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*DECK TRIHWW
SUBROUTINE TRIHWW(NBMIX,NBLOS,IELEM,LL4F,LL4W,MAT,SIDE,ZZ,FRZ,
1 QFR,IPERT,KN,SGD,XSGD,MUW,IPBBW,LC,R,V,BBW,TTF,AW,C11W)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of system matrices for a Thomas-Raviart-Schneider (dual)
* finite element method in hexagonal 3-D diffusion approximation.
* Note: system matrices should be initialized by the calling program.
*
*Copyright:
* Copyright (C) 2006 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.
* NBLOS number of lozenges per direction, taking into account
* mesh-splitting.
* 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).
* ISPLH mesh-splitting index. Each hexagon is splitted into 3*ISPLH**2
* lozenges.
* LL4F number of flux components.
* LL4W number of W-directed currents.
* LL4X number of X-directed currents.
* LL4Y number of Y-directed currents.
* LL4Z number of Z-directed currents.
* MAT mixture index assigned to each element.
* SIDE side of an hexagon.
* ZZ Z-directed mesh spacings.
* FRZ volume fractions for the axial SYME boundary condition.
* QFR element-ordered boundary conditions.
* IPERT mixture permutation index.
* KN ADI permutation indices for the volumes and currents.
* SGD nuclear properties by material mixture:
* SGD(L,1)= X-oriented diffusion coefficients;
* SGD(L,2)= Y-oriented diffusion coefficients;
* SGD(L,3)= Z-oriented diffusion coefficients;
* SGD(L,4)= removal macroscopic cross section.
* XSGD one over nuclear properties.
* MUW W-directed compressed storage mode indices.
* MUX X-directed compressed storage mode indices.
* MUY Y-directed compressed storage mode indices.
* MUZ Z-directed compressed storage mode indices.
* IPBBW W-directed perdue storage 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.
* BBW W-directed flux-current matrices.
* BBX X-directed flux-current matrices.
* BBY Y-directed flux-current matrices.
* BBZ Z-directed flux-current matrices.
*
*Parameters: output
* TTF flux-flux matrices.
* AW W-directed main current-current matrices. Dimensionned to
* MUW(LL4W).
* AX X-directed main current-current matrices. Dimensionned to
* MUX(LL4X).
* AY Y-directed main current-current matrices. Dimensionned to
* MUY(LL4Y).
* AZ Z-directed main current-current matrices. Dimensionned to
* MUZ(LL4Z).
* C11W W-directed main current-current matrices to be factorized.
* Dimensionned to MUW(LL4W).
* C11X X-directed main current-current matrices to be factorized.
* Dimensionned to MUX(LL4X).
* C11Y Y-directed main current-current matrices to be factorized.
* Dimensionned to MUY(LL4Y).
* C11Z Z-directed main current-current matrices to be factorized.
* Dimensionned to MUZ(LL4Z).
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,NBLOS,IELEM,LL4F,LL4W,MAT(3,NBLOS),IPERT(NBLOS),
1 KN(NBLOS,3+6*(IELEM+2)*IELEM**2),MUW(LL4W),IPBBW(2*IELEM,LL4W),LC
REAL SIDE,ZZ(3,NBLOS),FRZ(NBLOS),QFR(NBLOS,8),SGD(NBMIX,4),
1 XSGD(NBMIX,4),R(LC,LC),V(LC,LC-1),TTF(LL4F),BBW(2*IELEM,LL4W),
2 AW(*),C11W(*)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION FFF,TTTT
REAL QQ(5,5)
*----
* W-ORIENTED COUPLINGS
*----
DO 25 I0=1,IELEM
DO 20 J0=1,IELEM
FFF=0.0D0
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=0.0D0
QQ(I0,J0)=REAL(FFF)
20 CONTINUE
25 CONTINUE
*
NELEH=(IELEM+1)*IELEM**2
IIMAW=MUW(LL4W)
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
NUM=0
DO 50 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 50
NUM=NUM+1
IBM=MAT(1,IPERT(KEL))
IF(IBM.EQ.0) GO TO 50
DZ=ZZ(1,IPERT(KEL))
VOL0=REAL(TTTT*DZ*FRZ(KEL))
DINV=XSGD(IBM,1)
SIG3=SGD(IBM,3)/(DZ*DZ)
SIG4=SGD(IBM,4)
DO 34 K5=0,1
DO 33 K4=0,IELEM-1
DO 32 K3=0,IELEM-1
DO 31 K2=1,IELEM+1
KNW1=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=ABS(KNW1)
DO 30 K1=1,IELEM+1
KNW2=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
INW2=ABS(KNW2)
IF((KNW2.NE.0).AND.(KNW1.NE.0)) THEN
L=MUW(INW1)-INW1+INW2
SG=REAL(SIGN(1,KNW1)*SIGN(1,KNW2))
IF(K1.LE.K2) AW(L)=AW(L)-(4./3.)*SG*VOL0*DINV*R(K2,K1)
IF(K1.EQ.K2) THEN
IF((K1.EQ.1).AND.(K5.EQ.0)) AW(L)=AW(L)-QFR(NUM,1)
IF((K1.EQ.IELEM+1).AND.(K5.EQ.1)) AW(L)=AW(L)-QFR(NUM,2)
ENDIF
ENDIF
30 CONTINUE
31 CONTINUE
32 CONTINUE
33 CONTINUE
34 CONTINUE
DO 42 K3=0,IELEM-1
DO 41 K2=0,IELEM-1
DO 40 K1=0,IELEM-1
JND1=(NUM-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
JND2=(KN(NUM,1)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
JND3=(KN(NUM,2)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
TTF(JND1)=TTF(JND1)+VOL0*SIG4+VOL0*QQ(K3+1,K3+1)*SIG3
TTF(JND2)=TTF(JND2)+VOL0*SIG4+VOL0*QQ(K3+1,K3+1)*SIG3
TTF(JND3)=TTF(JND3)+VOL0*SIG4+VOL0*QQ(K3+1,K3+1)*SIG3
40 CONTINUE
41 CONTINUE
42 CONTINUE
50 CONTINUE
*----
* COMPUTE THE W-ORIENTED SYSTEM MATRIX AFTER FLUX ELIMINATION
*----
DO 60 I0=1,IIMAW
C11W(I0)=-AW(I0)
60 CONTINUE
MUIM1=0
DO 90 I=1,LL4W
MUI=MUW(I)
DO 80 J=I-(MUI-MUIM1)+1,I
KEY=MUI-I+J
DO 75 I0=1,2*IELEM
II=IPBBW(I0,I)
IF(II.EQ.0) GO TO 80
DO 70 J0=1,2*IELEM
JJ=IPBBW(J0,J)
IF(II.EQ.JJ) C11W(KEY)=C11W(KEY)+BBW(I0,I)*BBW(J0,J)/TTF(II)
70 CONTINUE
75 CONTINUE
80 CONTINUE
MUIM1=MUI
90 CONTINUE
RETURN
END
*
SUBROUTINE TRIHWX(NBMIX,NBLOS,IELEM,LL4F,LL4W,LL4X,MAT,SIDE,ZZ,
1 FRZ,QFR,IPERT,KN,XSGD,MUX,IPBBX,LC,R,BBX,TTF,AX,C11X)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,NBLOS,IELEM,LL4F,LL4W,LL4X,MAT(3,NBLOS),
1 MUX(LL4X),IPBBX(2*IELEM,LL4X),LC,IPERT(NBLOS),
2 KN(NBLOS,3+6*(IELEM+2)*IELEM**2)
REAL SIDE,ZZ(3,NBLOS),FRZ(NBLOS),QFR(NBLOS,8),XSGD(NBMIX,4),
1 R(LC,LC),TTF(LL4F),BBX(2*IELEM,LL4X),AX(*),C11X(*)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION TTTT
*----
* X-ORIENTED COUPLINGS
*----
NELEH=(IELEM+1)*IELEM**2
IIMAX=MUX(LL4X)
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
NUM=0
DO 120 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 120
NUM=NUM+1
IBM=MAT(1,IPERT(KEL))
IF(IBM.EQ.0) GO TO 120
VOL0=REAL(TTTT*ZZ(1,IPERT(KEL))*FRZ(KEL))
DINV=XSGD(IBM,1)
DO 114 K5=0,1
DO 113 K4=0,IELEM-1
DO 112 K3=0,IELEM-1
DO 111 K2=1,IELEM+1
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INX1=ABS(KNX1)-LL4W
DO 110 K1=1,IELEM+1
KNX2=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
INX2=ABS(KNX2)-LL4W
IF((KNX2.NE.0).AND.(KNX1.NE.0)) THEN
L=MUX(INX1)-INX1+INX2
SG=REAL(SIGN(1,KNX1)*SIGN(1,KNX2))
IF(K1.LE.K2) AX(L)=AX(L)-(4./3.)*SG*VOL0*DINV*R(K2,K1)
IF(K1.EQ.K2) THEN
IF((K1.EQ.1).AND.(K5.EQ.0)) AX(L)=AX(L)-QFR(NUM,3)
IF((K1.EQ.IELEM+1).AND.(K5.EQ.1)) AX(L)=AX(L)-QFR(NUM,4)
ENDIF
ENDIF
110 CONTINUE
111 CONTINUE
112 CONTINUE
113 CONTINUE
114 CONTINUE
120 CONTINUE
*----
* COMPUTE THE X-ORIENTED SYSTEM MATRIX AFTER FLUX ELIMINATION
*----
DO 130 I0=1,IIMAX
C11X(I0)=-AX(I0)
130 CONTINUE
MUIM1=0
DO 160 I=1,LL4X
MUI=MUX(I)
DO 150 J=I-(MUI-MUIM1)+1,I
KEY=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)+BBX(I0,I)*BBX(J0,J)/TTF(II)
140 CONTINUE
145 CONTINUE
150 CONTINUE
MUIM1=MUI
160 CONTINUE
RETURN
END
*
SUBROUTINE TRIHWY(NBMIX,NBLOS,IELEM,LL4F,LL4W,LL4X,LL4Y,MAT,
1 SIDE,ZZ,FRZ,QFR,IPERT,KN,XSGD,MUY,IPBBY,LC,R,BBY,TTF,AY,C11Y)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,NBLOS,IELEM,LL4F,LL4W,LL4X,LL4Y,MAT(3,NBLOS),
1 MUY(LL4Y),IPBBY(2*IELEM,LL4Y),LC,IPERT(NBLOS),
2 KN(NBLOS,3+6*(IELEM+2)*IELEM**2)
REAL SIDE,ZZ(3,NBLOS),FRZ(NBLOS),QFR(NBLOS,8),XSGD(NBMIX,4),
1 R(LC,LC),TTF(LL4F),BBY(2*IELEM,LL4Y),AY(*),C11Y(*)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION TTTT
*----
* Y-ORIENTED COUPLINGS
*----
NELEH=(IELEM+1)*IELEM**2
IIMAY=MUY(LL4Y)
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
NUM=0
DO 220 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 220
NUM=NUM+1
IBM=MAT(1,IPERT(KEL))
IF(IBM.EQ.0) GO TO 220
VOL0=REAL(TTTT*ZZ(1,IPERT(KEL))*FRZ(KEL))
DINV=XSGD(IBM,1)
DO 214 K5=0,1
DO 213 K4=0,IELEM-1
DO 212 K3=0,IELEM-1
DO 211 K2=1,IELEM+1
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INY1=ABS(KNY1)-LL4W-LL4X
DO 210 K1=1,IELEM+1
KNY2=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K1)
INY2=ABS(KNY2)-LL4W-LL4X
IF((KNY2.NE.0).AND.(KNY1.NE.0)) THEN
L=MUY(INY1)-INY1+INY2
SG=REAL(SIGN(1,KNY1)*SIGN(1,KNY2))
IF(K1.LE.K2) AY(L)=AY(L)-(4./3.)*SG*VOL0*DINV*R(K2,K1)
IF(K1.EQ.K2) THEN
IF((K1.EQ.1).AND.(K5.EQ.0)) AY(L)=AY(L)-QFR(NUM,5)
IF((K1.EQ.IELEM+1).AND.(K5.EQ.1)) AY(L)=AY(L)-QFR(NUM,6)
ENDIF
ENDIF
210 CONTINUE
211 CONTINUE
212 CONTINUE
213 CONTINUE
214 CONTINUE
220 CONTINUE
*----
* COMPUTE THE Y-ORIENTED SYSTEM MATRIX AFTER FLUX ELIMINATION
*----
DO 230 I0=1,IIMAY
C11Y(I0)=-AY(I0)
230 CONTINUE
MUIM1=0
DO 260 I=1,LL4Y
MUI=MUY(I)
DO 250 J=I-(MUI-MUIM1)+1,I
KEY=MUI-I+J
DO 245 I0=1,2*IELEM
II=IPBBY(I0,I)
IF(II.EQ.0) GO TO 250
DO 240 J0=1,2*IELEM
JJ=IPBBY(J0,J)
IF(II.EQ.JJ) C11Y(KEY)=C11Y(KEY)+BBY(I0,I)*BBY(J0,J)/TTF(II)
240 CONTINUE
245 CONTINUE
250 CONTINUE
MUIM1=MUI
260 CONTINUE
RETURN
END
*
SUBROUTINE TRIHWZ(NBMIX,NBLOS,IELEM,ICOL,LL4F,LL4W,LL4X,LL4Y,
1 LL4Z,MAT,SIDE,ZZ,FRZ,QFR,IPERT,KN,XSGD,MUZ,IPBBZ,LC,R,BBZ,TTF,
2 AZ,C11Z)
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NBMIX,NBLOS,IELEM,ICOL,LL4F,LL4W,LL4X,LL4Y,LL4Z,
1 MAT(3,NBLOS),MUZ(LL4Z),IPBBZ(2*IELEM,LL4Z),LC,IPERT(NBLOS),
2 KN(NBLOS,3+6*(IELEM+2)*IELEM**2)
REAL SIDE,ZZ(3,NBLOS),FRZ(NBLOS),QFR(NBLOS,8),XSGD(NBMIX,4),
1 R(LC,LC),TTF(LL4F),BBZ(2*IELEM,LL4Z),AZ(*),C11Z(*)
*----
* LOCAL VARIABLES
*----
DOUBLE PRECISION TTTT
*----
* Z-ORIENTED COUPLINGS
*----
NELEH=(IELEM+1)*IELEM**2
IIMAZ=MUZ(LL4Z)
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
NUM=0
DO 340 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 340
NUM=NUM+1
IBM=MAT(1,IPERT(KEL))
IF(IBM.EQ.0) GO TO 340
VOL0=REAL(TTTT*ZZ(1,IPERT(KEL))*FRZ(KEL))
DINV=XSGD(IBM,3)
DO 292 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 291 K2=0,IELEM-1
DO 290 K1=0,IELEM-1
KNZ1=KN(NUM,3+6*NELEH+2*K5*IELEM**2+K2*IELEM+K1+1)
KNZ2=KN(NUM,3+6*NELEH+(2*K5+1)*IELEM**2+K2*IELEM+K1+1)
INZ1=ABS(KNZ1)-LL4W-LL4X-LL4Y
INZ2=ABS(KNZ2)-LL4W-LL4X-LL4Y
IF(KNZ1.NE.0) THEN
KEY=MUZ(INZ1)
AZ(KEY)=AZ(KEY)-VOL0*R(1,1)*DINV-QFR(NUM,7)
ENDIF
IF(KNZ2.NE.0) THEN
KEY=MUZ(INZ2)
AZ(KEY)=AZ(KEY)-VOL0*R(IELEM+1,IELEM+1)*DINV-QFR(NUM,8)
ENDIF
IF((ICOL.NE.2).AND.(KNZ1.NE.0).AND.(KNZ2.NE.0)) THEN
IF(INZ2.GT.INZ1) KEY=MUZ(INZ2)-INZ2+INZ1
IF(INZ2.LE.INZ1) KEY=MUZ(INZ1)-INZ1+INZ2
SG=REAL(SIGN(1,KNZ1)*SIGN(1,KNZ2))
IF(INZ1.EQ.INZ2) SG=2.0*SG
AZ(KEY)=AZ(KEY)-SG*VOL0*R(IELEM+1,1)*DINV
ENDIF
290 CONTINUE
291 CONTINUE
292 CONTINUE
340 CONTINUE
*
DO 350 I0=1,IIMAZ
C11Z(I0)=-AZ(I0)
350 CONTINUE
MUIM1=0
DO 380 I=1,LL4Z
MUI=MUZ(I)
DO 370 J=I-(MUI-MUIM1)+1,I
KEY=MUI-I+J
DO 365 I0=1,2*IELEM
II=IPBBZ(I0,I)
IF(II.EQ.0) GO TO 370
DO 360 J0=1,2*IELEM
JJ=IPBBZ(J0,J)
IF(II.EQ.JJ) C11Z(KEY)=C11Z(KEY)+BBZ(I0,I)*BBZ(J0,J)/TTF(II)
360 CONTINUE
365 CONTINUE
370 CONTINUE
MUIM1=MUI
380 CONTINUE
RETURN
END
|
