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|
*DECK BIVPRH
SUBROUTINE BIVPRH (MAXEV,MAXKN,IMPX,ISPLH,LX,IHEX,NCODE,ICODE,
1 ZCODE,MAT,SIDE,LL4,NELEM,VOL,KN,QFR,IQFR,BFR,MUW)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Numbering corresponding to a mesh corner finite difference or linear
* Lagrangian finite element discretization of a 2-D hexagonal 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
* MAXEV maximum number of unknowns.
* MAXKN dimension for arrays KN, QFR and BFR.
* IMPX print parameter.
* ISPLH type of hexagonal mesh-splitting:
* =1: hexagonal elements; >1: 6*(ISPLH-1)**2 triangular elements
* per hexagon.
* LX number of hexagons.
* IHEX type of hexagonal boundary condition.
* 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)=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 hexagon.
* SIDE side of the hexagon.
*
*Parameters: output
* LL4 order of system matrices.
* NELEM number of finite elements (hexagons or triangles) excluding
* the virtual elements.
* VOL volume of each hexagon.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* IQFR element-ordered physical albedo indices.
* BFR element-ordered surface fractions.
* MUW compressed storage mode indices.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MAXEV,MAXKN,IMPX,ISPLH,LX,IHEX,NCODE(4),ICODE(4),MAT(LX),
1 LL4,NELEM,KN(MAXKN),IQFR(MAXKN),MUW(LL4)
REAL ZCODE(4),SIDE,VOL(LX),QFR(MAXKN),BFR(MAXKN)
*----
* LOCAL VARIABLES
*----
INTEGER ISR(6,2),JCR(6),KK(6),ISRH(6,2),ISRT(3,2),ISRT2(3,2)
CHARACTER HSMG*131
LOGICAL LOG
INTEGER, DIMENSION(:), ALLOCATABLE :: IGAR,KN1
ALB(X)=0.5*(1.0-X)/(1.0+X)
DATA ISRH/2,1,4,5,6,3,1,4,5,6,3,2/
DATA ISRT/1,2,3,2,3,1/
DATA ISRT2/3,1,2,2,3,1/
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IGAR(MAXEV),KN1(MAXKN))
*
IF(IMPX.GT.0) WRITE(6,500)
IF(ISPLH.EQ.1) THEN
NSURF=6
MAXNH=LX
ELSE
NSURF=3
MAXNH=(6*(ISPLH-1)**2)*LX
ENDIF
CALL BIVSBH (MAXNH,MAXKN,IMPX,ISPLH,LX,SIDE,NELEM,IHEX,NCODE,
1 MAT,VOL,KN1,QFR)
IF(NELEM*NSURF.GT.MAXKN) THEN
WRITE(HSMG,'(28HBIVPRH: INSUFFICIENT MAXKN (,I7,10H). SHOULD ,
1 15HBE INCREASED TO,I7,1H.)') MAXKN,NELEM*NSURF
CALL XABORT(HSMG)
ENDIF
*----
* PRODUCE STANDARD MESH CORNER FINITE DIFFERENCE NUMBERING.
*----
DO 10 I=1,NELEM*(NSURF+1)
KN(I)=-98
10 CONTINUE
DO 20 IC=1,NSURF
IF(ISPLH.EQ.1) THEN
JCR(IC)=IC+3-(IC/4)*6
ISR(IC,1)=ISRH(IC,1)
ISR(IC,2)=ISRH(IC,2)
ELSE
IF(IC.EQ.1) JCR(1)=1
IF(IC.EQ.2) JCR(2)=3
IF(IC.EQ.3) JCR(3)=2
ISR(IC,1)=ISRT(IC,1)
ISR(IC,2)=ISRT(IC,2)
ENDIF
20 CONTINUE
*----
* SET ZERO BOUNDARY CONDITIONS
*----
NUM1=0
DO 30 KX=1,NELEM
DO 26 IC=1,NSURF
KY=ABS(KN1(NUM1+IC))
DO 25 I1=1,2
IF((KY.GT.NELEM).AND.(NCODE(1).EQ.7)) KN(NUM1+ISR(IC,I1))=-99
25 CONTINUE
26 CONTINUE
NUM1=NUM1+NSURF+1
30 CONTINUE
*
SURFTOT=0.0
LL4=0
NUM1=0
DO 50 KX=1,NELEM
DO 40 IC=1,NSURF
IF(NSURF.EQ.6) THEN
BFR(NUM1+IC)=QFR(NUM1+IC)*QFR(NUM1+7)/(1.5*SQRT(3.0)*SIDE)
IF((NCODE(1).EQ.1).AND.(ICODE(1).EQ.0)) THEN
QFR(NUM1+IC)=ALB(ZCODE(1))*QFR(NUM1+IC)*QFR(NUM1+7)/
1 (1.5*SQRT(3.0)*SIDE)
ELSE IF(NCODE(1).EQ.1) THEN
QFR(NUM1+IC)=QFR(NUM1+IC)*QFR(NUM1+7)/(1.5*SQRT(3.0)*SIDE)
ELSE
QFR(NUM1+IC)=0.0
ENDIF
ELSE
AA=SIDE/REAL(ISPLH-1)
BFR(NUM1+IC)=QFR(NUM1+IC)*QFR(NUM1+4)/(0.25*SQRT(3.0)*AA)
IF((NCODE(1).EQ.1).AND.(ICODE(1).EQ.0)) THEN
QFR(NUM1+IC)=ALB(ZCODE(1))*QFR(NUM1+IC)*QFR(NUM1+4)/
1 (0.25*SQRT(3.0)*AA)
ELSE IF(NCODE(1).EQ.1) THEN
QFR(NUM1+IC)=QFR(NUM1+IC)*QFR(NUM1+4)/(0.25*SQRT(3.0)*AA)
ELSE
QFR(NUM1+IC)=0.0
ENDIF
ENDIF
IQFR(NUM1+IC)=ICODE(1)
SURFTOT=SURFTOT+BFR(NUM1+IC)
KY0=KN1(NUM1+IC)
IF((KY0.LT.0).AND.(IHEX.NE.5).AND.(IHEX.NE.6)) GO TO 40
KY=ABS(KY0)
DO 35 I1=1,2
IND=ISR(IC,I1)
IF((KY.GT.NELEM).OR.(KY0.LT.0)) THEN
IF(KN(NUM1+IND).EQ.-98) THEN
LL4=LL4+1
KN(NUM1+IND)=LL4
ENDIF
ELSE
JND=ISR(JCR(IC),I1+1-(I1/2)*2)
IOF2=(KY-1)*(NSURF+1)+JND
IF(IOF2.GT.MAXKN) CALL XABORT('BIVPRH: ALGORITHM FAILURE 2.')
LOG=.FALSE.
IF(KN(IOF2).EQ.-99) THEN
KN(NUM1+IND)=-99
ELSE IF(KN(NUM1+IND).EQ.-98) THEN
LL4=LL4+1
KN(NUM1+IND)=LL4
IF(KY.NE.KX) KN(IOF2)=LL4
IF((KY.NE.KX).AND.(ISPLH.GT.1)) LOG=.TRUE.
ELSE IF(KN(NUM1+IND).EQ.-99) THEN
GO TO 35
ELSE IF((KN(IOF2).EQ.-98).AND.(KY.NE.KX)) THEN
KN(IOF2)=KN(NUM1+IND)
IF((KY.NE.KX).AND.(ISPLH.GT.1)) LOG=.TRUE.
ELSE IF((KN(NUM1+IND).NE.KN(IOF2)).AND.(KY.NE.KX)) THEN
CALL XABORT('BIVPRH: ALGORITHM FAILURE 3.')
ELSE IF((KY.NE.KX).AND.(ISPLH.GT.1)) THEN
LOG=.TRUE.
ENDIF
IF(LOG) THEN
KND=0
IF(JND.EQ.1) KND=2
IF(JND.EQ.2) KND=1
IF(JND.EQ.3) KND=3
KZ=KN1((KY-1)*4+ISRT2(JCR(IC),I1+1-(I1/2)*2))
IF((KZ.GT.0).AND.(KZ.LE.NELEM).AND.(KZ.NE.KY)) THEN
IF(KN((KZ-1)*4+KND).EQ.-99) THEN
KN(NUM1+IND)=-99
ELSE
KN((KZ-1)*4+KND)=KN(NUM1+IND)
ENDIF
ENDIF
ENDIF
ENDIF
35 CONTINUE
40 CONTINUE
KN(NUM1+NSURF+1)=KN1(KX*(NSURF+1))
NUM1=NUM1+NSURF+1
50 CONTINUE
*----
* COMPUTE THE SURFACE FRACTIONS.
*----
IF(SURFTOT.GT.0.0) THEN
DO 55 I=1,NUM1
BFR(I)=BFR(I)/SURFTOT
55 CONTINUE
ENDIF
*
NUM1=0
DO 150 KX=1,NELEM
DO 60 IC=1,NSURF
KK(IC)=KN1(NUM1+IC)
60 CONTINUE
IF(ISPLH.EQ.1) THEN
IF((KX.EQ.1).AND.((IHEX.EQ.1).OR.(IHEX.EQ.10))) THEN
DO 70 I=1,6
KN(I)=KN(2)
70 CONTINUE
ELSE IF((KX.EQ.1).AND.((IHEX.EQ.2).OR.(IHEX.EQ.11))) THEN
DO 80 I=1,6
KN(I)=KN(2)
80 CONTINUE
ELSE IF((KX.EQ.1).AND.(IHEX.EQ.3)) THEN
KN(3)=KN(1)
KN(4)=KN(2)
KN(5)=KN(1)
KN(6)=KN(2)
ELSE IF((KX.EQ.1).AND.(IHEX.EQ.4)) THEN
KN(3)=KN(1)
KN(4)=KN(1)
KN(5)=KN(2)
KN(6)=KN(1)
ELSE IF((KX.EQ.1).AND.(IHEX.EQ.5)) THEN
KN(3)=KN(1)
KN(4)=KN(2)
KN(5)=KN(1)
KN(6)=KN(2)
ELSE IF((KX.EQ.1).AND.(IHEX.EQ.6)) THEN
KN(4)=KN(3)
KN(5)=KN(2)
KN(6)=KN(1)
ELSE IF((KK(1).EQ.-KK(5)).AND.(KK(2).EQ.-KK(4)).AND.
1 (KK(3).EQ.-KK(5)).AND.(KK(6).EQ.-KK(4))) THEN
DO 90 I=1,6
KN(NUM1+I)=KN(NUM1+6)
90 CONTINUE
ELSE IF((KK(1).EQ.-KK(3)).AND.(KK(4).EQ.-KK(2)).AND.
1 (KK(5).EQ.-KK(3)).AND.(KK(6).EQ.-KK(2))) THEN
DO 100 I=1,6
KN(NUM1+I)=KN(NUM1+4)
100 CONTINUE
ELSE IF((KK(1).EQ.-KK(6)).AND.(KK(2).EQ.-KK(5)).AND.
1 (KK(3).EQ.-KK(4))) THEN
KN(NUM1+3)=KN(NUM1+1)
KN(NUM1+6)=KN(NUM1+4)
ELSE IF((KK(5).EQ.-KK(4)).AND.(KK(6).EQ.-KK(3)).AND.
1 (KK(1).EQ.-KK(2))) THEN
KN(NUM1+4)=KN(NUM1+2)
KN(NUM1+5)=KN(NUM1+3)
ELSE IF((KK(1).EQ.-KK(3)).AND.(KK(4).EQ.-KK(3)).AND.
1 (KK(5).EQ.-KK(2)).AND.(KK(6).EQ.-KK(3))) THEN
KN(NUM1+1)=KN(NUM1+4)
KN(NUM1+2)=KN(NUM1+5)
KN(NUM1+3)=KN(NUM1+4)
KN(NUM1+6)=KN(NUM1+4)
ELSE IF((KK(2).EQ.-KK(6)).AND.(KK(3).EQ.-KK(5)).AND.
1 (KK(2).LT.0)) THEN
KN(NUM1+1)=KN(NUM1+2)
KN(NUM1+4)=KN(NUM1+3)
KN(NUM1+5)=KN(NUM1+6)
ELSE IF((KK(1).EQ.-KK(3)).AND.(KK(6).EQ.-KK(4)).AND.
1 (KK(1).LT.0)) THEN
KN(NUM1+1)=KN(NUM1+4)
KN(NUM1+2)=KN(NUM1+5)
KN(NUM1+3)=KN(NUM1+6)
ELSE IF((KK(4).EQ.-KK(2)).AND.(KK(5).EQ.-KK(1)).AND.
1 (KK(4).LT.0)) THEN
KN(NUM1+3)=KN(NUM1+2)
KN(NUM1+5)=KN(NUM1+4)
KN(NUM1+6)=KN(NUM1+1)
ELSE IF((KK(3).EQ.-KK(1)).AND.(KK(4).EQ.-KK(6)).AND.
1 (KK(3).LT.0)) THEN
KN(NUM1+4)=KN(NUM1+1)
KN(NUM1+5)=KN(NUM1+2)
KN(NUM1+6)=KN(NUM1+3)
ENDIF
DO 120 IC=1,NSURF
IF((KK(IC).LT.0).AND.((IHEX.EQ.5).OR.(IHEX.EQ.6)).AND.
1 (KX.GT.1)) THEN
IS=0
DO 110 I=1,6
IF(-KN1((-KK(IC)-1)*7+I).EQ.KX) IS=I
110 CONTINUE
IF(IS.EQ.0) CALL XABORT('BIVPRH: ALGORITHM FAILURE 4.')
KN((-KK(IC)-1)*7+ISRH(IS,2))=KN(NUM1+ISRH(IC,1))
KN((-KK(IC)-1)*7+ISRH(IS,1))=KN(NUM1+ISRH(IC,2))
ENDIF
120 CONTINUE
ELSE
IF((IHEX.NE.5).AND.(IHEX.NE.6)) THEN
IF((KK(1).EQ.-KK(2)).AND.(KK(1).LT.0)) THEN
KN(NUM1+1)=KN(NUM1+3)
ELSE IF((KK(1).EQ.-KK(3)).AND.(KK(1).LT.0)) THEN
KN(NUM1+2)=KN(NUM1+3)
ELSE IF((KK(2).EQ.-KK(3)).AND.(KK(2).LT.0)) THEN
KN(NUM1+2)=KN(NUM1+1)
ELSE IF((KK(2).EQ.-KK(1)).AND.(KK(2).LT.0)) THEN
KN(NUM1+3)=KN(NUM1+1)
ELSE IF((KK(3).EQ.-KK(1)).AND.(KK(3).LT.0)) THEN
KN(NUM1+3)=KN(NUM1+2)
ELSE IF((KK(3).EQ.-KK(2)).AND.(KK(3).LT.0)) THEN
KN(NUM1+1)=KN(NUM1+2)
ENDIF
ENDIF
DO 140 IC=1,NSURF
IF((KK(IC).LT.0).AND.((IHEX.EQ.5).OR.(IHEX.EQ.6))) THEN
IS=0
DO 130 I=1,3
IF(-KN1((-KK(IC)-1)*4+I).EQ.KX) IS=I
130 CONTINUE
IF(IS.EQ.0) CALL XABORT('BIVPRH: ALGORITHM FAILURE 5.')
KY=-KK(IC)
DO 135 I1=1,2
J1=I1+1-(I1/2)*2
IND=ISRT(IC,I1)
JND=ISRT(IS,J1)
KN((-KK(IC)-1)*4+JND)=KN(NUM1+IND)
KND=0
IF(JND.EQ.1) KND=2
IF(JND.EQ.2) KND=1
IF(JND.EQ.3) KND=3
KZ=KN1((-KK(IC)-1)*4+ISRT2(IS,J1))
IF((KZ.GT.0).AND.(KZ.LE.NELEM).AND.(KZ.NE.KY)) THEN
KNZ=KN((KZ-1)*4+KND)
KN((KZ-1)*4+KND)=KN(NUM1+IND)
IF(IHEX.EQ.6) THEN
DO 132 L=1,NELEM
DO 131 LC=1,NSURF
IF(KN((L-1)*4+LC).EQ.KNZ) KN((L-1)*4+LC)=KN(NUM1+IND)
131 CONTINUE
132 CONTINUE
ENDIF
ENDIF
135 CONTINUE
ENDIF
140 CONTINUE
ENDIF
NUM1=NUM1+NSURF+1
150 CONTINUE
LL5=0
DO 170 I=1,MAXEV
IGAR(I)=0
170 CONTINUE
NUM1=0
DO 190 I=1,NELEM
DO 180 IC=1,NSURF
IND=KN(NUM1+IC)
IF(IND.GT.MAXEV) THEN
WRITE(HSMG,'(28HBIVPRH: INSUFFICIENT MAXEV (,I7,10H). SHOULD ,
1 15HBE INCREASED TO,I7,1H.)') MAXEV,IND
CALL XABORT(HSMG)
ELSE IF(IND.EQ.-98) THEN
CALL XABORT('BIVPRH: ALGORITHM FAILURE 6.')
ELSE IF(IND.EQ.-99) THEN
KN(NUM1+IC)=0
ELSE IF(IGAR(IND).EQ.0) THEN
LL5=LL5+1
IGAR(IND)=LL5
ENDIF
180 CONTINUE
NUM1=NUM1+NSURF+1
190 CONTINUE
NUM1=0
DO 210 I=1,NELEM
DO 200 IC=1,NSURF
IF(KN(NUM1+IC).NE.0) THEN
IF(IGAR(KN(NUM1+IC)).EQ.0) CALL XABORT('BIVPRH: ALGORITHM FAI'
1 //'LURE 7.')
KN(NUM1+IC)=IGAR(KN(NUM1+IC))
ENDIF
200 CONTINUE
NUM1=NUM1+NSURF+1
210 CONTINUE
LL4=LL5
IF(IMPX.GT.0) WRITE(6,570) LL4
IF(LL4.GT.MAXEV) THEN
WRITE(HSMG,'(28HBIVPRH: INSUFFICIENT MAXEV (,I7,10H). SHOULD ,
1 15HBE INCREASED TO,I7,1H.)') MAXEV,LL4
CALL XABORT(HSMG)
ENDIF
IF(LL4.GT.MAXEV) CALL XABORT('BIVPRH: INSUFFICIENT MAXEV.')
*
IF((IMPX.GT.1).AND.(NSURF.EQ.6)) THEN
WRITE(6,510)
NUM1=0
DO 220 I=1,NELEM
WRITE(6,520) I,KN(NUM1+7),(KN(NUM1+J),J=1,6),(QFR(NUM1+J),
1 J=1,7)
NUM1=NUM1+7
220 CONTINUE
NUM1=0
WRITE (6,580)
DO 225 I=1,NELEM
IF(MAT(I).LE.0) GO TO 225
WRITE (6,590) I,(BFR(NUM1+J),J=1,6)
NUM1=NUM1+7
225 CONTINUE
ELSE IF((IMPX.GT.1).AND.(NSURF.EQ.3)) THEN
WRITE(6,530)
NUM1=0
DO 230 I=1,NELEM
WRITE(6,540) I,KN(NUM1+4),(KN(NUM1+J),J=1,3),(QFR(NUM1+J),
1 J=1,4),(BFR(NUM1+J),J=1,3)
NUM1=NUM1+4
230 CONTINUE
ENDIF
*----
* COMPUTE THE SYSTEM MATRIX BANDWIDTH.
*----
DO 240 I=1,LL4
MUW(I)=1
240 CONTINUE
NUM1=0
DO 270 K=1,NELEM
DO 260 I=1,NSURF
IND1=KN(NUM1+I)
IF(IND1.EQ.0) GO TO 260
DO 250 J=1,NSURF
IND2=KN(NUM1+J)
IF(IND2.EQ.0) GO TO 250
MUW(IND1)=MAX0(MUW(IND1),IND1-IND2+1)
250 CONTINUE
260 CONTINUE
NUM1=NUM1+NSURF+1
270 CONTINUE
IIMAX=0
DO 280 I=1,LL4
IIMAX=IIMAX+MUW(I)
MUW(I)=IIMAX
280 CONTINUE
IF(IMPX.GT.6) WRITE(6,550) 'MUW :',(MUW(I),I=1,LL4)
IF(IMPX.GT.2) WRITE(6,560) IIMAX
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(KN1,IGAR)
RETURN
*
500 FORMAT(//52H BIVPRH: NUMBERING FOR A MESH CORNER FINITE DIFFEREN,
1 60HCE OR LINEAR LAGRANGIAN FINITE ELEMENT DISCRETIZATION IN HEX,
2 16HAGONAL GEOMETRY.)
510 FORMAT(/31H BIVPRH: NUMBERING OF UNKNOWNS./1X,30(1H-)/9X,
1 7HHEXAGON,3X,8HUNKNOWNS,29X,23HVOID BOUNDARY CONDITION,45X,
2 6HVOLUME)
520 FORMAT (1X,2I6,2X,6I6,2X,1P,6E11.2,5X,E13.6)
530 FORMAT(/31H BIVPRH: NUMBERING OF UNKNOWNS./1X,30(1H-)/9X,
1 7HHEXAGON,3X,8HUNKNOWNS,11X,23HVOID BOUNDARY CONDITION,12X,
2 6HVOLUME,13X,16HSURFACE FRACTION)
540 FORMAT (1X,2I6,2X,3I6,2X,1P,3E11.2,5X,E13.6,5X,3E10.2)
550 FORMAT(/1X,A5/(1X,20I6))
560 FORMAT(/52H NUMBER OF TERMS IN THE COMPRESSED SYSTEM MATRICES =,
> I6)
570 FORMAT(/39H BIVPRH: NUMBER OF UNKNOWNS PER GROUP =,I6/)
580 FORMAT (//17H SURFACE FRACTION//8H HEXAGON,5X,3HBFR)
590 FORMAT (3X,I4,4X,1P,6E10.2)
END
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