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*DECK PNDH2E
SUBROUTINE PNDH2E(ITY,IELEM,ICOL,NBLOS,L4,NBMIX,IIMAX,SIDE,MAT,
1 IPERT,SIGT,KN,QFR,NLF,NVD,NAN,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
* simplified PN method approximation (2D hexagonal geometry).
*
*Copyright:
* Copyright (C) 2009 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.
* 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).
* NBLOS number of lozenges per direction, taking into account
* mesh-splitting.
* L4 number of unknowns per energy group and per set of two
* Legendre orders.
* NBMIX number of mixtures.
* IIMAX allocated dimension of array SYS.
* SIDE side of the hexagons.
* MAT mixture index assigned to each element.
* SIGT total minus self-scattering macroscopic cross sections.
* SIGT(:,NAN) generally contains the total cross section only.
* KN element-ordered unknown list.
* QFR element-ordered boundary conditions.
* NLF number of Legendre orders for the flux (even number).
* NVD type of void boundary condition if NLF>0 and ICOL=3.
* NAN number of Legendre orders for the cross sections.
* 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,ICOL,NBLOS,L4,NBMIX,IIMAX,MAT(3,NBLOS),
1 IPERT(NBLOS),KN(NBLOS,4+6*IELEM*(IELEM+1)),NLF,NVD,NAN,MU(L4),LC
REAL SIDE,SIGT(NBMIX,NAN),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)),VAR1
*
TTTT=REAL(0.5D0*SQRT(3.D00)*SIDE*SIDE)
IF(IELEM.GT.MAXIEL) CALL XABORT('PNDH2E: MAXIEL OVERFLOW.')
NZMAR=65
IF(ICOL.EQ.3) THEN
IF(NVD.EQ.0) THEN
NZMAR=NLF+1
ELSE IF(NVD.EQ.1) THEN
NZMAR=NLF
ELSE IF(NVD.EQ.2) THEN
NZMAR=65
ENDIF
ENDIF
MUMAX=MU(L4)
NELEM=IELEM*(IELEM+1)
COEF=REAL(2.0D0*SIDE*SIDE/SQRT(3.D00))
*----
* COMPUTE THE TRANVERSE COUPLING PIOLAT UNIT MATRIX
*----
CTRAN(:MAXIEL*(MAXIEL+1),:MAXIEL*(MAXIEL+1))=0.0D0
CNORM=REAL(SIDE*SIDE/SQRT(3.D00))
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
*----
* ASSEMBLY OF THE MAIN COEFFICIENT MATRIX AT ORDER IL.
*----
DO 100 IL=0,NLF-1
ZMARS=0.0
IF(MOD(IL,2).EQ.1) ZMARS=PNMAR2(NZMAR,IL,IL)
FACT=REAL(2*IL+1)
NUM=0
KEY=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
GARS=SIGT(IBM,MIN(IL+1,NAN))
IF(MOD(IL,2).EQ.0) THEN
* EVEN PARITY EQUATION.
DO 35 K2=0,IELEM-1
DO 30 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
KEY=(IL/2)*MUMAX+MU(JND1)
SYS(KEY)=SYS(KEY)+FACT*TTTT*GARS
KEY=(IL/2)*MUMAX+MU(JND2)
SYS(KEY)=SYS(KEY)+FACT*TTTT*GARS
KEY=(IL/2)*MUMAX+MU(JND3)
SYS(KEY)=SYS(KEY)+FACT*TTTT*GARS
30 CONTINUE
35 CONTINUE
ELSE
* ODD PARITY EQUATION.
DO 52 K4=0,1
DO 51 K3=0,IELEM-1
DO 50 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 40 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
KEY=(IL/2)*MUMAX+MU(INW1)-INW1+INW2
SG=REAL(SIGN(1,KNW1)*SIGN(1,KNW2))
SYS(KEY)=SYS(KEY)-SG*FACT*COEF*GARS*R(K2,K1)
ENDIF
IF((KNX2.NE.0).AND.(KNX1.NE.0).AND.(INX1.GE.INX2)) THEN
KEY=(IL/2)*MUMAX+MU(INX1)-INX1+INX2
SG=REAL(SIGN(1,KNX1)*SIGN(1,KNX2))
SYS(KEY)=SYS(KEY)-SG*FACT*COEF*GARS*R(K2,K1)
ENDIF
IF((KNY2.NE.0).AND.(KNY1.NE.0).AND.(INY1.GE.INY2)) THEN
KEY=(IL/2)*MUMAX+MU(INY1)-INY1+INY2
SG=REAL(SIGN(1,KNY1)*SIGN(1,KNY2))
SYS(KEY)=SYS(KEY)-SG*FACT*COEF*GARS*R(K2,K1)
ENDIF
40 CONTINUE
IF(ITY.EQ.0) THEN
IF(KNW1.NE.0) THEN
KEY=(IL/2)*MUMAX+MU(INW1)
IF((K2.EQ.1).AND.(K4.EQ.0)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,1)*ZMARS
ELSE IF((K2.EQ.IELEM+1).AND.(K4.EQ.1)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,2)*ZMARS
ENDIF
ENDIF
IF(KNX1.NE.0) THEN
KEY=(IL/2)*MUMAX+MU(INX1)
IF((K2.EQ.1).AND.(K4.EQ.0)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,3)*ZMARS
ELSE IF((K2.EQ.IELEM+1).AND.(K4.EQ.1)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,4)*ZMARS
ENDIF
ENDIF
IF(KNY1.NE.0) THEN
KEY=(IL/2)*MUMAX+MU(INY1)
IF((K2.EQ.1).AND.(K4.EQ.0)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,5)*ZMARS
ELSE IF((K2.EQ.IELEM+1).AND.(K4.EQ.1)) THEN
SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM,6)*ZMARS
ENDIF
ENDIF
ENDIF
50 CONTINUE
51 CONTINUE
52 CONTINUE
*
ITRS=0
DO I=1,NBLOS
IF(KN(I,1).EQ.KN(NUM,4)) THEN
ITRS=I
GO TO 60
ENDIF
ENDDO
CALL XABORT('PNDH2E: ITRS FAILURE.')
60 DO 75 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 70 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)
VAR1=FACT*GARS*CTRAN(I,J)
IF((KNY2.NE.0).AND.(KNW1.NE.0).AND.(INW1.LT.INY2)) THEN
KEY=(IL/2)*MUMAX+MU(INY2)-INY2+INW1
SG=REAL(SIGN(1,KNW1)*SIGN(1,KNY2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! y w
ELSE IF((KNY2.NE.0).AND.(KNW1.NE.0).AND.(INW1.GT.INY2)) THEN
KEY=(IL/2)*MUMAX+MU(INW1)-INW1+INY2
SG=REAL(SIGN(1,KNW1)*SIGN(1,KNY2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! w y
ENDIF
IF((KNW2.NE.0).AND.(KNX1.NE.0).AND.(INW2.LT.INX1)) THEN
KEY=(IL/2)*MUMAX+MU(INX1)-INX1+INW2
SG=REAL(SIGN(1,KNX1)*SIGN(1,KNW2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! x w
ELSE IF((KNW2.NE.0).AND.(KNX1.NE.0).AND.(INW2.GT.INX1)) THEN
KEY=(IL/2)*MUMAX+MU(INW2)-INW2+INX1
SG=REAL(SIGN(1,KNX1)*SIGN(1,KNW2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! w x
ENDIF
IF((KNX2.NE.0).AND.(KNY1.NE.0).AND.(INX2.LT.INY1)) THEN
KEY=(IL/2)*MUMAX+MU(INY1)-INY1+INX2
SG=REAL(SIGN(1,KNY1)*SIGN(1,KNX2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! y x
ELSE IF((KNX2.NE.0).AND.(KNY1.NE.0).AND.(INX2.GT.INY1)) THEN
KEY=(IL/2)*MUMAX+MU(INX2)-INX2+INY1
SG=REAL(SIGN(1,KNY1)*SIGN(1,KNX2))
SYS(KEY)=SYS(KEY)-SG*REAL(VAR1) ! x y
ENDIF
70 CONTINUE
75 CONTINUE
*
IF(ITY.EQ.0) THEN
DO 83 K4=0,1
DO 82 K3=0,IELEM-1
DO 81 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 80 K1=0,IELEM-1
IF(V(K2,K1+1).EQ.0.0) GO TO 80
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
IF(JND1.GT.INW1) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+INW1
IF(JND1.LT.INW1) KEY=(IL/2)*MUMAX+MU(INW1)-INW1+JND1
SG=REAL(SIGN(1,KNW1))
SYS(KEY)=SYS(KEY)+SG*SSS*REAL(IL)*SIDE*V(K2,K1+1)
ENDIF
IF(KNX1.NE.0) THEN
IF(JND2.GT.INX1) KEY=(IL/2)*MUMAX+MU(JND2)-JND2+INX1
IF(JND2.LT.INX1) KEY=(IL/2)*MUMAX+MU(INX1)-INX1+JND2
SG=REAL(SIGN(1,KNX1))
SYS(KEY)=SYS(KEY)+SG*SSS*REAL(IL)*SIDE*V(K2,K1+1)
ENDIF
IF(KNY1.NE.0) THEN
IF(JND3.GT.INY1) KEY=(IL/2)*MUMAX+MU(JND3)-JND3+INY1
IF(JND3.LT.INY1) KEY=(IL/2)*MUMAX+MU(INY1)-INY1+JND3
SG=REAL(SIGN(1,KNY1))
SYS(KEY)=SYS(KEY)+SG*SSS*REAL(IL)*SIDE*V(K2,K1+1)
ENDIF
80 CONTINUE
81 CONTINUE
82 CONTINUE
83 CONTINUE
ENDIF
ENDIF
90 CONTINUE
100 CONTINUE
RETURN
END
|
