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*DECK NSS4TR
SUBROUTINE NSS4TR(NEL,NMIX,MAT,XX,IQFR,QFR,DIFF,SIGR,FD,A11)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of leakage system matrices for the coarse mesh finite
* difference method.
*
*Copyright:
* Copyright (C) 2021 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
* NEL number of nodes
* NMIX number of mixtures
* MAT node mixtures
* XX node widths
* IQFR boundary conditions
* QFR albedo functions
* DIFF diffusion coefficients
* SIGR macroscopic removal cross sections
* FD discontinuity factors
*
*Parameters: output
* A11 assembly matrix.
*
*-----------------------------------------------------------------------
*
INTEGER NEL,NMIX,MAT(NEL),IQFR(6,NEL)
REAL XX(NEL),QFR(6,NEL),DIFF(NMIX),SIGR(NMIX),FD(NMIX,2),
1 A11(3*NEL,3*NEL)
*
A11(:3*NEL,:3*NEL)=0.0
! WEIGHT RESIDUAL EQUATIONS:
NUM1=0
DO KEL=1,NEL
IBM=MAT(KEL)
DX2=XX(KEL)**2
SIGG=SIGR(IBM)
DIDD=DIFF(IBM)
A11(NUM1+1,NUM1+1)=SIGG
A11(NUM1+1,NUM1+3)=-2.0*DIDD/DX2
A11(NUM1+2,NUM1+2)=SIGG/12.0
A11(NUM1+3,NUM1+3)=SIGG/180.0
NUM1=NUM1+3
ENDDO
! continuity relations:
NUM1=0
DO KEL=1,NEL-1
IBM=MAT(KEL)
IBMP=MAT(KEL+1)
DIDD=DIFF(IBM)
DIDDP=DIFF(IBMP)
NUM2=NUM1+3
! flux continuity:
FDP=FD(IBM,2)
FDM=FD(IBMP,1)
A11(NUM1+2,NUM1+1)=FDP
A11(NUM1+2,NUM1+2)=FDP/2.0
A11(NUM1+2,NUM1+3)=FDP/6.0
A11(NUM1+2,NUM2+1)=-FDM
A11(NUM1+2,NUM2+2)=FDM/2.0
A11(NUM1+2,NUM2+3)=-FDM/6.0
! current contunuity:
A11(NUM1+3,NUM1+2)=DIDD/XX(KEL)
A11(NUM1+3,NUM1+3)=DIDD/XX(KEL)
A11(NUM1+3,NUM2+2)=-DIDDP/XX(KEL+1)
A11(NUM1+3,NUM2+3)=DIDDP/XX(KEL+1)
NUM1=NUM1+3
ENDDO
! left boundary condition:
IBM=MAT(1)
IF((IQFR(1,1) == -1).OR.(IQFR(1,1) > 0)) THEN
! VOID
AFACTOR=QFR(1,1)
A11(NUM1+2,1)=AFACTOR
A11(NUM1+2,2)=-(AFACTOR/2.0+DIFF(IBM)/XX(1))
A11(NUM1+2,3)=(AFACTOR/6.0+DIFF(IBM)/XX(1))
ELSE IF(IQFR(1,1) == -2) THEN
! REFL
A11(NUM1+2,2)=1.0
A11(NUM1+2,3)=-1.0
ELSE IF(IQFR(1,1) == -3) THEN
! ZERO
A11(NUM1+2,1)=1.0
A11(NUM1+2,2)=-1.0/2.0
A11(NUM1+2,3)=1.0/6.0
ENDIF
! right boundary condition:
IBM=MAT(NEL)
IF((IQFR(2,NEL) == -1).OR.(IQFR(2,NEL) > 0)) THEN
NUM2=3*(NEL-1)
! VOID
AFACTOR=QFR(2,NEL)
A11(NUM1+3,NUM2+1)=AFACTOR
A11(NUM1+3,NUM2+2)=(AFACTOR/2.0+DIFF(IBM)/XX(NEL))
A11(NUM1+3,NUM2+3)=(AFACTOR/6.0+DIFF(IBM)/XX(NEL))
ELSE IF(IQFR(2,NEL) == -2) THEN
NUM2=3*(NEL-1)
! REFL
A11(NUM1+3,NUM2+2)=1.0
A11(NUM1+3,NUM2+3)=1.0
ELSE IF(IQFR(2,NEL) == -3) THEN
NUM2=3*(NEL-1)
! ZERO
A11(NUM1+3,NUM2+1)=1.0
A11(NUM1+3,NUM2+2)=1.0/2.0
A11(NUM1+3,NUM2+3)=1.0/6.0
ENDIF
END SUBROUTINE NSS4TR
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