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*DECK BIVA01
SUBROUTINE BIVA01(ITY,MAXKN,SGD,CYLIND,NREG,LL4,NBMIX,IIMAX,XX,
1 YY,DD,MAT,KN,QFR,VOL,MU,LC,R,RS,Q,QS,SYS)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of a within-group (leakage and removal) or out-of-group
* system matrix in mesh corner finite difference or 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.
* MAXKN dimension of array KN.
* 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).
* NREG number of elements in BIVAC.
* LL4 order of matrix SYS.
* NBMIX number of macro-mixtures.
* IIMAX allocated dimension of array SYS.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* DD value 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.
* RS cylindrical mass matrix.
* Q Cartesian stiffness matrix.
* QS cylindrical stiffness matrix.
*
*Parameters: output
* SYS system matrix.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER ITY,MAXKN,NREG,LL4,NBMIX,IIMAX,MAT(NREG),KN(MAXKN),
1 MU(LL4),LC
REAL SGD(NBMIX,3),XX(NREG),YY(NREG),DD(NREG),QFR(4*NREG),
1 VOL(NREG),R(LC,LC),RS(LC,LC),Q(LC,LC),QS(LC,LC),SYS(IIMAX)
LOGICAL CYLIND
*----
* LOCAL VARIABLES
*----
INTEGER IJ1(25),IJ2(25),ISR(4,5)
REAL Q2DP1(25,25),Q2DP2(25,25),R2DP(25,25),Q2DC1(25,25),
1 Q2DC2(25,25),R2DC(25,25)
*----
* COMPUTE VECTORS IJ1, IJ2 AND MATRIX ISR.
*----
LL=LC*LC
DO 10 I=1,LL
IJ1(I)=1+MOD(I-1,LC)
IJ2(I)=1+(I-IJ1(I))/LC
10 CONTINUE
DO 20 I=1,LC
ISR(1,I)=(I-1)*LC+1
ISR(2,I)=I*LC
ISR(3,I)=I
ISR(4,I)=LL-LC+I
20 CONTINUE
*----
* COMPUTE THE CARTESIAN 2-D MASS AND STIFFNESS MATRICES FROM TENSORIAL
* PRODUCTS OF 1-D MATRICES.
*----
DO 40 I=1,LL
I1=IJ1(I)
I2=IJ2(I)
DO 30 J=1,LL
J1=IJ1(J)
J2=IJ2(J)
Q2DP1(I,J)=Q(I1,J1)*R(I2,J2)
Q2DP2(I,J)=R(I1,J1)*Q(I2,J2)
R2DP(I,J)=R(I1,J1)*R(I2,J2)
Q2DC1(I,J)=QS(I1,J1)*R(I2,J2)
Q2DC2(I,J)=RS(I1,J1)*Q(I2,J2)
R2DC(I,J)=RS(I1,J1)*R(I2,J2)
30 CONTINUE
40 CONTINUE
*----
* ASSEMBLY OF A SYSTEM MATRIX.
*----
IF(ITY.EQ.0) THEN
* LEAKAGE-REMOVAL SYSTEM MATRIX ASSEMBLY.
NUM1=0
NUM2=0
DO 110 K=1,NREG
L=MAT(K)
IF(L.EQ.0) GO TO 110
IF(VOL(K).EQ.0.0) GO TO 100
DX=XX(K)
DY=YY(K)
DO 60 I=1,LL
IND1=KN(NUM1+I)
IF(IND1.EQ.0) GO TO 60
KEY1=MU(IND1)-IND1
DO 50 J=1,LL
IND2=KN(NUM1+J)
IF((IND2.EQ.0).OR.(IND2.GT.IND1)) GO TO 50
IF(CYLIND) THEN
QQX=(Q2DP1(I,J)+Q2DC1(I,J)*DX/DD(K))/(DX*DX)
QQY=(Q2DP2(I,J)+Q2DC2(I,J)*DX/DD(K))/(DY*DY)
RR=R2DP(I,J)+R2DC(I,J)*DX/DD(K)
ELSE
QQX=Q2DP1(I,J)/(DX*DX)
QQY=Q2DP2(I,J)/(DY*DY)
RR=R2DP(I,J)
ENDIF
IF((QQX.EQ.0.0).AND.(QQY.EQ.0.0).AND.(RR.EQ.0.0)) GO TO 50
KEY=KEY1+IND2
SYS(KEY)=SYS(KEY)+(QQX*SGD(L,1)+QQY*SGD(L,2)+RR*SGD(L,3))
1 *VOL(K)
50 CONTINUE
60 CONTINUE
DO 90 IC=1,4
QFR1=QFR(NUM2+IC)
IF(QFR1.EQ.0.0) GO TO 90
DO 80 I1=1,LC
IND1=KN(NUM1+ISR(IC,I1))
IF(IND1.EQ.0) GO TO 80
KEY1=MU(IND1)-IND1
DO 70 J1=1,LC
IND2=KN(NUM1+ISR(IC,J1))
IF((IND2.EQ.0).OR.(IND2.GT.IND1)) GO TO 70
IF(CYLIND) THEN
CRZ=0.0
IF(IC.EQ.1) THEN
CRZ=-0.5*R(I1,J1)
ELSE IF(IC.EQ.2) THEN
CRZ=0.5*R(I1,J1)
ELSE IF(IC.EQ.3) THEN
CRZ=RS(I1,J1)
ELSE IF(IC.EQ.4) THEN
CRZ=RS(I1,J1)
ENDIF
RR=R(I1,J1)+CRZ*DX/DD(K)
ELSE
RR=R(I1,J1)
ENDIF
IF(RR.EQ.0.0) GO TO 70
KEY=KEY1+IND2
SYS(KEY)=SYS(KEY)+RR*QFR1
70 CONTINUE
80 CONTINUE
90 CONTINUE
100 NUM1=NUM1+LL
NUM2=NUM2+4
110 CONTINUE
ELSE
* CROSS SECTION SYSTEM MATRIX ASSEMBLY.
NUM1=0
DO 150 K=1,NREG
L=MAT(K)
IF(L.EQ.0) GO TO 150
IF(VOL(K).EQ.0.0) GO TO 140
DX=XX(K)
DO 130 I=1,LL
IND1=KN(NUM1+I)
IF(IND1.EQ.0) GO TO 130
KEY1=MU(IND1)-IND1
DO 120 J=1,LL
IND2=KN(NUM1+J)
IF((IND2.EQ.0).OR.(IND2.GT.IND1)) GO TO 120
IF(CYLIND) THEN
RR=R2DP(I,J)+R2DC(I,J)*DX/DD(K)
ELSE
RR=R2DP(I,J)
ENDIF
IF(RR.EQ.0.0) GO TO 120
KEY=KEY1+IND2
SYS(KEY)=SYS(KEY)+RR*SGD(L,1)*VOL(K)
120 CONTINUE
130 CONTINUE
140 NUM1=NUM1+LL
150 CONTINUE
ENDIF
RETURN
END
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