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*DECK NSS2TR
SUBROUTINE NSS2TR(ITRIAL,NEL,NMIX,MAT,XX,IQFR,QFR,DIFF,SIGR,SIGT,
1 FD,A11)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Assembly of non-leakage system matrices for the nodal expansion 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
* ITRIAL type of base (=1: polynomial; =2: hyperbolic).
* 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 section.
* SIGT macroscopic cross section.
* FD discontinuity factors
*
*Parameters: output
* A11 assembly matrix.
*
*-----------------------------------------------------------------------
*
INTEGER ITRIAL(NMIX),NEL,NMIX,MAT(NEL),IQFR(6,NEL)
REAL XX(NEL),QFR(6,NEL),DIFF(NMIX),SIGR(NMIX),SIGT(NMIX),
1 FD(NMIX,2),A11(5*NEL,5*NEL)
*
A11(:5*NEL,:5*NEL)=0.0
NUM1=0
DO KEL=1,NEL
IBM=MAT(KEL)
SIGG=SIGT(IBM)
ETA=XX(KEL)*SQRT(SIGR(IBM)/DIFF(IBM))
! WEIGHT RESIDUAL EQUATIONS:
A11(NUM1+1,NUM1+1)=SIGG
A11(NUM1+2,NUM1+2)=SIGG/12.0
A11(NUM1+3,NUM1+3)=SIGG/20.0
IF(ITRIAL(IBM) == 1) THEN
A11(NUM1+2,NUM1+4)=-SIGG/120.0
A11(NUM1+3,NUM1+5)=-SIGG/700.0
ELSE
ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0)
ALP2=((12.0+ETA**2)*SINH(ETA/2.0)-6.0*ETA*COSH(ETA/2.0))/ETA
A11(NUM1+2,NUM1+4)=SIGG*ALP1/(ETA**2)
A11(NUM1+3,NUM1+5)=SIGG*ALP2/(ETA**2)
ENDIF
NUM1=NUM1+5
ENDDO
! continuity relations:
NUM1=0
DO KEL=1,NEL-1
IBM=MAT(KEL)
IBMP=MAT(KEL+1)
DIDD=DIFF(IBM)
DIDDP=DIFF(IBMP)
ETA=XX(KEL)*SQRT(SIGR(IBM)/DIDD)
ETAP=XX(KEL+1)*SQRT(SIGR(IBMP)/DIDDP)
NUM2=NUM1+5
! flux continuity:
FDP=FD(IBM,2)
FDM=FD(IBMP,1)
A11(NUM1+4,NUM1+1)=-FDP
A11(NUM1+4,NUM1+2)=-FDP/2.0
A11(NUM1+4,NUM1+3)=-FDP/2.0
A11(NUM1+4,NUM2+1)=FDM
A11(NUM1+4,NUM2+2)=-FDM/2.0
A11(NUM1+4,NUM2+3)=FDM/2.0
IF(ITRIAL(IBM) == 2) THEN
ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0)
A11(NUM1+4,NUM1+4)=-FDP*SINH(ETA/2.0)
A11(NUM1+4,NUM1+5)=-FDP*ALP1/ETA
ENDIF
IF(ITRIAL(IBMP) == 2) THEN
ALP1P=ETAP*COSH(ETAP/2.0)-2.0*SINH(ETAP/2.0)
A11(NUM1+4,NUM2+4)=-FDM*SINH(ETAP/2.0)
A11(NUM1+4,NUM2+5)=FDM*ALP1P/ETAP
ENDIF
NUM1=NUM1+5
ENDDO
! left boundary condition:
IBM=MAT(1)
ETA=XX(1)*SQRT(SIGR(IBM)/DIFF(IBM))
IF((IQFR(1,1) == -1).OR.(IQFR(1,1) > 0)) THEN
! VOID
AFACTOR=QFR(1,1)
A11(NUM1+4,1)=-AFACTOR
A11(NUM1+4,2)=AFACTOR/2.0
A11(NUM1+4,3)=-AFACTOR/2.0
IF(ITRIAL(IBM) == 2) THEN
ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0)
A11(NUM1+4,4)=AFACTOR*SINH(ETA/2.0)
A11(NUM1+4,5)=-AFACTOR*ALP1/ETA
ENDIF
ENDIF
! right boundary condition:
IBM=MAT(NEL)
ETA=XX(NEL)*SQRT(SIGR(IBM)/DIFF(IBM))
IF((IQFR(2,NEL) == -1).OR.(IQFR(2,NEL) > 0)) THEN
NUM2=5*(NEL-1)
! VOID
AFACTOR=QFR(2,NEL)
A11(NUM1+5,NUM2+1)=-AFACTOR
A11(NUM1+5,NUM2+2)=-AFACTOR/2.0
A11(NUM1+5,NUM2+3)=-AFACTOR/2.0
IF(ITRIAL(IBM) == 2) THEN
ALP1=ETA*COSH(ETA/2.0)-2.0*SINH(ETA/2.0)
A11(NUM1+5,NUM2+4)=-AFACTOR*SINH(ETA/2.0)
A11(NUM1+5,NUM2+5)=-AFACTOR*ALP1/ETA
ENDIF
ENDIF
RETURN
END SUBROUTINE NSS2TR
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