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*DECK PNFH3E
SUBROUTINE PNFH3E (IL,NBMIX,NBLOS,IELEM,ICOL,NLF,NVD,NAN,L4,LL4F,
1 MAT,SIGTI,SIDE,ZZ,FRZ,QFR,IPERT,KN,LC,R,V,SUNKNO,FUNKNO)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Perform a one-group SPN flux iteration in hexagonal 3D geometry.
* Raviart-Thomas-Schneider method in hexagonal geometry.
*
*Copyright:
* Copyright (C) 2009 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
* IL current Legendre order.
* 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); =4 (quartic).
* ICOL type of quadrature: =1 (analytical integration);
* =2 (Gauss-Lobatto); =3 (Gauss-Legendre).
* 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.
* L4 number of unknowns per energy group and per set of two
* Legendre orders.
* LL4F number of flux components.
* MAT index-number of the mixture type assigned to each volume.
* SIGTI inverse macroscopic cross sections ordered by mixture.
* SIGTI(:,NAN) generally contains the inverse total cross
* section only.
* 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.
* LC order of the unit matrices.
* R unit Cartesian mass matrix.
* V unit nodal coupling matrix.
* SUNKNO sources.
* FUNKNO initial fluxes.
*
*Parameters: output
* FUNKNO right-hand-side of the linear system.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IL,NBMIX,NBLOS,IELEM,ICOL,NLF,NVD,NAN,L4,LL4F,
1 MAT(3,NBLOS),IPERT(NBLOS),KN(NBLOS,3+6*(IELEM+2)*IELEM**2),LC
REAL SIGTI(NBMIX,NAN),SIDE,ZZ(3,NBLOS),FRZ(NBLOS),QFR(NBLOS,8),
1 R(LC,LC),V(LC,LC-1),SUNKNO(L4*NLF/2),FUNKNO(L4*NLF/2)
*----
* LOCAL VARIABLES
*----
REAL QQ(5,5)
DOUBLE PRECISION FFF,TTTT,UUUU,VOL0,GARSI,FACT,VAR1
*
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 16 I0=1,IELEM
DO 15 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)
15 CONTINUE
16 CONTINUE
JOFF=(IL/2)*L4
FACT=REAL(2*IL+1)
IF(MOD(IL,2).EQ.0) THEN
DO 20 I=1,L4
FUNKNO(JOFF+I)=SUNKNO(JOFF+I)
20 CONTINUE
ENDIF
*----
* COMPUTE THE SOLUTION AT ORDER IL.
*----
NELEH=(IELEM+1)*IELEM**2
TTTT=0.5D0*SQRT(3.D00)*SIDE*SIDE
NUM=0
DO 150 KEL=1,NBLOS
IF(IPERT(KEL).EQ.0) GO TO 150
NUM=NUM+1
DZ=ZZ(1,IPERT(KEL))
VOL0=TTTT*DZ*FRZ(KEL)
UUUU=SIDE*DZ*FRZ(KEL)
IF(MOD(IL,2).EQ.0) THEN
* EVEN PARITY EQUATION
IF(IL.GE.2) THEN
DO 34 K5=0,1 ! TWO LOZENGES PER HEXAGON
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)
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=JOFF+LL4F+ABS(KNW1)
INX1=JOFF+LL4F+ABS(KNX1)
INY1=JOFF+LL4F+ABS(KNY1)
DO 30 K1=0,IELEM-1
IF(V(K2,K1+1).EQ.0.0) GO TO 30
IF(K5.EQ.0) THEN
SSS=(-1.0)**K1
JND1=JOFF+(((NUM-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
JND2=JOFF+(((KN(NUM,1)-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
JND3=JOFF+(((KN(NUM,2)-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
ELSE
SSS=1.0
JND1=JOFF+(((KN(NUM,1)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
JND2=JOFF+(((KN(NUM,2)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
JND3=JOFF+(((KN(NUM,3)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
ENDIF
VAR1=SSS*REAL(IL)*UUUU*V(K2,K1+1)
IF(KNW1.NE.0) THEN
SG=REAL(SIGN(1,KNW1))
FUNKNO(JND1)=FUNKNO(JND1)-SG*REAL(VAR1)*FUNKNO(INW1-L4)
ENDIF
IF(KNX1.NE.0) THEN
SG=REAL(SIGN(1,KNX1))
FUNKNO(JND2)=FUNKNO(JND2)-SG*REAL(VAR1)*FUNKNO(INX1-L4)
ENDIF
IF(KNY1.NE.0) THEN
SG=REAL(SIGN(1,KNY1))
FUNKNO(JND3)=FUNKNO(JND3)-SG*REAL(VAR1)*FUNKNO(INY1-L4)
ENDIF
30 CONTINUE
31 CONTINUE
32 CONTINUE
33 CONTINUE
34 CONTINUE
DO 43 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 42 K2=0,IELEM-1
DO 41 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=JOFF+LL4F+ABS(KNZ1)
INZ2=JOFF+LL4F+ABS(KNZ2)
DO 40 K3=0,IELEM-1
IF(K5.EQ.0) THEN
JND1=JOFF+((((NUM-1)*IELEM)+K3)*IELEM+K2)*IELEM+K1+1
ELSE
JND1=JOFF+(((KN(NUM,K5)-1)*IELEM+K3)*IELEM+K2)*IELEM+K1+1
ENDIF
IF(KNZ1.NE.0) THEN
SG=REAL(SIGN(1,KNZ1))
VAR1=SG*(VOL0/DZ)*REAL(IL)*V(1,K3+1)*FUNKNO(INZ1-L4)
FUNKNO(JND1)=FUNKNO(JND1)-REAL(VAR1)
ENDIF
IF(KNZ2.NE.0) THEN
SG=REAL(SIGN(1,KNZ2))
VAR1=SG*(VOL0/DZ)*REAL(IL)*V(IELEM+1,K3+1)*
1 FUNKNO(INZ2-L4)
FUNKNO(JND1)=FUNKNO(JND1)-REAL(VAR1)
ENDIF
40 CONTINUE
41 CONTINUE
42 CONTINUE
43 CONTINUE
ENDIF
ELSE
* PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION
* OF THE EVEN PARITY EQUATION.
IBM=MAT(1,IPERT(KEL))
IF(IBM.EQ.0) GO TO 150
IF(IELEM.GT.1) THEN
DO 52 K3=0,IELEM-1
DO 51 K2=0,IELEM-1
DO 50 K1=0,IELEM-1
IF(QQ(K3+1,K3+1).EQ.0.0) GO TO 50
JND1=JOFF+(NUM-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
JND2=JOFF+(KN(NUM,1)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
JND3=JOFF+(KN(NUM,2)-1)*IELEM**3+K3*IELEM**2+K2*IELEM+K1+1
IF(IL.GE.3) THEN
GARSI=SIGTI(IBM,MIN(IL-1,NAN))
KND1=JND1-L4
KND2=JND2-L4
KND3=JND3-L4
VAR1=(REAL(IL-1)*REAL(IL-2))*VOL0*QQ(K3+1,K3+1)*GARSI
1 /(REAL(2*IL-3)*DZ*DZ)
FUNKNO(JND1)=FUNKNO(JND1)-REAL(VAR1)*FUNKNO(KND1)
FUNKNO(JND2)=FUNKNO(JND2)-REAL(VAR1)*FUNKNO(KND2)
FUNKNO(JND3)=FUNKNO(JND3)-REAL(VAR1)*FUNKNO(KND3)
ENDIF
IF(IL.LE.NLF-3) THEN
GARSI=SIGTI(IBM,MIN(IL+1,NAN))
KND1=JND1+L4
KND2=JND2+L4
KND3=JND3+L4
VAR1=(REAL(IL)*REAL(IL+1))*VOL0*QQ(K3+1,K3+1)*GARSI
1 /(FACT*DZ*DZ)
FUNKNO(JND1)=FUNKNO(JND1)-REAL(VAR1)*FUNKNO(KND1)
FUNKNO(JND2)=FUNKNO(JND2)-REAL(VAR1)*FUNKNO(KND2)
FUNKNO(JND3)=FUNKNO(JND3)-REAL(VAR1)*FUNKNO(KND3)
ENDIF
50 CONTINUE
51 CONTINUE
52 CONTINUE
ENDIF
*
* ODD PARITY EQUATION
DO 93 K5=0,1 ! TWO LOZENGES PER HEXAGON
DO 92 K4=0,IELEM-1
DO 91 K3=0,IELEM-1
DO 90 K2=1,IELEM+1
KNW1=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=JOFF+LL4F+ABS(KNW1)
INX1=JOFF+LL4F+ABS(KNX1)
INY1=JOFF+LL4F+ABS(KNY1)
IF(KNW1.NE.0) THEN
DO 60 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 60
ZMARS=PNMAR2(NZMAR,IL2,IL)
INW2=(IL2/2)*L4+LL4F+ABS(KNW1)
IF((K2.EQ.1).AND.(K5.EQ.0)) THEN
VAR1=0.5*FACT*QFR(NUM,1)*ZMARS*FUNKNO(INW2)
FUNKNO(INW1)=FUNKNO(INW1)+REAL(VAR1)
ELSE IF((K2.EQ.IELEM+1).AND.(K5.EQ.1)) THEN
VAR1=0.5*FACT*QFR(NUM,2)*ZMARS*FUNKNO(INW2)
FUNKNO(INW1)=FUNKNO(INW1)+REAL(VAR1)
ENDIF
60 CONTINUE
ENDIF
IF(KNX1.NE.0) THEN
DO 70 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 70
ZMARS=PNMAR2(NZMAR,IL2,IL)
INX2=(IL2/2)*L4+LL4F+ABS(KNX1)
IF((K2.EQ.1).AND.(K5.EQ.0)) THEN
VAR1=0.5*FACT*QFR(NUM,3)*ZMARS*FUNKNO(INX2)
FUNKNO(INX1)=FUNKNO(INX1)+REAL(VAR1)
ELSE IF((K2.EQ.IELEM+1).AND.(K5.EQ.1)) THEN
VAR1=0.5*FACT*QFR(NUM,4)*ZMARS*FUNKNO(INX2)
FUNKNO(INX1)=FUNKNO(INX1)+REAL(VAR1)
ENDIF
70 CONTINUE
ENDIF
IF(KNY1.NE.0) THEN
DO 80 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 80
ZMARS=PNMAR2(NZMAR,IL2,IL)
INY2=(IL2/2)*L4+LL4F+ABS(KNY1)
IF((K2.EQ.1).AND.(K5.EQ.0)) THEN
VAR1=0.5*FACT*QFR(NUM,5)*ZMARS*FUNKNO(INY2)
FUNKNO(INY1)=FUNKNO(INY1)+REAL(VAR1)
ELSE IF((K2.EQ.IELEM+1).AND.(K5.EQ.1)) THEN
VAR1=0.5*FACT*QFR(NUM,6)*ZMARS*FUNKNO(INY2)
FUNKNO(INY1)=FUNKNO(INY1)+REAL(VAR1)
ENDIF
80 CONTINUE
ENDIF
90 CONTINUE
91 CONTINUE
92 CONTINUE
93 CONTINUE
DO 122 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 121 K2=0,IELEM-1
DO 120 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=JOFF+LL4F+ABS(KNZ1)
INZ2=JOFF+LL4F+ABS(KNZ2)
IF((QFR(NUM,7).NE.0.0).AND.(KNZ1.NE.0)) THEN
* ZINF SIDE.
DO 100 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 100
ZMARS=PNMAR2(NZMAR,IL2,IL)
INDL=(IL2/2)*L4+LL4F+ABS(KNZ1)
VAR1=0.5*FACT*QFR(NUM,7)*ZMARS*FUNKNO(INDL)
FUNKNO(INZ1)=FUNKNO(INZ1)+REAL(VAR1)
100 CONTINUE
ENDIF
IF((QFR(NUM,8).NE.0.0).AND.(KNZ2.NE.0)) THEN
* ZSUP SIDE.
DO 110 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 110
ZMARS=PNMAR2(NZMAR,IL2,IL)
INDL=(IL2/2)*L4+LL4F+ABS(KNZ2)
VAR1=0.5*FACT*QFR(NUM,8)*ZMARS*FUNKNO(INDL)
FUNKNO(INZ2)=FUNKNO(INZ2)+REAL(VAR1)
110 CONTINUE
ENDIF
120 CONTINUE
121 CONTINUE
122 CONTINUE
*
IF(IL.LE.NLF-3) THEN
DO 134 K5=0,1 ! TWO LOZENGES PER HEXAGON
DO 133 K4=0,IELEM-1
DO 132 K3=0,IELEM-1
DO 131 K2=1,IELEM+1
KNW1=KN(NUM,3+K5*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNX1=KN(NUM,3+(K5+2)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
KNY1=KN(NUM,3+(K5+4)*NELEH+(K4*IELEM+K3)*(IELEM+1)+K2)
INW1=JOFF+LL4F+ABS(KNW1)
INX1=JOFF+LL4F+ABS(KNX1)
INY1=JOFF+LL4F+ABS(KNY1)
DO 130 K1=0,IELEM-1
IF(V(K2,K1+1).EQ.0.0) GO TO 130
IF(K5.EQ.0) THEN
SSS=(-1.0)**K1
JND1=JOFF+(((NUM-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
JND2=JOFF+(((KN(NUM,1)-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
JND3=JOFF+(((KN(NUM,2)-1)*IELEM+K4)*IELEM+K3)*IELEM+K1+1
ELSE
SSS=1.0
JND1=JOFF+(((KN(NUM,1)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
JND2=JOFF+(((KN(NUM,2)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
JND3=JOFF+(((KN(NUM,3)-1)*IELEM+K4)*IELEM+K1)*IELEM+K3+1
ENDIF
VAR1=SSS*REAL(IL+1)*UUUU*V(K2,K1+1)
IF(KNW1.NE.0) THEN
SG=REAL(SIGN(1,KNW1))
FUNKNO(INW1)=FUNKNO(INW1)-SG*REAL(VAR1)*FUNKNO(JND1+L4)
ENDIF
IF(KNX1.NE.0) THEN
SG=REAL(SIGN(1,KNX1))
FUNKNO(INX1)=FUNKNO(INX1)-SG*REAL(VAR1)*FUNKNO(JND2+L4)
ENDIF
IF(KNY1.NE.0) THEN
SG=REAL(SIGN(1,KNY1))
FUNKNO(INY1)=FUNKNO(INY1)-SG*REAL(VAR1)*FUNKNO(JND3+L4)
ENDIF
130 CONTINUE
131 CONTINUE
132 CONTINUE
133 CONTINUE
134 CONTINUE
DO 143 K5=0,2 ! THREE LOZENGES PER HEXAGON
DO 142 K2=0,IELEM-1
DO 141 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=JOFF+LL4F+ABS(KNZ1)
INZ2=JOFF+LL4F+ABS(KNZ2)
DO 140 K3=0,IELEM-1
IF(K5.EQ.0) THEN
JND1=JOFF+((((NUM-1)*IELEM)+K3)*IELEM+K2)*IELEM+K1+1
ELSE
JND1=JOFF+(((KN(NUM,K5)-1)*IELEM+K3)*IELEM+K2)*IELEM+K1+1
ENDIF
IF(KNZ1.NE.0) THEN
SG=REAL(SIGN(1,KNZ1))
VAR1=SG*(VOL0/DZ)*REAL(IL+1)*V(1,K3+1)*FUNKNO(JND1+L4)
FUNKNO(INZ1)=FUNKNO(INZ1)-REAL(VAR1)
ENDIF
IF(KNZ2.NE.0) THEN
SG=REAL(SIGN(1,KNZ2))
VAR1=SG*(VOL0/DZ)*REAL(IL+1)*V(IELEM+1,K3+1)*
1 FUNKNO(JND1+L4)
FUNKNO(INZ2)=FUNKNO(INZ2)-REAL(VAR1)
ENDIF
140 CONTINUE
141 CONTINUE
142 CONTINUE
143 CONTINUE
ENDIF
ENDIF
150 CONTINUE
RETURN
END
|
