7)END SPREAD
®<DEND J
SUM(AIO),SUM(AI1),SUM(AI2)
(D^>SUBPR0CESS0RS(iMlJ7°n
NN
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JAERI-Data/Code 97-032
(3), 7 7
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- 5 -
JAERI-Data/Code 97-032
4 .
[1] J.W. Connor, R.J. Hastie, and J.B. Taylor, Phys. Rev. Lett. 40, 396 (1978).
[2] L.E. Zakharov, in Plasma Physics and Controlled Nuclear Fusion Research 1978 (IAEA,
Vienna, 1979), Vol. 1, p. 689.
[3] C.Z. Cheng, Phys. Fluids 25, 1020 (1982); Nucl. Fusion 22, 773 (1982).
[4] A. Hirose, L. Zhang, and M. Elia, Phys. Rev. Lett. 72, 3993 (1994); Phys. Plasmas 2,
859 (1995).
[5] A. Hirose and M. Elia, Phys. Rev. Lett. 76, 628 (1996).
[6] Z. Chang etaL, Phys. Rev. Lett. 76, 1071 (1996).
[7] M. Yamagiwa, A. Hirose, and M. Elia, Plasma Phys. Control. Fusion 39, 531 (1997).
[8] UXP/M 7t7^f •? teffl#31#, g±ii*fe$;&tt, 1992^2/?.[9] UXP/M VPP FORTRAN77EX/VPP 1 £ f f l ^ I#V12 ffl, 1994^1 R.
- 6 -
OO
ex-count270000
270000270000270000270000270000270000270000
270000270000270000270000270000270000270000270000
270000540000005400000054000000
54000000.2160E11.2160E11
.2160E11
.4634E10
true v-cost1350000
13770000137700001377000081000010800001458000019440000
270000270000810000810000810000810000810000810000
540000.2700E0954000000.2970E10
.1080E09
.2374E10
.5934E09
21.5 .1780E10
.9267E10
s-cost1350000
1377000013770000137700008100001080000
1458000019440000
270000270000810000810000810000810000810000810000
540000.2700E0954000000.2970E10
.1080E09
.8640E11
.2160E11
.6480E11
.9267E10
SMSS
VVV
V
COMPLEX FUNCTION Y2(T,Y,P,W)COMPLEX Y,P,W,AINTEG,AI0,AIl,AI2,UeT,UINTEGREAL PI, T,JO, DXI.DXJCOMMON/COMMOl/ HH.MAX, EP.ETA.BO, N, S,A,AKPARA2,Q,
& E, TAU, ETAe, ETAi, IFLUIDe
PI = 4.*ATAN(1.)SI = SIN(T)CO = COS(T)ZETA = S*T-A*SIF = 2.*EP*(C0+ZETA*SI)ARG = SQRT(B0*(l.+ZETA**2))DELTA=SQRT(AKPARA2*2./BO)*EP/Q
C
DXI = 0.025DXJ = 0.025AINTEG = CMPLX(O.)AIO=CMPLX(O.)AI1=CMPLX(O.)AI2=CMPLX(0. )UINTEG = CMPLX(O. )UeT=CMPLX(O.)
Cvocl loop.noeval,nopreexDO 10 1=1,200
XI = FLOAT(I-1)*DXI +.5*DXIXI2 = XI*XI —, <j= ®JO = BESJO( SQRT(2.)*ARG*XI ) —J
Cvocl 1oop,noeval,nopreexDO 20 J=-200,199
XJ = FLOAT(J)*DXJ +.5*DXJXJ2 = XJ*XJ
IF( (XI2+XJ2) .GT. 25.0 ) GO TO 20
>IIo
oSL
IoOO
2 The Original Subroutine Y2
ICO
I
.1697E11
.1697E11
.1697E11
.1697E11
.2160E1154000000270000270000270000
270000
0
0
0
0
000000
0
0
0
.7877E11
.7458E10
.1072E11
.1072E11
.1780E10
.1620E09299700002997000029970000
0.0 540000
0 0
0
0
0
000000
0 0
0
0
.2867E13
.2715E12
.3902E12
.3902E12
.6480E11
.1620E09299700002997000029970000
540000
0
0
0
0
000000
0
0
0
V
VVVVV
VVVVVV
V
V
c
t
c1/
r-L
r
r
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c
&&
2010
&
&
AINTEG = ( W*TAU+1.+ETA1*( XI2+XJ2-1.5 ) )/ ( W*TAU+F*( XI2/2.+ XJ2 )-DELTA*XJ ) * J0**2* EXP(- XI2 - XJ2) * XI
AI0=AI0+AINTEG*DXI*DXJ —,AI1=AI1+AINTEG*DXI*DXJ*XJ <j= ©AI2=AI2+AINTEG*DXI*DXJ*XJ2 —•
CONTINUECONTINUEAI0=2.*AI0/SQRT(PI)AI1=2.*AI1/SQRT(PI)AI2=2.*AI2/SQRT(PI)
IF( E .GT. 0.0 ) THEN
IF(IFLUIDe.EQ.l) THEN
UeT=((W-7.0/3.0*F/2.)*(W-1.0)-ETAe*F/2.)/((W-5.0/3.0*F/2. )**2-10.0/9.0*(F/2. )**2)
UeT=SQRT(E)*UeT
ELSE
DO 11 1=1,200XI = FLOAT(I-1)*DXI + 0.5*DXIXI2 = XI*XI
DO 21 J=l,200XJ = FLOAT(J-1)*DXJ + 0.5*DXJXJ2 = XJ*XJ
IF( ( (XI2+XJ2) .GT. 25.0 ) .OR.( XI2 .LT. (XJ2*(1.0-E)/(2.0*E)) ) ) GO TO 21
UINTEG = ( W-1.0-ETAe*( XI2+XJ2-1.5 ) )
>WSTa
a.
C3IjON3
2 The Original Subroutine Y2 (continued)
o
I
0
000
0
270000
270000
270000270000
0
000
0
0
.1094E09
0540000
0 V
0 V0 V0
0
0
.1094E09
0540000
pu.
PL
r
CCCMYCMYCMYCMYr
L
c
nL
&&
2111
&&&&&&
/ ( W-F*( XI2/2. + XJ2 ) )* EXP(- XI2 - XJ2) * XI
UeT = UeT+UINTEG*DXI*DXJ
CONTINUECONTINUEUeT = 4.*UeT/SQRT(PI)
ENDIF
WRITE(6,*) UeTWRITE(6,*) HH)MAX)EP,ETA,B0,N,S,A,AKPARA2,QWRITE(6,*) E,TAU,ETAe,ETAi,IFLUIDeSTOP
ENDIF
Y2 = -2.*ZETA*(S-A*CO)/(1.+ZETA**2) * P+ A/(4.*(ETA+1.)*EP*(1.+ZETA**2))* ( ( (1.0-sqrt(E))*(W-1.0) - AI1*DELTA )* ( (1.0-0.6*sqrt(E))*(W-1.0) - AI1*DELTA )/ ( 1.0 + TAU - TAU*AI0 - UeT )- (1.0-0.6*sqrt(E))*( (W-F)*(W-1.0) + ETAe*F )+ AI2*DELTA**2/TAU ) * Y
RETURNEND
OP
9a.to
-J
IoCOto
'2 The Original Subroutine Y2 (continued)
2010
DO 10 1=1,200XI = FLOAT(I-1)*DXI +.5*DXIXI2 = XI*XIJO = BESJO( SQRT(2.)*ARG*XI )
DO 20 J=-200,199
AIO=AIO+AINTEG*DXI*DXJAI1=AI1+AINTEG*DXI*DXJ*XJAI2=AI2+AINTEG*DXI*DXJ*XJ2
CONTINUECONTINUE
C©2
1PE 2PE
2010
DO 10 1=1,50 O50 =~710AT.XI2 = XI*XIJO = BESJO
DO 20 J=-200,199
AI0=AI0+AINTEG*.AI1=AI1+AINTEG*.AI2=AI2+AINTEG*.
CONTINUECONTINUE
2010
DO 10 1=51,100 <XI = FLOAT.XI2 = XI*XIJO = BESJO.
DO 20 J=-200,199
AIO=AIO+AINTEG*.AI1=AI1+AINTEG*.AI2=AI2+AINTEG*.
CONTINUECONTINUE
3PE
2010
DO 10 1=101,150XI = FLOAT.XI2 = XI*XIJO = BESJO.
DO 20 J=-200,199
AIO=AIO+AINTEG*.AI1=AI1+AINTEG*.AI2=AI2+AINTEG*.
CONTINUECONTINUE
4PE
2010
DO 10 1=151,200XI = FLOAT.XI2 = XI*XIJO = BESJO
DO 20 J=-200,199
AI0=AI0+AINTEG*.AI1=AI1+AINTEG*AI2=AI2+AINTEG*
CONTINUECONTINUE
2To
otoN3
3 The Image of Parallel Processing
JAERI-Data/Code 97-032
•INCLUDE PARM!XOCL PROCESSOR PP(NN)
COMPLEX W,0COMPLEX FAICOMPLEX Y
CCOUNT = 0
!XOCL PARALLEL REGION <J=> ©Ih (VAR.GE.0.0) THEN
10 CONTINUEBO = VARA2 = A * AS2 = S * SETA = ( TAU*ETAe + ETAi ) / ( TAU + 1.0 )AKPARA2 = 1 . 0 / 3 . 0
& * ( 1.0 + S2*(PI2/3.0-0.5)& - 8.0*A*S/3.0 + 3.0*A2/4.0 )& / ( 1.0 + S2/3.0*(PI2-7.5)& - 10.0*A*S/9.0 + 5.0*A2/12.0 )
AKPARA2 = AKPARA2 * PARAKFC
CALL ZROOT(Y,EPS(NSIG,PRTB,W,ITMAX)INFER,IER)C08/03/96 0 = W*SQRT(B0*A/(4.*EP*(l.+ETA)))
0 = W*SQRT(B0*A/(2.*(l.+TAU)/TAU**2*EP*(l.+ETA)))C
COUNT = COUNT + 1WRITE(6,99) VAR,W,O,INFER,INSERT(COUNT)
C WRITE(2,92) VAR,W,O,INFER,INSERT(COUNT)C
IF ((AIMAG(W).LT.O.0).OR.(VAR.LT.VARMIN)) GOTO 100C
VAR = VAR + INCLUDEC
GOTO 10ENDIF
C100 CONTINUE!XOCL END PARALLEL <=> (3)C
WRITE(6,93)IT = 0
DO T = 0., MAX, HHIT = IT + 1IF( M0D(IT,25) .EQ. 1 ) WRITE(6,94) THETA(IT),FAI(IT)
END DO
STOP91 FORMAT(1X,F7.4,2X,2(1X,F9.4),2X,2(1X,F9.4),3X,I3,3X,A)92 FORMAT( F7.4,2X,2(1X,F9.4),2X,2(1X,F9.4),3X)I3.3X.A)93 FORMAT{//,' THETA1,1 ', r REAL FAI1,'
& ' IMAG FAI1)94 F0RMAT(F7.4,' ', F9.4,1 ', F9.4)99 FORMAT(F7.4,' ', 4(F9.4,' ' ) , 13,' ', A)
END
[4 The Parallel Version of MAIN routine
- 1 2 -
JAERI-Data/Code 97-032
COMPLEX FUNCTION Y2(T,Y,P,W)•INCLUDE PARM!XOCL PROCESSOR PP(NN) <= Q!XOCL SUBPROCLSSOR QQ(NN) <=• (2)
COMPLEX Y,P,W,AINTEG,AIO,All,AI2,UeT,UINTEGREAL PI, T.JO, DXI.DXJCOMMON/COMM01/ HH.MAX, EP.ETA.BO, N, S,A,AKPARA2,Q,
& E, TAU, ETAe, ETAi, IFLUIDeC
PI = 4.*ATAN(1.)SI = SIN(T)CO = COS(T)ZETA = S*T-A*SIF = 2.*EP*(C0+ZETA*SI)ARG = SQRT(BO*(1.+ZETA**2))DELTA=SQRT(AKPARA2*2./BO)*EP/Q
CDXI = 0.025DXJ = 0.025AINTEG = CMPLX(O.)AIO=CMPLX(O.)AI1=CMPLX(O.)AI2=CMPLX(0.)UINTEG = CMPLX(O.)UeT=CMPLX(O.)
CCvocl loop.noeval.nopreex!XOCL SPREAD DO/(QQ) C= ©
DO 10 1=1,200XI = FLOAT(I-1)*DXI +.5*DXIXI2 = XI*XIJO = BESJO( SQRT(2.)*ARG*XI )
Cvocl loop.noeval.nopreexDO 20 J=-200,199
XJ = FLOAT(J)*DXJ +.5*DXJXJ2 = XJ*XJ
c
IF( (XI2+XJ2) .GT. 25.0 ) GO TO 20c
AINTEG = ( W*TAU+l.+ETAi*( XI2+XJ2-1.5 ) )& I ( W*TAU+F*( XI2/2.+ XJ2 )-DELTA*XJ ) * J0**2& * EXP(- XI2 - XJ2) * XI
AIO=AIO+AINTEG*DXI*DXJAI1=AI1+AINTEG*DXI*DXJ*XJAI2=AI2+AINTEG*DXI*DXJ*XJ2
20 CONTINUE10 CONTINUE
!XOCL END SPREAD SUM(AIO),SUM(AI1),SUM(AI2) O ©AIO=2.*A1O/SORI(P1)AI1=2.*AI1/SQRT(PI)AI2=2.*AI2/SQRT(PI)
IF( E .GT. 0.0 ) THENCc
IF(IFLUIDe. EQ.l) THENc
UeT=((W-7.0/3.0*F/2.)*(W-1.0)-ETAe*F/2.)
5 The Parallel Version of Subroutine Y2
- 1 3 -
JAERI-Data/Code 97-032
& /((W-5.O/3.O*F/2. )**2-10.0/9.0*(F/2.)**2)UeT=SQRT(E)*UeT
CELSE
C!XOCL SPREAD DO/(QQ) <= (5)
UU 11 1=1,200XI = FLOAT(I-1)*DXI + 0.5*DXIXI2 = XI*XI
DO 21 J=l,200XJ = FLOAT(J-1)*DXJ + 0.5*DXJXJ2 = XJ*XJ
CIF( ( (XI2+XJ2) .GT. 25.0 ) .OR.
& ( XI2 .LT. (XJ2*(1.0-E)/(2.0*E)) ) ) GO TO 21C
UINTEG = ( W-1.0-ETAe*( XI2+XJ2-1.5 ) )& / ( W-F*( XI2/2. + XJ2 ) )& * EXP(- XI2 - XJ2) * XI
CUeT = UeT+UINTEG*DXI*DXJ
C21 CONTINUE11 CONTINUE
!XOCL END SPREAD SUM(UeT) o ©UeT = 4.*UeT/SQRT(PI)
CENDIF
CCCMY WRITE(6,*) UeTCMY WRITE(6,*) HH.MAX.EP.ETA.BO.N.S.A.AKPARAZ.QCMY WRITE(6,*) EJAU.ETAe.ETAi, IFLUIDeCMY STOPC
ENDIF
Y2 = -2.*ZETA*(S-A*CO)/(1.+ZETA**2) * P& + A/(4.*(ETA+1.)*EP*(1.+ZETA**2))& * ( ( (1.0-sqrt(E))*(W-1.0) - AI1*DELTA )& * ( (1.0-0.6*sqrt(E))*(W-1.0) - AI1*DELTA )& / ( 1.0 + TAU - TAU*AI0 - UeT )& - (1.0-0.6*sqrt(E))*( (W-F)*(W-1.0) + ETAe*F& + AI2*DELTA**2/TAU ) * Y
RETURNEND
15 The Parallel Version of Subroutine Y2 (continued)
- 1 4 -
vectorize
nameY2BESJOYMAINZROOTTAGGER(total)
- total 1
ex-count270000
5400000027121
H I Dynamic Behavior of
•jet _1ST
v-cost.1273E12.2053E1111745837
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m
1 Pa-s(N-s/m !)=10P(# r X) (g / ( c m -s ) )
lm2 /s=104St(x v-9 x ) (cm 2 / s )
E
n
MPa( = 10bar)
1
0.0980665
0.101325
1.33322 x 10"*
6.89476 x 10'3
kgf /cm *
10.1972
1
1.03323
1.35951 x 10'3
7.03070 x 10" *
a t m
9.86923
0.967841
1
1.31579 x 10-3
6.80460 x 10-'
mmHg(Torr)
7.50062 x 103
735.559
760
1
51.7149
Ibf/in2(psi)
145.038
14.2233
14.6959
1.93368x10-'
1
X
1
fi:*
ft
J( = 10'erg)
1
9.80665
3.6x10'
4.18605
1055.06
1.35582
1.60218 x 1 0 "
kgf-m
0.101972
1
3.67098 x 10s
0.426858
107.586
0.138255
1.63377 x 1<T!O
k W - h
2.77778x10"
2.72407 x 10-'
1
1.16279 x 10-'
2.93072x10"'
3.76616x10-'
4.45050x10'"
cald+ftft)
0.238889
2.34270
8.59999 x 10 s
1
252.042
0.323890
3.82743 xlO"'0
Btu
9.47813 x 10"'
9.29487 x 10-3
3412.13
3.96759 x 10"3
1
1.28506 xlO"3
1.51857x10""
ft • lbf
0.737562
7.23301
2.65522 x 10'
3.08747
778.172
1
1.18171 x lO""
eV
6.24150x10"
6.12082 x 10"
2.24694 x 10"
2.61272x10"
6.58515x10"
8.46233x10"
1
Bq
3.7 x 10"
Ci
2.70270 x 10"
1
8
Gy
1
0.01
rad
100
1
C/kg
1
2.58 x 10"
3876
1
1 cal = 4.18605
= 4.184 J (.Ml?-)
= 4.1855 J (15 *C)
= 4.1
1 PS
= 75 kgf-m/s
= 735.499 W
Sv
1
0.01
100
1
26BSS)
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