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*DECK BIVA02
SUBROUTINE BIVA02(ITY,SGD,CYLIND,IELEM,ICOL,NREG,LL4,NBMIX,IIMAX,
1 XX,YY,DD,MAT,KN,QFR,VOL,MU,LC,R,V,SYS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of a within-group (leakage and removal) or out-of-group
* system matrix in mixed-dual finite element diffusion approximation
* (Cartesian geometry).
*
*Copyright:
* Copyright (C) 2002 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
* ITY type of assembly: =0: leakage-removal matrix assembly;
* =1: cross section matrix assembly.
* SGD nuclear properties. SGD(:,1) and SGD(:,2) are diffusion
* coefficients. SGD(:,3) are removal macroscopic cross sections.
* CYLIND cylinderization flag (=.true. for cylindrical geometry).
* 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).
* NREG number of elements in BIVAC.
* LL4 number of unknowns per group in BIVAC.
* NBMIX number of macro-mixtures.
* IIMAX allocated dimension of array SYS.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* DD value used used with a cylindrical geometry.
* MAT mixture index per region.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* VOL volume of regions.
* MU indices used with compressed diagonal storage mode matrix SYS.
* LC number of polynomials in a complete 1-D basis.
* R cartesian mass matrix.
* V nodal coupling matrix.
*
*Parameters: output
* SYS system matrix.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER ITY,IELEM,ICOL,NREG,LL4,NBMIX,IIMAX,MAT(NREG),KN(5*NREG),
1 MU(LL4),LC
REAL SGD(NBMIX,3),XX(NREG),YY(NREG),DD(NREG),QFR(4*NREG),
1 VOL(NREG),R(LC,LC),V(LC,LC-1),SYS(IIMAX)
LOGICAL CYLIND
*----
* LOCAL VARIABLES
*----
REAL QQ(5,5)
*
IF((CYLIND).AND.((IELEM.GT.1).OR.(ICOL.NE.2)))
1 CALL XABORT('BIVA02: TYPE OF DISCRETIZATION NOT IMPLEMENTED.')
*----
* ASSEMBLY OF A SYSTEM MATRIX.
*----
IF(ITY.EQ.0) THEN
* LEAKAGE-REMOVAL SYSTEM MATRIX ASSEMBLY.
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
NUM1=0
NUM2=0
DO 80 K=1,NREG
L=MAT(K)
IF(L.EQ.0) GO TO 80
VOL0=VOL(K)
IF(VOL0.EQ.0.0) GO TO 70
DX=XX(K)
DY=YY(K)
IF(CYLIND) THEN
DIN=1.0-0.5*DX/DD(K)
DOT=1.0+0.5*DX/DD(K)
ELSE
DIN=1.0
DOT=1.0
ENDIF
*
DO 60 I0=1,IELEM
INX1=ABS(KN(NUM1+2))+I0-1
INX2=ABS(KN(NUM1+3))+I0-1
INY1=ABS(KN(NUM1+4))+I0-1
INY2=ABS(KN(NUM1+5))+I0-1
DO 50 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
KEY=MU(JND1)
SYS(KEY)=SYS(KEY)+VOL0*SGD(L,3)
DO 20 K0=1,J0
IF(QQ(J0,K0).EQ.0.0) GO TO 20
KND1=KN(NUM1+1)+(I0-1)*IELEM+K0-1
KEY=MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+VOL0*QQ(J0,K0)*SGD(L,1)/(DX*DX)
20 CONTINUE
IF(KN(NUM1+2).NE.0) THEN
IF(JND1.GT.INX1) KEY=MU(JND1)-JND1+INX1
IF(JND1.LT.INX1) KEY=MU(INX1)-INX1+JND1
SG=REAL(SIGN(1,KN(NUM1+2)))
SYS(KEY)=SYS(KEY)+SG*(VOL0/DX)*DIN*V(1,J0)
ENDIF
IF(KN(NUM1+3).NE.0) THEN
IF(INX2.GT.JND1) KEY=MU(INX2)-INX2+JND1
IF(INX2.LT.JND1) KEY=MU(JND1)-JND1+INX2
SG=REAL(SIGN(1,KN(NUM1+3)))
SYS(KEY)=SYS(KEY)+SG*(VOL0/DX)*DOT*V(IELEM+1,J0)
ENDIF
JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
DO 30 K0=1,J0
IF(QQ(J0,K0).EQ.0.0) GO TO 30
KND1=KN(NUM1+1)+(K0-1)*IELEM+I0-1
KEY=MU(JND1)-JND1+KND1
SYS(KEY)=SYS(KEY)+VOL0*QQ(J0,K0)*SGD(L,2)/(DY*DY)
30 CONTINUE
IF(KN(NUM1+4).NE.0) THEN
IF(JND1.GT.INY1) KEY=MU(JND1)-JND1+INY1
IF(JND1.LT.INY1) KEY=MU(INY1)-INY1+JND1
SG=REAL(SIGN(1,KN(NUM1+4)))
SYS(KEY)=SYS(KEY)+SG*(VOL0/DY)*V(1,J0)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
IF(INY2.GT.JND1) KEY=MU(INY2)-INY2+JND1
IF(INY2.LT.JND1) KEY=MU(JND1)-JND1+INY2
SG=REAL(SIGN(1,KN(NUM1+5)))
SYS(KEY)=SYS(KEY)+SG*(VOL0/DY)*V(IELEM+1,J0)
ENDIF
50 CONTINUE
IF(KN(NUM1+2).NE.0) THEN
KEY=MU(INX1)
SYS(KEY)=SYS(KEY)-DIN*(VOL0*R(1,1)/SGD(L,1)+QFR(NUM2+1))
ENDIF
IF(KN(NUM1+3).NE.0) THEN
KEY=MU(INX2)
SYS(KEY)=SYS(KEY)-DOT*(VOL0*R(IELEM+1,IELEM+1)/SGD(L,1)
1 +QFR(NUM2+2))
ENDIF
IF(KN(NUM1+4).NE.0) THEN
KEY=MU(INY1)
SYS(KEY)=SYS(KEY)-VOL0*R(1,1)/SGD(L,2)-QFR(NUM2+3)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
KEY=MU(INY2)
SYS(KEY)=SYS(KEY)-VOL0*R(IELEM+1,IELEM+1)/SGD(L,2)
1 -QFR(NUM2+4)
ENDIF
IF(ICOL.NE.2) THEN
IF((KN(NUM1+2).NE.0).AND.(KN(NUM1+3).NE.0)) THEN
IF(INX2.GT.INX1) KEY=MU(INX2)-INX2+INX1
IF(INX2.LE.INX1) KEY=MU(INX1)-INX1+INX2
SG=REAL(SIGN(1,KN(NUM1+2))*SIGN(1,KN(NUM1+3)))
IF(INX1.EQ.INX2) SG=2.0*SG
SYS(KEY)=SYS(KEY)-SG*VOL0*R(IELEM+1,1)/SGD(L,1)
ENDIF
IF((KN(NUM1+4).NE.0).AND.(KN(NUM1+5).NE.0)) THEN
IF(INY2.GT.INY1) KEY=MU(INY2)-INY2+INY1
IF(INY2.LE.INY1) KEY=MU(INY1)-INY1+INY2
SG=REAL(SIGN(1,KN(NUM1+4))*SIGN(1,KN(NUM1+5)))
IF(INY1.EQ.INY2) SG=2.0*SG
SYS(KEY)=SYS(KEY)-SG*VOL0*R(IELEM+1,1)/SGD(L,2)
ENDIF
ENDIF
60 CONTINUE
70 NUM1=NUM1+5
NUM2=NUM2+4
80 CONTINUE
ELSE
* CROSS SECTION SYSTEM MATRIX ASSEMBLY. COMPONENTS WITH 1E-10
* FACTORS ARE INTRODUCED TO MAKE THE MATRIX INVERTIBLE.
NUM1=0
DO 110 K=1,NREG
L=MAT(K)
IF(L.EQ.0) GO TO 110
VOL0=VOL(K)
IF(VOL0.EQ.0.0) GO TO 100
DO 95 I0=1,IELEM
INX1=ABS(KN(NUM1+2))+I0-1
INX2=ABS(KN(NUM1+3))+I0-1
INY1=ABS(KN(NUM1+4))+I0-1
INY2=ABS(KN(NUM1+5))+I0-1
IF(KN(NUM1+2).NE.0) SYS(MU(INX1))=SYS(MU(INX1))+1.0E-30
IF(KN(NUM1+3).NE.0) SYS(MU(INX2))=SYS(MU(INX2))+1.0E-30
IF(KN(NUM1+4).NE.0) SYS(MU(INY1))=SYS(MU(INY1))+1.0E-30
IF(KN(NUM1+5).NE.0) SYS(MU(INY2))=SYS(MU(INY2))+1.0E-30
DO 90 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
KEY=MU(JND1)
SYS(KEY)=SYS(KEY)+VOL0*SGD(L,1)
90 CONTINUE
95 CONTINUE
100 NUM1=NUM1+5
110 CONTINUE
ENDIF
RETURN
END
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