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|
*DECK BIVPKN
SUBROUTINE BIVPKN (MAXEV,IMPX,LX,LY,CYLIND,IELEM,L4,NCODE,ICODE,
1 ZCODE,MAT,VOL,XXX,YYY,XX,YY,DD,KN,QFR,IQFR,BFR,MU)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Numbering corresponding to a mesh corner finite difference or primal
* 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).
* 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 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 values 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.
* MU compressed storage mode indices.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER MAXEV,IMPX,LX,LY,IELEM,L4,NCODE(4),ICODE(4),MAT(LX*LY),
1 KN(LX*LY*IELEM*IELEM),IQFR(4*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 LOG1,LOG2,LOG3,LOG4
INTEGER, DIMENSION(:), ALLOCATABLE :: IP,IWRK
*
ALB(X)=0.5*(1.0-X)/(1.0+X)
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IP((IELEM*LX+1)*(IELEM*LY+1)))
ALLOCATE(IWRK((IELEM*LX+1)*(IELEM*LY+1)))
*----
* IDENTIFICATION OF THE GEOMETRY. MAIN LOOP OVER THE ELEMENTS.
*----
IF(IMPX.GT.0) WRITE(6,700) LX,LY
LC=1+IELEM
LL=LC*LC
IX=LX*(LC-1)+1
IXY=(LY*(LC-1)+1)*IX
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).LE.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=(LC-1)*((K1-1)*IX+(K2-1))
L=0
DO 15 I=1,LC
DO 10 J=1,LC
L=L+1
KN(NUM1+L)=IND1+(I-1)*IX+J
10 CONTINUE
15 CONTINUE
DO 20 IC=1,4
QFR(NUM2+IC)=0.0
IQFR(NUM2+IC)=0
BFR(NUM2+IC)=0.0
20 CONTINUE
KK1=KEL-1
KK2=KEL+1
KK3=KEL-LX
KK4=KEL+LX
FRX=1.0
FRY=1.0
*----
* VOID, REFL OR ZERO BOUNDARY CONDITION.
*----
IF(K2.EQ.1) THEN
LOG1=.TRUE.
ELSE
LOG1=(MAT(KK1).EQ.0)
ENDIF
IF(LOG1) THEN
IF(NCODE(1).EQ.1) THEN
IF(ICODE(1).EQ.0) THEN
QFR(NUM2+1)=ALB(ZCODE(1))
ELSE
QFR(NUM2+1)=1.0
IQFR(NUM2+1)=ICODE(1)
ENDIF
ELSE IF(NCODE(1).EQ.7) THEN
L=0
DO 35 I=1,LC
DO 30 J=1,LC
L=L+1
IF(J.EQ.1) KN(NUM1+L)=0
30 CONTINUE
35 CONTINUE
ENDIF
ENDIF
*
IF(K2.EQ.LX) THEN
LOG2=.TRUE.
ELSE
LOG2=(MAT(KK2).EQ.0)
ENDIF
IF(LOG2) THEN
IF(NCODE(2).EQ.1) THEN
IF(ICODE(2).EQ.0) THEN
QFR(NUM2+2)=ALB(ZCODE(2))
ELSE
QFR(NUM2+2)=1.0
IQFR(NUM2+2)=ICODE(2)
ENDIF
ELSE IF(NCODE(2).EQ.7) THEN
L=0
DO 45 I=1,LC
DO 40 J=1,LC
L=L+1
IF(J.EQ.LC) KN(NUM1+L)=0
40 CONTINUE
45 CONTINUE
ENDIF
ENDIF
*
IF(K1.EQ.1) THEN
LOG3=.TRUE.
ELSE
LOG3=(MAT(KK3).EQ.0)
ENDIF
IF(LOG3) THEN
IF(NCODE(3).EQ.1) THEN
IF(ICODE(3).EQ.0) THEN
QFR(NUM2+3)=ALB(ZCODE(3))
ELSE
QFR(NUM2+3)=1.0
IQFR(NUM2+3)=ICODE(3)
ENDIF
ELSE IF(NCODE(3).EQ.7) THEN
L=0
DO 55 I=1,LC
DO 50 J=1,LC
L=L+1
IF(I.EQ.1) KN(NUM1+L)=0
50 CONTINUE
55 CONTINUE
ENDIF
ENDIF
*
IF(K1.EQ.LY) THEN
LOG4=.TRUE.
ELSE
LOG4=(MAT(KK4).EQ.0)
ENDIF
IF(LOG4) THEN
IF(NCODE(4).EQ.1) THEN
IF(ICODE(4).EQ.0) THEN
QFR(NUM2+4)=ALB(ZCODE(4))
ELSE
QFR(NUM2+4)=1.0
IQFR(NUM2+4)=ICODE(4)
ENDIF
ELSE IF(NCODE(4).EQ.7) THEN
L=0
DO 65 I=1,LC
DO 60 J=1,LC
L=L+1
IF(I.EQ.LC) KN(NUM1+L)=0
60 CONTINUE
65 CONTINUE
ENDIF
ENDIF
*----
* TRAN BOUNDARY CONDITION.
*----
IF((K2.EQ.LX).AND.(NCODE(2).EQ.4)) THEN
DO 70 I=1,LC
M=(I-1)*LC+LC
KN(NUM1+M)=KN(NUM1+M)-IX+1
70 CONTINUE
ENDIF
IF((K1.EQ.LY).AND.(NCODE(4).EQ.4)) THEN
DO 80 I=1,LC
M=(LC-1)*LC+I
KN(NUM1+M)=KN(NUM1+M)-IXY+IX
80 CONTINUE
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
DO 95 I=1,LC
DO 90 J=1,(LC+1)/2
L=(I-1)*LC+J
M=(I-1)*LC+(LC-J+1)
KN(NUM1+L)=KN(NUM1+M)
90 CONTINUE
95 CONTINUE
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
DO 105 I=1,LC
DO 100 J=(LC+2)/2,LC
L=(I-1)*LC+J
M=(I-1)*LC+(LC-J+1)
KN(NUM1+L)=KN(NUM1+M)
100 CONTINUE
105 CONTINUE
ENDIF
IF((NCODE(3).EQ.5).AND.(K1.EQ.1)) THEN
QFR(NUM2+3)=QFR(NUM2+4)
IQFR(NUM2+3)=IQFR(NUM2+4)
FRY=0.5
DO 115 I=1,(LC+1)/2
DO 110 J=1,LC
L=(I-1)*LC+J
M=(LC-I)*LC+J
KN(NUM1+L)=KN(NUM1+M)
110 CONTINUE
115 CONTINUE
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
DO 125 I=(LC+2)/2,LC
DO 120 J=1,LC
L=(I-1)*LC+J
M=(LC-I)*LC+J
KN(NUM1+L)=KN(NUM1+M)
120 CONTINUE
125 CONTINUE
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+LL
NUM2=NUM2+4
150 CONTINUE
151 CONTINUE
* END OF THE MAIN LOOP OVER THE 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
*----
* TREATMENT OF 1D CASES.
*----
LOG1=(LX.EQ.1).AND.(NCODE(1).EQ.2).AND.(NCODE(2).EQ.5)
1 .AND.(IELEM.GT.1)
LOG2=(LX.EQ.1).AND.(NCODE(1).EQ.5).AND.(NCODE(2).EQ.2)
1 .AND.(IELEM.GT.1)
IF(LOG1.OR.LOG2) THEN
NUM1=0
DO 170 KEL=1,LX*LY
IF(MAT(KEL).EQ.0) GO TO 170
DO 165 I=1,LC
DO 160 J=2,LC
KN(NUM1+(I-1)*LC+J)=KN(NUM1+(I-1)*LC+1)
160 CONTINUE
165 CONTINUE
NUM1=NUM1+LL
170 CONTINUE
ENDIF
LOG1=(LY.EQ.1).AND.(NCODE(3).EQ.2).AND.(NCODE(4).EQ.5)
1 .AND.(IELEM.GT.1)
LOG2=(LY.EQ.1).AND.(NCODE(3).EQ.5).AND.(NCODE(4).EQ.2)
1 .AND.(IELEM.GT.1)
IF(LOG1.OR.LOG2) THEN
NUM1=0
DO 190 KEL=1,LX*LY
IF(MAT(KEL).EQ.0) GO TO 190
DO 185 I=2,LC
DO 180 J=1,LC
KN(NUM1+(I-1)*LC+J)=KN(NUM1+J)
180 CONTINUE
185 CONTINUE
NUM1=NUM1+LL
190 CONTINUE
ENDIF
*----
* JUXTAPOSITION OF A CHECKERBOARD OVER THE REACTOR DOMAIN.
*----
LYTOT=LY*(LC-1)+1
LXTOT=LX*(LC-1)+1
DO 220 I=1,LXTOT*LYTOT
IWRK(I)=-1
220 CONTINUE
NUM1=0
KEL=0
DO 245 K1=1,LY
LK1=(K1-1)*(LC-1)
DO 240 K2=1,LX
KEL=KEL+1
IF(MAT(KEL).EQ.0) GO TO 240
LK2=(K2-1)*(LC-1)
L=0
DO 235 IK1=LK1+1,LK1+LC
I1=(IK1-1)*LXTOT
DO 230 IK2=LK2+1,LK2+LC
I2=I1+IK2
L=L+1
IND1=KN(NUM1+L)
IF(IND1.EQ.0) THEN
IWRK(I2)=0
GO TO 230
ENDIF
IF(IWRK(I2).EQ.-1) THEN
IWRK(I2)=IND1
ELSE IF(IWRK(I2).EQ.0) THEN
KN(NUM1+L)=0
ELSE IF(IWRK(I2).NE.IND1) THEN
CALL XABORT('BIVPKN: FAILURE OF THE RENUMBERING ALGORITHM(1).')
ENDIF
230 CONTINUE
235 CONTINUE
NUM1=NUM1+LL
240 CONTINUE
245 CONTINUE
*----
* COMPUTE THE PERMUTATION VECTOR IP AND RENUMBER THE UNKNOWNS.
*----
DO 250 I=1,MAXEV
IP(I)=0
250 CONTINUE
L4=0
IF(NCODE(1).EQ.5) THEN
K2MIN=1+LC/2
ELSE
K2MIN=1
ENDIF
DO 265 K1=1,LYTOT
IK1=(K1-1)*LXTOT
DO 260 K2=K2MIN,LXTOT
I=IWRK(IK1+K2)
IF(I.LE.0) GO TO 260
IF(I.GT.MAXEV) THEN
CALL XABORT('BIVPKN: FAILURE OF THE RENUMBERING ALGORITHM(2).')
ENDIF
IF(IP(I).EQ.0) THEN
L4=L4+1
IP(I)=L4
ENDIF
260 CONTINUE
265 CONTINUE
DO 270 K=1,NUM1
KNK=KN(K)
IF(KNK.NE.0) KN(K)=IP(KNK)
270 CONTINUE
IF(L4.EQ.0) THEN
CALL XABORT('BIVPKN: FAILURE OF THE RENUMBERING ALGORITHM(3).')
ELSE IF(L4.GT.MAXEV) THEN
CALL XABORT('BIVPKN: INSUFFICIENT MAXEV.')
ENDIF
IF(IMPX.GT.2) WRITE (6,745) (VOL(I),I=1,LX*LY)
*----
* COMPUTE THE SYSTEM MATRIX BANDWIDTH.
*----
DO 450 I=1,L4
MU(I)=0
450 CONTINUE
NUM1=0
DO 480 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 480
DO 470 I=1,LL
IND1=KN(NUM1+I)
IF(IND1.EQ.0) GO TO 470
DO 460 J=1,LL
IND2=KN(NUM1+J)
IF(IND2.EQ.0) GO TO 460
MU(IND1)=MAX0(MU(IND1),IND1-IND2+1)
460 CONTINUE
470 CONTINUE
NUM1=NUM1+LL
480 CONTINUE
IIMAX=0
DO 490 I=1,L4
IIMAX=IIMAX+MU(I)
MU(I)=IIMAX
490 CONTINUE
*
IF(IMPX.GT.2) THEN
WRITE (6,720) IIMAX
NUM1=0
NUM2=0
IF(IELEM.EQ.1) THEN
WRITE (6,750)
DO 500 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 500
WRITE (6,755) K,(KN(NUM1+I),I=1,LL),(QFR(NUM2+I),I=1,4),
1 (BFR(NUM2+I),I=1,4)
NUM1=NUM1+LL
NUM2=NUM2+4
500 CONTINUE
ELSE IF(IELEM.EQ.2) THEN
WRITE (6,760)
DO 510 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 510
WRITE (6,765) K,(KN(NUM1+I),I=1,LL),(QFR(NUM2+I),I=1,4)
NUM1=NUM1+LL
NUM2=NUM2+4
510 CONTINUE
NUM2=0
WRITE (6,830)
DO 515 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 515
WRITE (6,820) K,(BFR(NUM2+I),I=1,4)
NUM2=NUM2+4
515 CONTINUE
ELSE IF((IELEM.EQ.3).OR.(IELEM.EQ.4)) THEN
WRITE (6,790)
DO 530 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 530
WRITE (6,800) K,(KN(NUM1+I),I=1,LL)
NUM1=NUM1+LL
530 CONTINUE
WRITE (6,810)
DO 540 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 540
WRITE (6,820) K,(QFR(NUM2+I),I=1,4)
NUM2=NUM2+4
540 CONTINUE
NUM2=0
WRITE (6,830)
DO 550 K=1,LX*LY
IF(MAT(K).LE.0) GO TO 550
WRITE (6,820) K,(BFR(NUM2+I),I=1,4)
NUM2=NUM2+4
550 CONTINUE
ENDIF
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(IWRK,IP)
RETURN
*
700 FORMAT(/38H BIVPKN: PRIMAL FINITE ELEMENT METHOD.//7H NUMBER,
1 27H OF ELEMENTS ALONG X AXIS =,I3/26H NUMBER OF ELEMENTS ALONG ,
2 8HY AXIS =,I3)
720 FORMAT(/52H NUMBER OF TERMS IN THE COMPRESSED SYSTEM MATRICES =,
1 I7)
745 FORMAT(/20H VOLUMES PER ELEMENT/(1X,1P,10E13.4))
750 FORMAT(/22H NUMBERING OF UNKNOWNS/1X,21(1H-)//
1 8H ELEMENT,5X,7HNUMBERS,23X,23HVOID BOUNDARY CONDITION,25X,
2 17HSURFACE FRACTIONS)
755 FORMAT (3X,I4,7X,4I5,6X,1P,4E11.2,5X,4E10.2)
760 FORMAT(/22H NUMBERING OF UNKNOWNS/1X,21(1H-)//
1 8H ELEMENT,5X,7HNUMBERS,47X,23HVOID BOUNDARY CONDITION)
765 FORMAT (3X,I4,7X,9I5,6X,1P,4E11.2)
790 FORMAT(/22H NUMBERING OF UNKNOWNS/1X,21(1H-)//5H ELE-/5H MENT,
1 3X,7HNUMBERS)
800 FORMAT (1X,I4,2X,25I5)
810 FORMAT (///24H VOID BOUNDARY CONDITION//8H ELEMENT,5X,3HQFR)
820 FORMAT (3X,I4,4X,1P,4E10.2)
830 FORMAT (///17H SURFACE FRACTION//8H ELEMENT,5X,3HBFR)
END
|
