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+*DECK BIVA05
+ SUBROUTINE BIVA05(ITY,SGD,IELEM,NBLOS,LL4,NBMIX,IIMAX,SIDE,MAT,
+ 1 IPERT,KN,QFR,MU,LC,R,V,H,SYS)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* Assembly of a within-group (leakage and removal) or out-of-group
+* system matrix in a Thomas-Raviart-Schneider (dual) finite element
+* diffusion approximation (hexagonal geometry).
+*
+*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
+* 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.
+* IELEM degree of the Lagrangian finite elements: =1 (linear);
+* =2 (parabolic); =3 (cubic); =4 (quartic).
+* NBLOS number of lozenges per direction, taking into account
+* mesh-splitting.
+* LL4 number of unknowns per group in BIVAC.
+* NBMIX number of macro-mixtures.
+* IIMAX allocated dimension of array SYS.
+* SIDE side of the hexagons.
+* MAT mixture index per lozenge.
+* IPERT mixture permutation index.
+* KN element-ordered unknown list.
+* QFR element-ordered boundary conditions.
+* MU indices used with compressed diagonal storage mode matrix SYS.
+* LC order of the unit matrices.
+* R Cartesian mass matrix.
+* V nodal coupling matrix.
+* H Piolat (hexagonal) coupling matrix.
+*
+*Parameters: output
+* SYS system matrix.
+*
+*-----------------------------------------------------------------------
+*
+*----
+* SUBROUTINE ARGUMENTS
+*----
+ INTEGER ITY,IELEM,NBLOS,LL4,NBMIX,IIMAX,MAT(3,NBLOS),IPERT(NBLOS),
+ 1 KN(NBLOS,4+6*IELEM*(IELEM+1)),MU(LL4),LC
+ REAL SGD(NBMIX,3),SIDE,QFR(NBLOS,6),R(LC,LC),V(LC,LC-1),
+ 1 H(LC,LC-1),SYS(IIMAX)
+*----
+* LOCAL VARIABLES
+*----
+ PARAMETER(MAXIEL=3)
+ DOUBLE PRECISION CTRAN(MAXIEL*(MAXIEL+1),MAXIEL*(MAXIEL+1))
+*----
+* ASSEMBLY OF A SYSTEM MATRIX.
+*----
+ TTTT=0.5*SQRT(3.0)*SIDE*SIDE
+ IF(IELEM.GT.MAXIEL) CALL XABORT('BIVA05: MAXIEL OVERFLOW.')
+ IF(ITY.EQ.0) THEN
+* COMPUTE THE TRANVERSE COUPLING PIOLAT UNIT MATRIX
+ CTRAN(:MAXIEL*(MAXIEL+1),:MAXIEL*(MAXIEL+1))=0.0D0
+ CNORM=SIDE*SIDE/SQRT(3.0)
+ I=0
+ DO 22 JS=1,IELEM
+ DO 21 JT=1,IELEM+1
+ J=0
+ I=I+1
+ SSS=1.0
+ DO 20 IT=1,IELEM
+ DO 10 IS=1,IELEM+1
+ J=J+1
+ CTRAN(I,J)=SSS*CNORM*H(IS,JS)*H(JT,IT)
+ 10 CONTINUE
+ SSS=-SSS
+ 20 CONTINUE
+ 21 CONTINUE
+ 22 CONTINUE
+*
+* LEAKAGE-REMOVAL SYSTEM MATRIX ASSEMBLY
+ NELEM=IELEM*(IELEM+1)
+ COEF=2.0*SIDE*SIDE/SQRT(3.0)
+ NUM=0
+ DO 70 KEL=1,NBLOS
+ IF(IPERT(KEL).EQ.0) GO TO 70
+ IBM=MAT(1,IPERT(KEL))
+ IF(IBM.EQ.0) GO TO 70
+ NUM=NUM+1
+ DINV=1.0/SGD(IBM,1)
+ SIG=SGD(IBM,3)
+ DO 43 K4=0,1
+ DO 42 K3=0,IELEM-1
+ DO 41 K2=1,IELEM+1
+ KNW1=KN(NUM,4+K4*NELEM+K3*(IELEM+1)+K2)
+ KNX1=KN(NUM,4+(K4+2)*NELEM+K3*(IELEM+1)+K2)
+ KNY1=KN(NUM,4+(K4+4)*NELEM+K3*(IELEM+1)+K2)
+ INW1=ABS(KNW1)
+ INX1=ABS(KNX1)
+ INY1=ABS(KNY1)
+ DO 30 K1=1,IELEM+1
+ KNW2=KN(NUM,4+K4*NELEM+K3*(IELEM+1)+K1)
+ KNX2=KN(NUM,4+(K4+2)*NELEM+K3*(IELEM+1)+K1)
+ KNY2=KN(NUM,4+(K4+4)*NELEM+K3*(IELEM+1)+K1)
+ INW2=ABS(KNW2)
+ INX2=ABS(KNX2)
+ INY2=ABS(KNY2)
+ IF((KNW2.NE.0).AND.(KNW1.NE.0).AND.(INW1.GE.INW2)) THEN
+ L=MU(INW1)-INW1+INW2
+ SG=REAL(SIGN(1,KNW1)*SIGN(1,KNW2))
+ SYS(L)=SYS(L)-SG*COEF*DINV*R(K2,K1)
+ IF(INW1.EQ.INW2) THEN
+ IF((K1.EQ.1).AND.(K4.EQ.0)) SYS(L)=SYS(L)-QFR(NUM,1)
+ IF((K1.EQ.IELEM+1).AND.(K4.EQ.1)) SYS(L)=SYS(L)-QFR(NUM,2)
+ ENDIF
+ ENDIF
+ IF((KNX2.NE.0).AND.(KNX1.NE.0).AND.(INX1.GE.INX2)) THEN
+ L=MU(INX1)-INX1+INX2
+ SG=REAL(SIGN(1,KNX1)*SIGN(1,KNX2))
+ SYS(L)=SYS(L)-SG*COEF*DINV*R(K2,K1)
+ IF(INX1.EQ.INX2) THEN
+ IF((K1.EQ.1).AND.(K4.EQ.0)) SYS(L)=SYS(L)-QFR(NUM,3)
+ IF((K1.EQ.IELEM+1).AND.(K4.EQ.1)) SYS(L)=SYS(L)-QFR(NUM,4)
+ ENDIF
+ ENDIF
+ IF((KNY2.NE.0).AND.(KNY1.NE.0).AND.(INY1.GE.INY2)) THEN
+ L=MU(INY1)-INY1+INY2
+ SG=REAL(SIGN(1,KNY1)*SIGN(1,KNY2))
+ SYS(L)=SYS(L)-SG*COEF*DINV*R(K2,K1)
+ IF(INY1.EQ.INY2) THEN
+ IF((K1.EQ.1).AND.(K4.EQ.0)) SYS(L)=SYS(L)-QFR(NUM,5)
+ IF((K1.EQ.IELEM+1).AND.(K4.EQ.1)) SYS(L)=SYS(L)-QFR(NUM,6)
+ ENDIF
+ ENDIF
+ 30 CONTINUE
+ DO 40 K1=0,IELEM-1
+ IF(V(K2,K1+1).EQ.0.0) GO TO 40
+ IF(K4.EQ.0) THEN
+ SSS=(-1.0)**K1
+ JND1=KN(NUM,1)+K3*IELEM+K1
+ JND2=KN(NUM,2)+K3*IELEM+K1
+ JND3=KN(NUM,3)+K3*IELEM+K1
+ ELSE
+ SSS=1.0
+ JND1=KN(NUM,2)+K1*IELEM+K3
+ JND2=KN(NUM,3)+K1*IELEM+K3
+ JND3=KN(NUM,4)+K1*IELEM+K3
+ ENDIF
+ IF(KNW1.NE.0) THEN
+ L=MU(JND1)-JND1+INW1
+ IF(JND1.LT.INW1) L=MU(INW1)-INW1+JND1
+ SG=REAL(SIGN(1,KNW1))
+ SYS(L)=SYS(L)+SG*SSS*SIDE*V(K2,K1+1)
+ ENDIF
+ IF(KNX1.NE.0) THEN
+ L=MU(JND2)-JND2+INX1
+ IF(JND2.LT.INX1) L=MU(INX1)-INX1+JND2
+ SG=REAL(SIGN(1,KNX1))
+ SYS(L)=SYS(L)+SG*SSS*SIDE*V(K2,K1+1)
+ ENDIF
+ IF(KNY1.NE.0) THEN
+ L=MU(JND3)-JND3+INY1
+ IF(JND3.LT.INY1) L=MU(INY1)-INY1+JND3
+ SG=REAL(SIGN(1,KNY1))
+ SYS(L)=SYS(L)+SG*SSS*SIDE*V(K2,K1+1)
+ ENDIF
+ 40 CONTINUE
+ 41 CONTINUE
+ 42 CONTINUE
+ 43 CONTINUE
+ ITRS=0
+ DO I=1,NBLOS
+ IF(KN(I,1).EQ.KN(NUM,4)) THEN
+ ITRS=I
+ GO TO 45
+ ENDIF
+ ENDDO
+ CALL XABORT('BIVA05: ITRS FAILURE.')
+ 45 DO 55 I=1,NELEM
+ KNW1=KN(ITRS,4+I)
+ KNX1=KN(NUM,4+2*NELEM+I)
+ KNY1=KN(NUM,4+4*NELEM+I)
+ INW1=ABS(KNW1)
+ INX1=ABS(KNX1)
+ INY1=ABS(KNY1)
+ DO 50 J=1,NELEM
+ KNW2=KN(NUM,4+NELEM+J)
+ KNX2=KN(NUM,4+3*NELEM+J)
+ KNY2=KN(NUM,4+5*NELEM+J)
+ INW2=ABS(KNW2)
+ INX2=ABS(KNX2)
+ INY2=ABS(KNY2)
+ IF((KNY2.NE.0).AND.(KNW1.NE.0).AND.(INW1.LT.INY2)) THEN
+ L=MU(INY2)-INY2+INW1
+ SG=REAL(SIGN(1,KNW1)*SIGN(1,KNY2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! y w
+ ELSE IF((KNY2.NE.0).AND.(KNW1.NE.0).AND.(INW1.GT.INY2)) THEN
+ L=MU(INW1)-INW1+INY2
+ SG=REAL(SIGN(1,KNW1)*SIGN(1,KNY2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! w y
+ ENDIF
+ IF((KNW2.NE.0).AND.(KNX1.NE.0).AND.(INW2.LT.INX1)) THEN
+ L=MU(INX1)-INX1+INW2
+ SG=REAL(SIGN(1,KNX1)*SIGN(1,KNW2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! x w
+ ELSE IF((KNW2.NE.0).AND.(KNX1.NE.0).AND.(INW2.GT.INX1)) THEN
+ L=MU(INW2)-INW2+INX1
+ SG=REAL(SIGN(1,KNX1)*SIGN(1,KNW2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! w x
+ ENDIF
+ IF((KNX2.NE.0).AND.(KNY1.NE.0).AND.(INX2.LT.INY1)) THEN
+ L=MU(INY1)-INY1+INX2
+ SG=REAL(SIGN(1,KNY1)*SIGN(1,KNX2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! y x
+ ELSE IF((KNX2.NE.0).AND.(KNY1.NE.0).AND.(INX2.GT.INY1)) THEN
+ L=MU(INX2)-INX2+INY1
+ SG=REAL(SIGN(1,KNY1)*SIGN(1,KNX2))
+ SYS(L)=SYS(L)-SG*DINV*REAL(CTRAN(I,J)) ! x y
+ ENDIF
+ 50 CONTINUE
+ 55 CONTINUE
+ DO 65 K2=0,IELEM-1
+ DO 60 K1=0,IELEM-1
+ JND1=KN(NUM,1)+K2*IELEM+K1
+ JND2=KN(NUM,2)+K2*IELEM+K1
+ JND3=KN(NUM,3)+K2*IELEM+K1
+ L=MU(JND1)
+ SYS(L)=SYS(L)+TTTT*SIG
+ L=MU(JND2)
+ SYS(L)=SYS(L)+TTTT*SIG
+ L=MU(JND3)
+ SYS(L)=SYS(L)+TTTT*SIG
+ 60 CONTINUE
+ 65 CONTINUE
+ 70 CONTINUE
+ ELSE
+* CROSS SECTION SYSTEM MATRIX ASSEMBLY
+ NUM=0
+ DO 90 KEL=1,NBLOS
+ IF(IPERT(KEL).EQ.0) GO TO 90
+ IBM=MAT(1,IPERT(KEL))
+ IF(IBM.EQ.0) GO TO 90
+ NUM=NUM+1
+ SIG=SGD(IBM,1)
+ DO 85 K2=0,IELEM-1
+ DO 80 K1=0,IELEM-1
+ JND1=KN(NUM,1)+K2*IELEM+K1
+ JND2=KN(NUM,2)+K2*IELEM+K1
+ JND3=KN(NUM,3)+K2*IELEM+K1
+ L=MU(JND1)
+ SYS(L)=SYS(L)+TTTT*SIG
+ L=MU(JND2)
+ SYS(L)=SYS(L)+TTTT*SIG
+ L=MU(JND3)
+ SYS(L)=SYS(L)+TTTT*SIG
+ 80 CONTINUE
+ 85 CONTINUE
+ 90 CONTINUE
+ ENDIF
+ RETURN
+ END
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