*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