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*DECK PNFL2E
SUBROUTINE PNFL2E (NREG,IELEM,ICOL,XX,YY,MAT,VOL,NBMIX,NLF,NVD,
1 NAN,SIGTI,L4,KN,QFR,MU,IIMAX,LC,R,V,SYS,SUNKNO,FUNKNO,NADI)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Perform a one-group SPN flux iteration in Cartesian 2D geometry.
* Raviart-Thomas method in Cartesian geometry.
*
*Copyright:
* Copyright (C) 2004 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
* NREG total number of regions.
* 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).
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* MAT index-number of the mixture type assigned to each volume.
* VOL volumes.
* NBMIX number of mixtures.
* 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.
* SIGTI inverse macroscopic cross sections ordered by mixture.
* SIGTI(:,NAN) generally contains the inverse total cross
* section only.
* L4 number of unknowns per energy group and per set of two
* Legendre orders.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* MU profiled storage indices for matrix SYS.
* IIMAX dimension of SYS.
* LC order of the unit matrices.
* R unit Cartesian mass matrix.
* V unit nodal coupling matrix.
* SYS LU factors of the system matrix.
* SUNKNO sources.
* FUNKNO initial fluxes.
* NADI number of inner ADI iterations.
*
*Parameters: output
* FUNKNO fluxes.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER NREG,IELEM,ICOL,MAT(NREG),NBMIX,NLF,NVD,NAN,L4,KN(5*NREG),
1 MU(L4),IIMAX,LC,NADI
REAL XX(NREG),YY(NREG),VOL(NREG),SIGTI(NBMIX,NAN),QFR(4*NREG),
1 R(LC,LC),V(LC,LC-1),SYS(IIMAX),SUNKNO(L4*NLF/2),FUNKNO(L4*NLF/2)
*----
* LOCAL VARIABLES
*----
REAL QQ(5,5)
*
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 12 I0=1,IELEM
DO 11 J0=1,IELEM
QQ(I0,J0)=0.0
DO 10 K0=2,IELEM
QQ(I0,J0)=QQ(I0,J0)+V(K0,I0)*V(K0,J0)/R(K0,K0)
10 CONTINUE
11 CONTINUE
12 CONTINUE
MUMAX=MU(L4)
DO 170 IADI=1,MAX(1,NADI)
DO 160 IL=0,NLF-1
FACT=REAL(2*IL+1)
IF(MOD(IL,2).EQ.0) THEN
DO 20 I=1,L4
FUNKNO((IL/2)*L4+I)=SUNKNO((IL/2)*L4+I)
20 CONTINUE
ENDIF
*----
* COMPUTE THE SOLUTION AT ORDER IL.
*----
NUM1=0
NUM2=0
DO 150 K=1,NREG
IBM=MAT(K)
IF(IBM.EQ.0) GO TO 150
VOL0=VOL(K)
IF(MOD(IL,2).EQ.0) THEN
* EVEN PARITY EQUATION
IF(IL.GE.2) THEN
DO 35 I0=1,IELEM
IND1=((IL-2)/2)*L4+ABS(KN(NUM1+2))+I0-1
IND2=((IL-2)/2)*L4+ABS(KN(NUM1+3))+I0-1
IND3=((IL-2)/2)*L4+ABS(KN(NUM1+4))+I0-1
IND4=((IL-2)/2)*L4+ABS(KN(NUM1+5))+I0-1
DO 30 J0=1,IELEM
JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1
IF(KN(NUM1+2).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+2)))
FUNKNO(JND1)=FUNKNO(JND1)-SG*REAL(IL)*VOL0*V(1,J0)*
1 FUNKNO(IND1)/XX(K)
ENDIF
IF(KN(NUM1+3).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+3)))
FUNKNO(JND1)=FUNKNO(JND1)-SG*REAL(IL)*VOL0*V(IELEM+1,J0)*
1 FUNKNO(IND2)/XX(K)
ENDIF
JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1
IF(KN(NUM1+4).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+4)))
FUNKNO(JND1)=FUNKNO(JND1)-SG*REAL(IL)*VOL0*V(1,J0)*
1 FUNKNO(IND3)/YY(K)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+5)))
FUNKNO(JND1)=FUNKNO(JND1)-SG*REAL(IL)*VOL0*V(IELEM+1,J0)*
1 FUNKNO(IND4)/YY(K)
ENDIF
30 CONTINUE
35 CONTINUE
ENDIF
ELSE
DO 140 I0=1,IELEM
* PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION
* OF THE EVEN PARITY EQUATION.
IF((IL.GE.3).AND.(IELEM.GT.1)) THEN
GARSI=SIGTI(IBM,MIN(IL-1,NAN))
DO 65 J0=1,IELEM
DO 50 K0=1,IELEM
IF(QQ(J0,K0).EQ.0.0) GO TO 50
JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1
KND1=((IL-2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1
FUNKNO(JND1)=FUNKNO(JND1)-(REAL(IL-1)*REAL(IL-2))*VOL0*
1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(REAL(2*IL-3)*XX(K)*XX(K))
50 CONTINUE
DO 60 K0=1,IELEM
IF(QQ(J0,K0).EQ.0.0) GO TO 60
JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1
KND1=((IL-2)/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1
FUNKNO(JND1)=FUNKNO(JND1)-(REAL(IL-1)*REAL(IL-2))*VOL0*
1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(REAL(2*IL-3)*YY(K)*YY(K))
60 CONTINUE
65 CONTINUE
ENDIF
IF((IL.LE.NLF-3).AND.(IELEM.GT.1)) THEN
GARSI=SIGTI(IBM,MIN(IL+1,NAN))
DO 85 J0=1,IELEM
DO 70 K0=1,IELEM
IF(QQ(J0,K0).EQ.0.0) GO TO 70
JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1
KND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1
FUNKNO(JND1)=FUNKNO(JND1)-(REAL(IL)*REAL(IL+1))*VOL0*
1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*XX(K)*XX(K))
70 CONTINUE
DO 80 K0=1,IELEM
IF(QQ(J0,K0).EQ.0.0) GO TO 80
JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1
KND1=((IL+2)/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1
FUNKNO(JND1)=FUNKNO(JND1)-(REAL(IL)*REAL(IL+1))*VOL0*
1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*YY(K)*YY(K))
80 CONTINUE
85 CONTINUE
ENDIF
*
* ODD PARITY EQUATION
IND1=(IL/2)*L4+ABS(KN(NUM1+2))+I0-1
IND2=(IL/2)*L4+ABS(KN(NUM1+3))+I0-1
IND3=(IL/2)*L4+ABS(KN(NUM1+4))+I0-1
IND4=(IL/2)*L4+ABS(KN(NUM1+5))+I0-1
IF((QFR(NUM2+1).NE.0.0).AND.(KN(NUM1+2).NE.0)) THEN
* XINF SIDE.
DO 90 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 90
ZMARS=PNMAR2(NZMAR,IL2,IL)
IND5=(IL2/2)*L4+ABS(KN(NUM1+2))+I0-1
FUNKNO(IND1)=FUNKNO(IND1)+0.5*FACT*QFR(NUM2+1)*ZMARS*
1 FUNKNO(IND5)
90 CONTINUE
ENDIF
IF((QFR(NUM2+2).NE.0.0).AND.(KN(NUM1+3).NE.0)) THEN
* XSUP SIDE.
DO 100 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 100
ZMARS=PNMAR2(NZMAR,IL2,IL)
IND5=(IL2/2)*L4+ABS(KN(NUM1+3))+I0-1
FUNKNO(IND2)=FUNKNO(IND2)+0.5*FACT*QFR(NUM2+2)*ZMARS*
1 FUNKNO(IND5)
100 CONTINUE
ENDIF
IF((QFR(NUM2+3).NE.0.0).AND.(KN(NUM1+4).NE.0)) THEN
* YINF SIDE.
DO 110 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 110
ZMARS=PNMAR2(NZMAR,IL2,IL)
IND5=(IL2/2)*L4+ABS(KN(NUM1+4))+I0-1
FUNKNO(IND3)=FUNKNO(IND3)+0.5*FACT*QFR(NUM2+3)*ZMARS*
1 FUNKNO(IND5)
110 CONTINUE
ENDIF
IF((QFR(NUM2+4).NE.0.0).AND.(KN(NUM1+5).NE.0)) THEN
* YSUP SIDE.
DO 120 IL2=1,NLF-1,2
IF(IL2.EQ.IL) GO TO 120
ZMARS=PNMAR2(NZMAR,IL2,IL)
IND5=(IL2/2)*L4+ABS(KN(NUM1+5))+I0-1
FUNKNO(IND4)=FUNKNO(IND4)+0.5*FACT*QFR(NUM2+4)*ZMARS*
1 FUNKNO(IND5)
120 CONTINUE
ENDIF
IF(IL.LE.NLF-3) THEN
DO 130 J0=1,IELEM
JND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1
IF(KN(NUM1+2).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+2)))
FUNKNO(IND1)=FUNKNO(IND1)-SG*REAL(IL+1)*VOL0*V(1,J0)*
1 FUNKNO(JND1)/XX(K)
ENDIF
IF(KN(NUM1+3).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+3)))
FUNKNO(IND2)=FUNKNO(IND2)-SG*REAL(IL+1)*VOL0*
1 V(IELEM+1,J0)*FUNKNO(JND1)/XX(K)
ENDIF
JND1=((IL+2)/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1
IF(KN(NUM1+4).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+4)))
FUNKNO(IND3)=FUNKNO(IND3)-SG*REAL(IL+1)*VOL0*V(1,J0)*
1 FUNKNO(JND1)/YY(K)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
SG=REAL(SIGN(1,KN(NUM1+5)))
FUNKNO(IND4)=FUNKNO(IND4)-SG*REAL(IL+1)*VOL0*
1 V(IELEM+1,J0)*FUNKNO(JND1)/YY(K)
ENDIF
130 CONTINUE
ENDIF
140 CONTINUE
ENDIF
NUM1=NUM1+5
NUM2=NUM2+4
150 CONTINUE
IF(MOD(IL,2).EQ.1) THEN
CALL ALLDLS(L4,MU,SYS((IL/2)*MUMAX+1),FUNKNO((IL/2)*L4+1))
ENDIF
160 CONTINUE
170 CONTINUE
RETURN
END
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