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|
*DECK PN3DXX
SUBROUTINE PN3DXX(NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,
1 SIGT,SIGTI,MAT,VOL,XX,YY,ZZ,KN,QFR,MUX,IPBBX,LC,R,V,BBX,TTF,
2 AX,C11X)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of system matrices for a Thomas-Raviart (dual) finite element
* method in 3-D simplified PN approximation. Note: system matrices
* should be initialized by the calling program.
*
*Copyright:
* Copyright (C) 2005 Ecole Polytechnique de Montreal
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version
*
*Author(s): A. Hebert
*
*Parameters: input
* NBMIX number of mixtures.
* IELEM degree of the Lagrangian finite elements: =1 (linear);
* =2 (parabolic); =3 (cubic).
* ICOL type of quadrature: =1 (analytical integration);
* =2 (Gauss-Lobatto); =3 (Gauss-Legendre).
* NEL total number of finite elements.
* NLF number of Legendre orders for the flux (even number).
* NVD type of void boundary condition if NLF>0 and ICOL=3.
* NAN number of Legendre orders for the cross sections.
* LL4F number of flux components.
* LL4X number of X-directed currents.
* LL4Y number of Y-directed currents.
* LL4Z number of Z-directed currents.
* SIGT total minus self-scattering macroscopic cross sections.
* SIGT(:,NAN) generally contains the total cross section only.
* SIGTI inverse macroscopic cross sections ordered by mixture.
* SIGTI(:,NAN) generally contains the inverse total cross
* section only.
* MAT mixture index assigned to each element.
* VOL volume of each element.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* ZZ Z-directed mesh spacings.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* MUX X-directed compressed storage mode indices.
* MUY Y-directed compressed storage mode indices.
* MUZ Z-directed compressed storage mode indices.
* IPBBX X-directed perdue storage indices.
* IPBBY Y-directed perdue storage indices.
* IPBBZ Z-directed perdue storage indices.
* LC order of the unit matrices.
* R unit matrix.
* V unit matrix.
* BBX X-directed flux-current matrices.
* BBY Y-directed flux-current matrices.
* BBZ Z-directed flux-current matrices.
*
*Parameters: output
* TTF flux-flux matrices.
* AX X-directed main current-current matrices. Dimensionned to
* MUX(LL4X)*NLF/2.
* AY Y-directed main current-current matrices. Dimensionned to
* MUY(LL4Y)*NLF/2.
* AZ Z-directed main current-current matrices. Dimensionned to
* MUZ(LL4Z)*NLF/2.
* C11X X-directed main current-current matrices to be factorized.
* Dimensionned to MUX(LL4X)*NLF/2.
* C11Y Y-directed main current-current matrices to be factorized.
* Dimensionned to MUY(LL4Y)*NLF/2.
* C11Z Z-directed main current-current matrices to be factorized.
* Dimensionned to MUZ(LL4Z)*NLF/2.
*
*Reference(s):
* J.J. Lautard, D. Schneider, A.M. Baudron, "Mixed Dual Methods for
* Neutronic Reactor Core Calculations in the CRONOS System," Proc.
* Int. Conf. on Mathematics and Computation, Reactor Physics and
* Environmental Analysis in Nuclear Applications, Madrid, Spain,
* September 27-30, 1999.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,MAT(NEL),
1 KN(NEL*(1+6*IELEM**2)),MUX(LL4X),IPBBX(2*IELEM,LL4X),LC
REAL SIGT(NBMIX,NAN),SIGTI(NBMIX,NAN),VOL(NEL),XX(NEL),YY(NEL),
1 ZZ(NEL),QFR(6*NEL),R(LC,LC),V(LC,LC-1),BBX(2*IELEM,LL4X),
2 TTF(LL4F*NLF/2),AX(*),C11X(*)
*----
* LOCAL VARIABLES
*----
REAL QQ(5,5)
*----
* X-ORIENTED COUPLINGS
*----
ZMARS=0.0
IF(ICOL.EQ.3) THEN
IF(NVD.EQ.0) THEN
NZMAR=NLF+1
ELSE IF(NVD.EQ.1) THEN
NZMAR=NLF
ELSE IF(NVD.EQ.2) THEN
NZMAR=65
ENDIF
ELSE
NZMAR=65
ENDIF
DO 25 I0=1,IELEM
DO 20 J0=1,IELEM
FFF=0.0
DO 10 K0=2,IELEM
FFF=FFF+V(K0,I0)*V(K0,J0)/R(K0,K0)
10 CONTINUE
IF(ABS(FFF).LE.1.0E-6) FFF=0.0
QQ(I0,J0)=FFF
20 CONTINUE
25 CONTINUE
MUMAX=MUX(LL4X)
DO 170 IL=0,NLF-1
IF(MOD(IL,2).EQ.1) ZMARS=PNMAR2(NZMAR,IL,IL)
FACT=REAL(2*IL+1)
*----
* ASSEMBLY OF THE X-ORIENTED COEFFICIENT MATRICES AT ORDER IL.
*----
NUM1=0
NUM2=0
DO 120 IE=1,NEL
IBM=MAT(IE)
IF(IBM.EQ.0) GO TO 120
VOL0=VOL(IE)
IF(VOL0.EQ.0.0) GO TO 110
DX=XX(IE)
DY=YY(IE)
DZ=ZZ(IE)
GARS=SIGT(IBM,MIN(IL+1,NAN))
IF(MOD(IL,2).EQ.0) THEN
* EVEN PARITY EQUATION.
DO 32 K3=0,IELEM-1
DO 31 K2=0,IELEM-1
DO 30 K1=0,IELEM-1
KEY=(IL/2)*LL4F+KN(NUM1+1)+(K3*IELEM+K2)*IELEM+K1
TTF(KEY)=TTF(KEY)+FACT*VOL0*GARS
30 CONTINUE
31 CONTINUE
32 CONTINUE
ELSE
GARSI=SIGTI(IBM,MIN(IL+1,NAN))
DO 105 K3=0,IELEM-1
DO 100 K2=0,IELEM-1
* PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION OF
* THE EVEN PARITY EQUATION.
DO 40 K1=0,IELEM-1
JND1=KN(NUM1+1)+(K3*IELEM+K2)*IELEM+K1
KEY=((IL-1)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL)**2)*VOL0*QQ(K1+1,K1+1)*GARSI/(FACT*
1 DX*DX)
IF(IL.LE.NLF-3) THEN
KEY=((IL+2)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL+1)**2)*VOL0*QQ(K1+1,K1+1)*GARSI/
1 (FACT*DX*DX)
ENDIF
KEY=((IL-1)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL)**2)*VOL0*QQ(K2+1,K2+1)*GARSI/
1 (FACT*DY*DY)
IF(IL.LE.NLF-3) THEN
KEY=((IL+2)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL+1)**2)*VOL0*QQ(K2+1,K2+1)*GARSI/
1 (FACT*DY*DY)
ENDIF
KEY=((IL-1)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL)**2)*VOL0*QQ(K3+1,K3+1)*GARSI/
1 (FACT*DZ*DZ)
IF(IL.LE.NLF-3) THEN
KEY=((IL+2)/2)*LL4F+JND1
TTF(KEY)=TTF(KEY)+(REAL(IL+1)**2)*VOL0*QQ(K3+1,K3+1)*GARSI/
1 (FACT*DZ*DZ)
ENDIF
40 CONTINUE
*
* ODD PARITY EQUATION.
DO 55 IC=1,2
IF(IC.EQ.1) IIC=1
IF(IC.EQ.2) IIC=IELEM+1
KN1=KN(NUM1+2+(IC-1)*IELEM**2+K3*IELEM+K2)
IND1=ABS(KN1)-LL4F
S1=REAL(SIGN(1,KN1))
DO 50 JC=1,2
IF(JC.EQ.1) JJC=1
IF(JC.EQ.2) JJC=IELEM+1
KN2=KN(NUM1+2+(JC-1)*IELEM**2+K3*IELEM+K2)
IND2=ABS(KN2)-LL4F
IF((KN1.NE.0).AND.(KN2.NE.0).AND.(IND1.GE.IND2)) THEN
S2=REAL(SIGN(1,KN2))
KEY=((IL-1)/2)*MUMAX+MUX(IND1)-IND1+IND2
AX(KEY)=AX(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
ENDIF
50 CONTINUE
55 CONTINUE
*
KN1=KN(NUM1+2+K3*IELEM+K2)
KN2=KN(NUM1+2+IELEM**2+K3*IELEM+K2)
IND1=ABS(KN1)-LL4F
IND2=ABS(KN2)-LL4F
IF((QFR(NUM2+1).NE.0.0).AND.(KN1.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUX(IND1)
AX(KEY)=AX(KEY)-0.5*FACT*QFR(NUM2+1)*ZMARS
ENDIF
IF((QFR(NUM2+2).NE.0.0).AND.(KN2.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUX(IND2)
AX(KEY)=AX(KEY)-0.5*FACT*QFR(NUM2+2)*ZMARS
ENDIF
100 CONTINUE
105 CONTINUE
ENDIF
110 NUM1=NUM1+1+6*IELEM**2
NUM2=NUM2+6
120 CONTINUE
*
IF(MOD(IL,2).EQ.1) THEN
DO 130 I0=1,MUMAX
C11X(((IL-1)/2)*MUMAX+I0)=-AX(((IL-1)/2)*MUMAX+I0)
130 CONTINUE
MUIM1=0
DO 160 I=1,LL4X
MUI=MUX(I)
DO 150 J=I-(MUI-MUIM1)+1,I
KEY=((IL-1)/2)*MUMAX+(MUI-I+J)
DO 145 I0=1,2*IELEM
II=IPBBX(I0,I)
IF(II.EQ.0) GO TO 150
DO 140 J0=1,2*IELEM
JJ=IPBBX(J0,J)
IF(II.EQ.JJ) C11X(KEY)=C11X(KEY)+REAL(IL**2)*BBX(I0,I)*
1 BBX(J0,J)/TTF(((IL-1)/2)*LL4F+II)
140 CONTINUE
145 CONTINUE
150 CONTINUE
MUIM1=MUI
160 CONTINUE
ENDIF
170 CONTINUE
RETURN
END
*
SUBROUTINE PN3DXY(NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,LL4Y,
1 SIGT,MAT,VOL,YY,KN,QFR,MUY,IPBBY,LC,R,BBY,TTF,AY,C11Y)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,LL4Y,MAT(NEL),
1 KN(NEL*(1+6*IELEM**2)),MUY(LL4Y),IPBBY(2*IELEM,LL4Y),LC
REAL SIGT(NBMIX,NAN),VOL(NEL),YY(NEL),QFR(6*NEL),R(LC,LC),
1 BBY(2*IELEM,LL4Y),TTF(LL4F*NLF/2),AY(*),C11Y(*)
*----
* Y-ORIENTED COUPLINGS
*----
ZMARS=0.0
IF(ICOL.EQ.3) THEN
IF(NVD.EQ.0) THEN
NZMAR=NLF+1
ELSE IF(NVD.EQ.1) THEN
NZMAR=NLF
ELSE IF(NVD.EQ.2) THEN
NZMAR=65
ENDIF
ELSE
NZMAR=65
ENDIF
MUMAX=MUY(LL4Y)
DO 320 IL=1,NLF-1,2
ZMARS=PNMAR2(NZMAR,IL,IL)
FACT=REAL(2*IL+1)
*----
* ASSEMBLY OF THE Y-ORIENTED COEFFICIENT MATRICES AT ODD ORDER IL.
*----
NUM1=0
NUM2=0
DO 270 IE=1,NEL
IBM=MAT(IE)
IF(IBM.EQ.0) GO TO 270
VOL0=VOL(IE)
IF(VOL0.EQ.0.0) GO TO 260
DY=YY(IE)
GARS=SIGT(IBM,MIN(IL+1,NAN))
*
DO 255 K3=0,IELEM-1
DO 250 K1=0,IELEM-1
DO 205 IC=3,4
IF(IC.EQ.3) IIC=1
IF(IC.EQ.4) IIC=IELEM+1
KN1=KN(NUM1+2+(IC-1)*IELEM**2+K3*IELEM+K1)
IND1=ABS(KN1)-LL4F-LL4X
S1=REAL(SIGN(1,KN1))
DO 200 JC=3,4
IF(JC.EQ.3) JJC=1
IF(JC.EQ.4) JJC=IELEM+1
KN2=KN(NUM1+2+(JC-1)*IELEM**2+K3*IELEM+K1)
IND2=ABS(KN2)-LL4F-LL4X
IF((KN1.NE.0).AND.(KN2.NE.0).AND.(IND1.GE.IND2)) THEN
S2=REAL(SIGN(1,KN2))
KEY=((IL-1)/2)*MUMAX+MUY(IND1)-IND1+IND2
AY(KEY)=AY(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
ENDIF
200 CONTINUE
205 CONTINUE
*
KN1=KN(NUM1+2+2*IELEM**2+K3*IELEM+K1)
KN2=KN(NUM1+2+3*IELEM**2+K3*IELEM+K1)
IND1=ABS(KN1)-LL4F-LL4X
IND2=ABS(KN2)-LL4F-LL4X
IF((QFR(NUM2+3).NE.0.0).AND.(KN1.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUY(IND1)
AY(KEY)=AY(KEY)-0.5*FACT*QFR(NUM2+3)*ZMARS
ENDIF
IF((QFR(NUM2+4).NE.0.0).AND.(KN2.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUY(IND2)
AY(KEY)=AY(KEY)-0.5*FACT*QFR(NUM2+4)*ZMARS
ENDIF
250 CONTINUE
255 CONTINUE
260 NUM1=NUM1+1+6*IELEM**2
NUM2=NUM2+6
270 CONTINUE
*
DO 280 I0=1,MUMAX
C11Y(((IL-1)/2)*MUMAX+I0)=-AY(((IL-1)/2)*MUMAX+I0)
280 CONTINUE
MUIM1=0
DO 310 I=1,LL4Y
MUI=MUY(I)
DO 300 J=I-(MUI-MUIM1)+1,I
KEY=((IL-1)/2)*MUMAX+(MUI-I+J)
DO 295 I0=1,2*IELEM
II=IPBBY(I0,I)
IF(II.EQ.0) GO TO 300
DO 290 J0=1,2*IELEM
JJ=IPBBY(J0,J)
IF(II.EQ.JJ) C11Y(KEY)=C11Y(KEY)+REAL(IL**2)*BBY(I0,I)*BBY(J0,J)/
1 TTF(((IL-1)/2)*LL4F+II)
290 CONTINUE
295 CONTINUE
300 CONTINUE
MUIM1=MUI
310 CONTINUE
320 CONTINUE
RETURN
END
*
SUBROUTINE PN3DXZ(NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,LL4Y,
1 LL4Z,SIGT,MAT,VOL,ZZ,KN,QFR,MUZ,IPBBZ,LC,R,BBZ,TTF,AZ,C11Z)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,IELEM,ICOL,NEL,NLF,NVD,NAN,LL4F,LL4X,LL4Y,LL4Z,
1 MAT(NEL),KN(NEL*(1+6*IELEM**2)),MUZ(LL4Z),IPBBZ(2*IELEM,LL4Z),LC
REAL SIGT(NBMIX,NAN),VOL(NEL),ZZ(NEL),QFR(6*NEL),R(LC,LC),
1 BBZ(2*IELEM,LL4Z),TTF(LL4F*NLF/2),AZ(*),C11Z(*)
*----
* Z-ORIENTED COUPLINGS
*----
ZMARS=0.0
IF(ICOL.EQ.3) THEN
IF(NVD.EQ.0) THEN
NZMAR=NLF+1
ELSE IF(NVD.EQ.1) THEN
NZMAR=NLF
ELSE IF(NVD.EQ.2) THEN
NZMAR=65
ENDIF
ELSE
NZMAR=65
ENDIF
MUMAX=MUZ(LL4Z)
DO 470 IL=1,NLF-1,2
ZMARS=PNMAR2(NZMAR,IL,IL)
FACT=REAL(2*IL+1)
*----
* ASSEMBLY OF THE Z-ORIENTED COEFFICIENT MATRICES AT ORDER IL.
*----
NUM1=0
NUM2=0
DO 420 IE=1,NEL
IBM=MAT(IE)
IF(IBM.EQ.0) GO TO 420
VOL0=VOL(IE)
IF(VOL0.EQ.0.0) GO TO 410
DZ=ZZ(IE)
GARS=SIGT(IBM,MIN(IL+1,NAN))
*
DO 405 K2=0,IELEM-1
DO 400 K1=0,IELEM-1
DO 355 IC=5,6
IF(IC.EQ.5) IIC=1
IF(IC.EQ.6) IIC=IELEM+1
KN1=KN(NUM1+2+(IC-1)*IELEM**2+K2*IELEM+K1)
IND1=ABS(KN1)-LL4F-LL4X-LL4Y
S1=REAL(SIGN(1,KN1))
DO 350 JC=5,6
IF(JC.EQ.5) JJC=1
IF(JC.EQ.6) JJC=IELEM+1
KN2=KN(NUM1+2+(JC-1)*IELEM**2+K2*IELEM+K1)
IND2=ABS(KN2)-LL4F-LL4X-LL4Y
IF((KN1.NE.0).AND.(KN2.NE.0).AND.(IND1.GE.IND2)) THEN
S2=REAL(SIGN(1,KN2))
KEY=((IL-1)/2)*MUMAX+MUZ(IND1)-IND1+IND2
AZ(KEY)=AZ(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
ENDIF
350 CONTINUE
355 CONTINUE
*
KN1=KN(NUM1+2+4*IELEM**2+K2*IELEM+K1)
KN2=KN(NUM1+2+5*IELEM**2+K2*IELEM+K1)
IND1=ABS(KN1)-LL4F-LL4X-LL4Y
IND2=ABS(KN2)-LL4F-LL4X-LL4Y
IF((QFR(NUM2+5).NE.0.0).AND.(KN1.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUZ(IND1)
AZ(KEY)=AZ(KEY)-0.5*FACT*QFR(NUM2+5)*ZMARS
ENDIF
IF((QFR(NUM2+6).NE.0.0).AND.(KN2.NE.0)) THEN
KEY=((IL-1)/2)*MUMAX+MUZ(IND2)
AZ(KEY)=AZ(KEY)-0.5*FACT*QFR(NUM2+6)*ZMARS
ENDIF
400 CONTINUE
405 CONTINUE
410 NUM1=NUM1+1+6*IELEM**2
NUM2=NUM2+6
420 CONTINUE
*
DO 430 I0=1,MUMAX
C11Z(((IL-1)/2)*MUMAX+I0)=-AZ(((IL-1)/2)*MUMAX+I0)
430 CONTINUE
MUIM1=0
DO 460 I=1,LL4Z
MUI=MUZ(I)
DO 450 J=I-(MUI-MUIM1)+1,I
KEY=((IL-1)/2)*MUMAX+(MUI-I+J)
DO 445 I0=1,2*IELEM
II=IPBBZ(I0,I)
IF(II.EQ.0) GO TO 450
DO 440 J0=1,2*IELEM
JJ=IPBBZ(J0,J)
IF(II.EQ.JJ) C11Z(KEY)=C11Z(KEY)+REAL(IL**2)*BBZ(I0,I)*BBZ(J0,J)/
1 TTF(((IL-1)/2)*LL4F+II)
440 CONTINUE
445 CONTINUE
450 CONTINUE
MUIM1=MUI
460 CONTINUE
470 CONTINUE
RETURN
END
|
