kbshootcdfjijib - qst.go.jp · it- hi, (t319-11 (t319-11 *5 f) t to this report is issued...

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**


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

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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


K (KBM) J

K KBSHOOT O

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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 )

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(1)

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(3)

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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 -


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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>;i/-^>MAIN£E14 tc ©PROCESSOR^V$£m

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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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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 -


MATN TAGGER

ZROOT

Y - BESJO

1 The Tree Structure of KBSHOOT code

7 -

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

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s-cost1350000

1377000013770000137700008100001080000

1458000019440000

270000270000810000810000810000810000810000810000

540000.2700E0954000000.2970E10

.1080E09

.8640E11

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.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

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270000

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0

0

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0.0 540000

0 0

0

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0

000000

0 0

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0

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540000

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V

VVVVV

VVVVVV

V

V

c

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&&

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

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0

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&&

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


•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 -


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 -


& /((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)

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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)

kbshootcdfjijib - qst.go.jp · it- hi, (t319-11 (t319-11 *5 f) t to this report is issued...

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