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*DECK BIVDKN
SUBROUTINE BIVDKN (MAXEV,IMPX,LX,LY,CYLIND,IELEM,ICOL,L4,NCODE,
1 ICODE,ZCODE,MAT,VOL,XXX,YYY,XX,YY,DD,KN,QFR,IQFR,BFR,IDL,MU)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Numbering corresponding to a mixed-dual formulation of the finite-
* element discretization in a 2-D geometry. This version does not
* support diagonal symmetries.
*
*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
* MAXEV allocated storage for vector MU.
* IMPX print parameter.
* LX number of elements along the X axis.
* LY number of elements along the Y axis.
* 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).
* NCODE type of boundary condition applied on each side
* (i=1: X- i=2: X+ i=3: Y- i=4: Y+):
* NCODE(I)=1: VOID; NCODE(I)=2: REFL; NCODE(I)=4: TRAN;
* NCODE(I)=5: SYME; NCODE(I)=7: ZERO.
* ICODE physical albedo index on each side of the domain.
* ZCODE ZCODE(I) is the albedo corresponding to boundary condition
* 'VOID' on each side (ZCODE(I)=0.0 by default).
* MAT mixture index assigned to each element.
* XXX Cartesian coordinates along the X axis.
* YYY Cartesian coordinates along the Y axis.
*
*Parameters: output
* L4 total number of unknown (variational coefficients) per
* energy group (order of system matrices).
* VOL volume of each element.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* DD value used with a cylindrical geometry.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* IQFR element-ordered physical albedo indices.
* BFR element-ordered surface fractions.
* IDL position of integrated fluxes into unknown vector.
* MU compressed storage mode indices.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MAXEV,IMPX,LX,LY,IELEM,ICOL,L4,NCODE(4),ICODE(4),
1 MAT(LX*LY),KN(5*LX*LY),IQFR(4*LX*LY),IDL(LX*LY),MU(MAXEV)
REAL ZCODE(4),VOL(LX*LY),XXX(LX+1),YYY(LY+1),XX(LX*LY),YY(LX*LY),
1 DD(LX*LY),QFR(4*LX*LY),BFR(4*LX*LY)
LOGICAL CYLIND
*----
* LOCAL VARIABLES
*----
LOGICAL COND,LOG1,LOG2,LOG3,LOG4
CHARACTER TEXT8*8
REAL ZALB(4)
INTEGER, DIMENSION(:), ALLOCATABLE :: IP
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IP(MAXEV))
*----
* IDENTIFICATION OF THE GEOMETRY. MAIN LOOP OVER THE ELEMENTS.
*----
DO 10 I=1,4
IF(ZCODE(I).NE.1.0) THEN
ZALB(I)=2.0*(1.0+ZCODE(I))/(1.0-ZCODE(I))
ELSE
ZALB(I)=1.0E20
ENDIF
10 CONTINUE
IF(IMPX.GT.0) WRITE(6,700) LX,LY
KN(:5*LX*LY)=0
SURFTOT=0.0
NUM1=0
NUM2=0
KEL=0
DO 151 K1=1,LY
DO 150 K2=1,LX
KEL=KEL+1
XX(KEL)=0.0
YY(KEL)=0.0
VOL(KEL)=0.0
IF(MAT(KEL).EQ.0) GO TO 150
XX(KEL)=XXX(K2+1)-XXX(K2)
YY(KEL)=YYY(K1+1)-YYY(K1)
IF(CYLIND) DD(KEL)=0.5*(XXX(K2)+XXX(K2+1))
IND1=(K1-1)*(3*LX+1)
KN(NUM1+1)=IND1+LX+2*K2
KN(NUM1+2)=IND1+LX+2*K2-1
KN(NUM1+3)=IND1+LX+2*K2+1
KN(NUM1+4)=IND1+K2
KN(NUM1+5)=IND1+3*LX+K2+1
QFR(NUM2+1:NUM2+4)=0.0
IQFR(NUM2+1:NUM2+4)=0
BFR(NUM2+1:NUM2+4)=0.0
FRX=1.0
FRY=1.0
*----
* VOID, REFL OR ZERO BOUNDARY CONTITION.
*----
IF(K2.EQ.1) THEN
LOG1=.TRUE.
ELSE
LOG1=(MAT(KEL-1).EQ.0)
ENDIF
IF(LOG1) THEN
COND=(NCODE(1).EQ.2).OR.((NCODE(1).EQ.1).AND.(ZCODE(1).EQ.1.0))
IF(COND) THEN
KN(NUM1+2)=0
ELSE IF(NCODE(1).EQ.1) THEN
IF(ICODE(1).EQ.0) THEN
QFR(NUM2+1)=ZALB(1)
ELSE
QFR(NUM2+1)=1.0
IQFR(NUM2+1)=ICODE(1)
ENDIF
ENDIF
ENDIF
*
IF(K2.EQ.LX) THEN
LOG2=.TRUE.
ELSE
LOG2=(MAT(KEL+1).EQ.0)
ENDIF
IF(LOG2) THEN
COND=(NCODE(2).EQ.2).OR.((NCODE(2).EQ.1).AND.(ZCODE(2).EQ.1.0))
IF(COND) THEN
KN(NUM1+3)=0
ELSE IF(NCODE(2).EQ.1) THEN
IF(ICODE(2).EQ.0) THEN
QFR(NUM2+2)=ZALB(2)
ELSE
QFR(NUM2+2)=1.0
IQFR(NUM2+2)=ICODE(2)
ENDIF
ENDIF
ENDIF
*
IF(K1.EQ.1) THEN
LOG3=.TRUE.
ELSE
LOG3=(MAT(KEL-LX).EQ.0)
ENDIF
IF(LOG3) THEN
COND=(NCODE(3).EQ.2).OR.((NCODE(3).EQ.1).AND.(ZCODE(3).EQ.1.0))
IF(COND) THEN
KN(NUM1+4)=0
ELSE IF(NCODE(3).EQ.1) THEN
IF(ICODE(3).EQ.0) THEN
QFR(NUM2+3)=ZALB(3)
ELSE
QFR(NUM2+3)=1.0
IQFR(NUM2+3)=ICODE(3)
ENDIF
ENDIF
ENDIF
*
IF(K1.EQ.LY) THEN
LOG4=.TRUE.
ELSE
LOG4=(MAT(KEL+LX).EQ.0)
ENDIF
IF(LOG4) THEN
COND=(NCODE(4).EQ.2).OR.((NCODE(4).EQ.1).AND.(ZCODE(4).EQ.1.0))
IF(COND) THEN
KN(NUM1+5)=0
ELSE IF(NCODE(4).EQ.1) THEN
IF(ICODE(4).EQ.0) THEN
QFR(NUM2+4)=ZALB(4)
ELSE
QFR(NUM2+4)=1.0
IQFR(NUM2+4)=ICODE(4)
ENDIF
ENDIF
ENDIF
*----
* TRAN BOUNDARY CONDITION.
*----
IF((K2.EQ.LX).AND.(NCODE(2).EQ.4)) THEN
KN(NUM1+3)=KN(NUM1+3)-2*LX
ENDIF
IF((K1.EQ.LY).AND.(NCODE(4).EQ.4)) THEN
KN(NUM1+5)=K2
ENDIF
*----
* SYME BOUNDARY CONDITION.
*----
IF((NCODE(1).EQ.5).AND.(K2.EQ.1)) THEN
QFR(NUM2+1)=QFR(NUM2+2)
IQFR(NUM2+1)=IQFR(NUM2+2)
FRX=0.5
KN(NUM1+2)=-KN(NUM1+3)
ELSE IF((NCODE(2).EQ.5).AND.(K2.EQ.LX)) THEN
QFR(NUM2+2)=QFR(NUM2+1)
IQFR(NUM2+2)=IQFR(NUM2+1)
FRX=0.5
KN(NUM1+3)=-KN(NUM1+2)
ENDIF
IF((NCODE(3).EQ.5).AND.(K1.EQ.1)) THEN
QFR(NUM2+3)=QFR(NUM2+4)
FRY=0.5
KN(NUM1+4)=-KN(NUM1+5)
ELSE IF((NCODE(4).EQ.5).AND.(K1.EQ.LY)) THEN
QFR(NUM2+4)=QFR(NUM2+3)
IQFR(NUM2+4)=IQFR(NUM2+3)
FRY=0.5
KN(NUM1+5)=-KN(NUM1+4)
ENDIF
*
VOL0=XX(KEL)*YY(KEL)*FRX*FRY
IF(CYLIND) THEN
VOL0=6.2831853072*DD(KEL)*VOL0
ENDIF
VOL(KEL)=VOL0
QFR(NUM2+1)=QFR(NUM2+1)*VOL0/XX(KEL)
QFR(NUM2+2)=QFR(NUM2+2)*VOL0/XX(KEL)
QFR(NUM2+3)=QFR(NUM2+3)*VOL0/YY(KEL)
QFR(NUM2+4)=QFR(NUM2+4)*VOL0/YY(KEL)
*
IF(((NCODE(1).EQ.1).OR.(NCODE(1).EQ.7)).AND.LOG1)
1 BFR(NUM2+1)=VOL0/XX(KEL)
IF(((NCODE(2).EQ.1).OR.(NCODE(2).EQ.7)).AND.LOG2)
1 BFR(NUM2+2)=VOL0/XX(KEL)
IF(((NCODE(3).EQ.1).OR.(NCODE(3).EQ.7)).AND.LOG3)
1 BFR(NUM2+3)=VOL0/YY(KEL)
IF(((NCODE(4).EQ.1).OR.(NCODE(4).EQ.7)).AND.LOG4)
1 BFR(NUM2+4)=VOL0/YY(KEL)
SURFTOT=SURFTOT+BFR(NUM2+1)+BFR(NUM2+2)+BFR(NUM2+3)+BFR(NUM2+4)
NUM1=NUM1+5
NUM2=NUM2+4
150 CONTINUE
151 CONTINUE
* END OF THE MAIN LOOP OVER ELEMENTS.
*
* COMPUTE THE SURFACE FRACTIONS.
IF(SURFTOT.GT.0.0) THEN
DO 155 I=1,4*LX*LY
BFR(I)=BFR(I)/SURFTOT
155 CONTINUE
ENDIF
*----
* REMOVING THE UNUSED UNKNOWNS INDICES FROM KN.
*----
LL4=LY*(3*LX+1)+LX
WRITE (TEXT8,'(I8)') LL4
IF(LL4.GT.MAXEV) CALL XABORT('BIVDKN: MAXEV SHOULD BE INCREASED '
1 //'TO'//TEXT8//'.')
DO 160 IND=1,LL4
IP(IND)=0
160 CONTINUE
DO 170 NUM1=1,5*LX*LY
IF(KN(NUM1).NE.0) IP(ABS(KN(NUM1)))=1
170 CONTINUE
L4=0
DO 180 IND=1,LL4
IF(IP(IND).EQ.1) THEN
L4=L4+1
IP(IND)=L4
ENDIF
180 CONTINUE
DO 190 NUM1=1,5*LX*LY
IF(KN(NUM1).NE.0) KN(NUM1)=SIGN(IP(ABS(KN(NUM1))),KN(NUM1))
190 CONTINUE
*----
* PROCESS CASES WITH IELEM.GT.1.
*----
IF(IELEM.GT.1) THEN
LL4=0
DO 220 IND=1,L4
IP(IND)=LL4+1
NUM1=0
DO 210 KEL=1,LX*LY
IF(MAT(KEL).EQ.0) GO TO 210
IF(ABS(KN(NUM1+1)).EQ.IND) THEN
LL4=LL4+IELEM**2
GO TO 220
ELSE
DO 200 I=2,5
IF(ABS(KN(NUM1+I)).EQ.IND) THEN
LL4=LL4+IELEM
GO TO 220
ENDIF
200 CONTINUE
ENDIF
NUM1=NUM1+5
210 CONTINUE
CALL XABORT('BIVDKN: FAILURE OF THE RENUMBERING ALGORITHM.')
220 CONTINUE
L4=LL4
DO 230 NUM1=1,5*LX*LY
IF(KN(NUM1).NE.0) KN(NUM1)=SIGN(IP(ABS(KN(NUM1))),KN(NUM1))
230 CONTINUE
ENDIF
NUM1=0
DO 235 KEL=1,LX*LY
IDL(KEL)=0
IF(MAT(KEL).EQ.0) GO TO 235
IDL(KEL)=KN(NUM1+1)
NUM1=NUM1+5
235 CONTINUE
WRITE (TEXT8,'(I8)') L4
IF(L4.GT.MAXEV) CALL XABORT('BIVDKN: MAXEV SHOULD BE INCREASED TO'
1 //TEXT8//'.')
IF(IMPX.GT.2) WRITE(6,710) (VOL(I),I=1,LX*LY)
*----
* COMPUTE THE SYSTEM MATRIX BANDWIDTH.
*----
DO 240 I=1,L4
MU(I)=1
240 CONTINUE
NUM1=0
DO 270 KEL=1,LX*LY
IF(MAT(KEL).EQ.0) GO TO 270
DO 260 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 250 J0=1,IELEM
JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
IF(IELEM.GE.4) MU(JND1)=MAX(MU(JND1),J0)
IF(KN(NUM1+2).NE.0) THEN
MU(JND1)=MAX(MU(JND1),JND1-INX1+1)
MU(INX1)=MAX(MU(INX1),INX1-JND1+1)
ENDIF
IF(KN(NUM1+3).NE.0) THEN
MU(INX2)=MAX(MU(INX2),INX2-JND1+1)
MU(JND1)=MAX(MU(JND1),JND1-INX2+1)
ENDIF
JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
IF(IELEM.GE.4) MU(JND1)=MAX(MU(JND1),(J0-1)*IELEM+1)
IF(KN(NUM1+4).NE.0) THEN
MU(JND1)=MAX(MU(JND1),JND1-INY1+1)
MU(INY1)=MAX(MU(INY1),INY1-JND1+1)
ENDIF
IF(KN(NUM1+5).NE.0) THEN
MU(INY2)=MAX(MU(INY2),INY2-JND1+1)
MU(JND1)=MAX(MU(JND1),JND1-INY2+1)
ENDIF
250 CONTINUE
IF(ICOL.NE.2) THEN
IF((KN(NUM1+2).NE.0).AND.(KN(NUM1+3).NE.0)) THEN
MU(INX2)=MAX(MU(INX2),INX2-INX1+1)
MU(INX1)=MAX(MU(INX1),INX1-INX2+1)
ENDIF
IF((KN(NUM1+4).NE.0).AND.(KN(NUM1+5).NE.0)) THEN
MU(INY2)=MAX(MU(INY2),INY2-INY1+1)
MU(INY1)=MAX(MU(INY1),INY1-INY2+1)
ENDIF
ENDIF
260 CONTINUE
NUM1=NUM1+5
270 CONTINUE
IIMAX=0
DO 280 I=1,L4
IIMAX=IIMAX+MU(I)
MU(I)=IIMAX
280 CONTINUE
*
IF(IMPX.GT.2) THEN
WRITE (6,720) IIMAX
NUM1=0
NUM2=0
WRITE (6,750)
DO 500 K=1,LX*LY
IF(MAT(K).EQ.0) GO TO 500
WRITE (6,755) K,(KN(NUM1+I),I=1,5),(QFR(NUM2+I),I=1,4),
1 (BFR(NUM2+I),I=1,4)
NUM1=NUM1+5
NUM2=NUM2+4
500 CONTINUE
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(IP)
RETURN
*
700 FORMAT(/42H BIVDKN: MIXED-DUAL FINITE ELEMENT METHOD.//7H NUMBER,
1 27H OF ELEMENTS ALONG X AXIS =,I3/26H NUMBER OF ELEMENTS ALONG ,
2 8HY AXIS =,I3)
710 FORMAT(/20H VOLUMES PER ELEMENT/(1X,1P,10E13.4))
720 FORMAT(/52H NUMBER OF TERMS IN THE COMPRESSED SYSTEM MATRICES =,
1 I7)
750 FORMAT(/22H NUMBERING OF UNKNOWNS/1X,21(1H-)//
1 8H ELEMENT,2X,7HNUMBERS,30X,23HVOID BOUNDARY CONDITION,23X,
2 17HSURFACE FRACTIONS)
755 FORMAT (1X,I4,2X,5I7,2X,1P,4E11.2,3X,4E10.2)
END
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