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*DECK TRIDKN
SUBROUTINE TRIDKN(IMPX,LX,LY,LZ,CYLIND,IELEM,L4,LL4F,LL4X,LL4Y,
1 LL4Z,NCODE,ICODE,ZCODE,MAT,VOL,XXX,YYY,ZZZ,XX,YY,ZZ,DD,KN,QFR,
2 IQFR,IDL)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Numbering corresponding to a Thomas-Raviart (dual) formulation of the
* finite element discretization in a 3-D 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
* IMPX print parameter.
* LX number of elements along the X axis.
* LY number of elements along the Y axis.
* LZ number of elements along the Z axis.
* CYLIND cylindrical geometry flag (set with CYLIND=.true.).
* 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+; I=5: Z-; I=6: Z+;
* NCODE(I)=1: VOID; NCODE(I)=2: REFL; NCODE(I)=4: TRAN;
* NCODE(I)=5: SYME; NCODE(I)=7: ZERO; NCODE(I)=20: CYLI.
* 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.
* ZZZ Cartesian coordinates along the Z axis.
*
*Parameters: output
* L4 total number of unknown (variational coefficients) per
* energy group (order of system matrices).
* LL4F number of flux unknowns.
* LL4X number of X-directed currents
* LL4Y number of Y-directed currents
* LL4Z number of Z-directed currents
* VOL volume of each element.
* XX X-directed mesh spacings.
* YY Y-directed mesh spacings.
* ZZ Z-directed mesh spacings.
* DD used with cylindrical geometry.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* IQFR element-ordered physical albedo indices.
* IDL position of integrated fluxes into unknown vector.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IMPX,LX,LY,LZ,IELEM,L4,LL4F,LL4X,LL4Y,LL4Z,NCODE(6),
1 ICODE(6),MAT(LX*LY*LZ),KN(LX*LY*LZ*(1+6*IELEM**2)),
2 IQFR(6*LX*LY*LZ),IDL(LX*LY*LZ)
REAL ZCODE(6),VOL(LX*LY*LZ),XXX(LX+1),YYY(LY+1),ZZZ(LZ+1),
1 XX(LX*LY*LZ),YY(LX*LY*LZ),ZZ(LX*LY*LZ),DD(LX*LY*LZ),
2 QFR(6*LX*LY*LZ)
LOGICAL CYLIND
*----
* LOCAL VARIABLES
*----
LOGICAL COND,LL1
REAL ZALB(6)
INTEGER, DIMENSION(:), ALLOCATABLE :: IP
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(IP((LX+1)*LY*LZ*IELEM*IELEM + LX*(LY+1)*LZ*IELEM*IELEM
1 + LX*LY*(LZ+1)*IELEM*IELEM + LX*LY*LZ*IELEM*IELEM*IELEM))
*----
* IDENTIFICATION OF THE GEOMETRY. MAIN LOOP OVER THE ELEMENTS
*----
DO 10 I=1,6
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,LZ
L2=LX*LY*LZ
KN(:L2*(1+6*IELEM**2))=0
LL4F0=LX*LY*LZ*IELEM**3
LL4X0=(LX+1)*LY*LZ*IELEM**2
LL4Y0=LX*(LY+1)*LZ*IELEM**2
LL4Z0=LX*LY*(LZ+1)*IELEM**2
NUM1=0
NUM2=0
KEL=0
DO 182 K0=1,LZ
DO 181 K1=1,LY
DO 180 K2=1,LX
KEL=KEL+1
XX(KEL)=0.0
YY(KEL)=0.0
ZZ(KEL)=0.0
VOL(KEL)=0.0
IF(MAT(KEL).EQ.0) GO TO 180
XX(KEL)=XXX(K2+1)-XXX(K2)
YY(KEL)=YYY(K1+1)-YYY(K1)
ZZ(KEL)=ZZZ(K0+1)-ZZZ(K0)
IF(CYLIND) DD(KEL)=0.5*(XXX(K2)+XXX(K2+1))
KN(NUM1+1)=((K0-1)*LX*LY+(K1-1)*LX+K2-1)*IELEM**3 + 1
DO 20 IEL=1,IELEM**2
KN(NUM1+1+IEL)=LL4F0+((K0-1)*LY+K1-1)*(LX+1)*IELEM**2+(LX+1)*
1 (IEL-1)+K2
KN(NUM1+1+IELEM**2+IEL)=KN(NUM1+1+IEL)+1
KN(NUM1+1+2*IELEM**2+IEL)=LL4F0+LL4X0+((K0-1)*LX+K2-1)*(LY+1)*
1 IELEM**2+(LY+1)*(IEL-1)+K1
KN(NUM1+1+3*IELEM**2+IEL)=KN(NUM1+1+2*IELEM**2+IEL)+1
KN(NUM1+1+4*IELEM**2+IEL)=LL4F0+LL4X0+LL4Y0+((K1-1)*LX+K2-1)*
1 (LZ+1)*IELEM**2+(LZ+1)*(IEL-1)+K0
KN(NUM1+1+5*IELEM**2+IEL)=KN(NUM1+1+4*IELEM**2+IEL)+1
20 CONTINUE
QFR(NUM2+1:NUM2+6)=0.0
IQFR(NUM2+1:NUM2+6)=0
FRX=1.0
FRY=1.0
FRZ=1.0
*----
* VOID, REFL OR ZERO BOUNDARY CONTITION
*----
IF(K2.EQ.1) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL-1).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(1).EQ.2).OR.((NCODE(1).EQ.1).AND.(ZCODE(1).EQ.1.0))
IF(COND) THEN
DO 30 IEL=1,IELEM**2
KN(NUM1+1+IEL)=0
30 CONTINUE
ELSE IF((NCODE(1).EQ.1).AND.(ICODE(1).EQ.0)) THEN
QFR(NUM2+1)=ZALB(1)
ELSE IF(NCODE(1).EQ.1) THEN
QFR(NUM2+1)=1.0
IQFR(NUM2+1)=ICODE(1)
ENDIF
ENDIF
*
IF(K2.EQ.LX) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL+1).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(2).EQ.2).OR.((NCODE(2).EQ.1).AND.(ZCODE(2).EQ.1.0))
IF(COND) THEN
DO 40 IEL=1,IELEM**2
KN(NUM1+1+IELEM**2+IEL)=0
40 CONTINUE
ELSE IF((NCODE(2).EQ.1).AND.(ICODE(2).EQ.0)) THEN
QFR(NUM2+2)=ZALB(2)
ELSE IF(NCODE(2).EQ.1) THEN
QFR(NUM2+2)=1.0
IQFR(NUM2+2)=ICODE(2)
ENDIF
ENDIF
*
IF(K1.EQ.1) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL-LX).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(3).EQ.2).OR.((NCODE(3).EQ.1).AND.(ZCODE(3).EQ.1.0))
IF(COND) THEN
DO 50 IEL=1,IELEM**2
KN(NUM1+1+2*IELEM**2+IEL)=0
50 CONTINUE
ELSE IF((NCODE(3).EQ.1).AND.(ICODE(3).EQ.0)) THEN
QFR(NUM2+3)=ZALB(3)
ELSE IF(NCODE(3).EQ.1) THEN
QFR(NUM2+3)=1.0
IQFR(NUM2+3)=ICODE(3)
ENDIF
ENDIF
*
IF(K1.EQ.LY) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL+LX).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(4).EQ.2).OR.((NCODE(4).EQ.1).AND.(ZCODE(4).EQ.1.0))
IF(COND) THEN
DO 60 IEL=1,IELEM**2
KN(NUM1+1+3*IELEM**2+IEL)=0
60 CONTINUE
ELSE IF((NCODE(4).EQ.1).AND.(ICODE(4).EQ.0)) THEN
QFR(NUM2+4)=ZALB(4)
ELSE IF(NCODE(4).EQ.1) THEN
QFR(NUM2+4)=1.0
IQFR(NUM2+4)=ICODE(4)
ENDIF
ENDIF
*
IF(K0.EQ.1) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL-LX*LY).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(5).EQ.2).OR.((NCODE(5).EQ.1).AND.(ZCODE(5).EQ.1.0))
IF(COND) THEN
DO 70 IEL=1,IELEM**2
KN(NUM1+1+4*IELEM**2+IEL)=0
70 CONTINUE
ELSE IF((NCODE(5).EQ.1).AND.(ICODE(5).EQ.0)) THEN
QFR(NUM2+5)=ZALB(5)
ELSE IF(NCODE(5).EQ.1) THEN
QFR(NUM2+5)=1.0
IQFR(NUM2+5)=ICODE(5)
ENDIF
ENDIF
*
IF(K0.EQ.LZ) THEN
LL1=.TRUE.
ELSE
LL1=(MAT(KEL+LX*LY).EQ.0)
ENDIF
IF(LL1) THEN
COND=(NCODE(6).EQ.2).OR.((NCODE(6).EQ.1).AND.(ZCODE(6).EQ.1.0))
IF(COND) THEN
DO 80 IEL=1,IELEM**2
KN(NUM1+1+5*IELEM**2+IEL)=0
80 CONTINUE
ELSE IF((NCODE(6).EQ.1).AND.(ICODE(6).EQ.0)) THEN
QFR(NUM2+6)=ZALB(6)
ELSE IF(NCODE(6).EQ.1) THEN
QFR(NUM2+6)=1.0
IQFR(NUM2+6)=ICODE(6)
ENDIF
ENDIF
*----
* TRAN BOUNDARY CONDITION
*----
IF((K2.EQ.LX).AND.(NCODE(2).EQ.4)) THEN
DO 90 IEL=1,IELEM**2
KN(NUM1+1+IELEM**2+IEL)=KN(NUM1+1+IELEM**2+IEL)-LX
90 CONTINUE
ENDIF
IF((K1.EQ.LY).AND.(NCODE(4).EQ.4)) THEN
DO 100 IEL=1,IELEM**2
KN(NUM1+1+3*IELEM**2+IEL)=KN(NUM1+1+3*IELEM**2+IEL)-LY
100 CONTINUE
ENDIF
IF((K0.EQ.LZ).AND.(NCODE(6).EQ.4)) THEN
DO 110 IEL=1,IELEM**2
KN(NUM1+1+5*IELEM**2+IEL)=KN(NUM1+1+5*IELEM**2+IEL)-LZ
110 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 120 IEL=1,IELEM**2
KN(NUM1+1+IEL)=-KN(NUM1+1+IELEM**2+IEL)
120 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 130 IEL=1,IELEM**2
KN(NUM1+1+IELEM**2+IEL)=-KN(NUM1+1+IEL)
130 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 140 IEL=1,IELEM**2
KN(NUM1+1+2*IELEM**2+IEL)=-KN(NUM1+1+3*IELEM**2+IEL)
140 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 150 IEL=1,IELEM**2
KN(NUM1+1+3*IELEM**2+IEL)=-KN(NUM1+1+2*IELEM**2+IEL)
150 CONTINUE
ENDIF
IF((NCODE(5).EQ.5).AND.(K0.EQ.1)) THEN
QFR(NUM2+5)=QFR(NUM2+6)
IQFR(NUM2+5)=IQFR(NUM2+6)
FRZ=0.5
DO 160 IEL=1,IELEM**2
KN(NUM1+1+4*IELEM**2+IEL)=-KN(NUM1+1+5*IELEM**2+IEL)
160 CONTINUE
ELSE IF((NCODE(6).EQ.5).AND.(K0.EQ.LZ)) THEN
QFR(NUM2+6)=QFR(NUM2+5)
IQFR(NUM2+6)=IQFR(NUM2+5)
FRZ=0.5
DO 170 IEL=1,IELEM**2
KN(NUM1+1+5*IELEM**2+IEL)=-KN(NUM1+1+4*IELEM**2+IEL)
170 CONTINUE
ENDIF
*
VOL0=XX(KEL)*YY(KEL)*ZZ(KEL)*FRX*FRY*FRZ
IF(CYLIND) VOL0=6.2831853072*DD(KEL)*VOL0
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)
QFR(NUM2+5)=QFR(NUM2+5)*VOL0/ZZ(KEL)
QFR(NUM2+6)=QFR(NUM2+6)*VOL0/ZZ(KEL)
NUM1=NUM1+1+6*IELEM**2
NUM2=NUM2+6
180 CONTINUE
181 CONTINUE
182 CONTINUE
* END OF THE MAIN LOOP OVER ELEMENTS.
*
*----
* REMOVING THE UNUSED UNKNOWNS INDICES FROM KN
*----
IP(:LL4F0+LL4X0+LL4Y0+LL4Z0)=0
DO 190 NUM1=1,L2*(1+6*IELEM**2)
IF(KN(NUM1).NE.0) IP(ABS(KN(NUM1)))=1
190 CONTINUE
LL4F=0
IND=0
DO 200 KEL=1,L2
IF(IP(IND+1).EQ.1) THEN
DO 195 IEL=1,IELEM**3
LL4F=LL4F+1
IP(IND+IEL)=LL4F
195 CONTINUE
ENDIF
IND=IND+IELEM**3
200 CONTINUE
LL4X=0
DO 210 IND=LL4F0+1,LL4F0+LL4X0
IF(IP(IND).EQ.1) THEN
LL4X=LL4X+1
IP(IND)=LL4F+LL4X
ENDIF
210 CONTINUE
LL4Y=0
DO 220 IND=LL4F0+LL4X0+1,LL4F0+LL4X0+LL4Y0
IF(IP(IND).EQ.1) THEN
LL4Y=LL4Y+1
IP(IND)=LL4F+LL4X+LL4Y
ENDIF
220 CONTINUE
LL4Z=0
DO 230 IND=LL4F0+LL4X0+LL4Y0+1,LL4F0+LL4X0+LL4Y0+LL4Z0
IF(IP(IND).EQ.1) THEN
LL4Z=LL4Z+1
IP(IND)=LL4F+LL4X+LL4Y+LL4Z
ENDIF
230 CONTINUE
DO 240 NUM1=1,L2*(1+6*IELEM**2)
IF(KN(NUM1).NE.0) KN(NUM1)=SIGN(IP(ABS(KN(NUM1))),KN(NUM1))
240 CONTINUE
L4=LL4F+LL4X+LL4Y+LL4Z
NUM1=0
DO 250 KEL=1,L2
IDL(KEL)=0
IF(MAT(KEL).EQ.0) GO TO 250
IDL(KEL)=KN(NUM1+1)
NUM1=NUM1+1+6*IELEM**2
250 CONTINUE
*
IF(IMPX.GT.0) WRITE(6,710) L4
IF(IMPX.GT.2) THEN
WRITE(6,720) (VOL(I),I=1,L2)
NUM1=0
WRITE (6,730)
DO 500 K=1,L2
IF(MAT(K).EQ.0) GO TO 500
WRITE (6,740) K,KN(NUM1+1),'X',(KN(NUM1+I),I=2,1+2*IELEM**2)
WRITE (6,750) 'Y',(KN(NUM1+I),I=2+2*IELEM**2,1+4*IELEM**2)
WRITE (6,750) 'Z',(KN(NUM1+I),I=2+4*IELEM**2,1+6*IELEM**2)
NUM1=NUM1+1+6*IELEM**2
500 CONTINUE
WRITE (6,760)
NUM2=0
DO 510 K=1,L2
IF(MAT(K).EQ.0) GO TO 510
WRITE (6,770) K,(QFR(NUM2+I),I=1,6)
NUM2=NUM2+6
510 CONTINUE
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(IP)
RETURN
*
700 FORMAT(/42H TRIDKN: MIXED-DUAL FINITE ELEMENT METHOD.//7H NUMBER,
1 27H OF ELEMENTS ALONG X AXIS =,I3/20X,14HALONG Y AXIS =,I3/
2 20X,14HALONG Z AXIS =,I3)
710 FORMAT(31H NUMBER OF UNKNOWNS PER GROUP =,I8)
720 FORMAT(/20H VOLUMES PER ELEMENT/(1X,1P,10E13.4))
730 FORMAT(/22H NUMBERING OF UNKNOWNS/1X,21(1H-)//8H ELEMENT,8X,
1 4HFLUX,6X,8HCURRENTS,89(1H.))
740 FORMAT (1X,I6,5X,I8,6X,A1,12I8/(27X,12I8))
750 FORMAT (26X,A1,12I8/(27X,12I8))
760 FORMAT(/8H ELEMENT,3X,23HVOID BOUNDARY CONDITION)
770 FORMAT (1X,I6,5X,1P,6E10.1)
END
|
