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+*DECK PNDM2E
+      SUBROUTINE PNDM2E(ITY,NEL,L4,IELEM,ICOL,MAT,VOL,NBMIX,NLF,NVD,
+     1 NAN,SIGT,SIGTI,XX,YY,KN,QFR,MU,IIMAX,LC,R,V,SYS)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* Assembly of system matrices for a mixed-dual formulation of the
+* simplified PN method in 2D Cartesian geometry.
+*
+*Copyright:
+* Copyright (C) 2004 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.
+* NEL     number of finite elements.
+* L4      number of unknowns per energy group and per set of two
+*         Legendre orders.
+* 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).
+* MAT     mixture index assigned to each element.
+* VOL     volume of each element.
+* NBMIX   number of mixtures.
+* 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.
+* SIGT    total minus self-scattering macroscopic cross sections.
+*         SIGT(:,NAN) generally contains the total cross section only.
+* SIGTI   inverse macroscopic cross sections ordered by mixture.
+*         SIGTI(:,NAN) generally contains the inverse total cross
+*         section only.
+* XX      X-directed mesh spacings.
+* YY      Y-directed mesh spacings.
+* KN      element-ordered unknown list.
+* QFR     element-ordered boundary conditions.
+* MU      compressed storage mode indices.
+* IIMAX   dimension of vector SYS.
+* LC      order of the unit matrices.
+* R       unit Cartesian mass matrix.
+* V       unit nodal coupling matrix.
+*
+*Parameters: output
+* SYS     system matrix.
+*
+*Reference:
+* J.J. Lautard, D. Schneider, A.M. Baudron, "Mixed Dual Methods for
+* Neutronic Reactor Core Calculations in the CRONOS System,"
+* Proc. Int. Conf. on Mathematics and Computation, Reactor
+* Physics and Environmental Analysis in Nuclear Applications,
+* Madrid, Spain, September 27-30, 1999.
+*
+*-----------------------------------------------------------------------
+*
+*----
+*  SUBROUTINE ARGUMENTS
+*----
+      INTEGER ITY,NEL,L4,IELEM,ICOL,MAT(NEL),NBMIX,NLF,NAN,KN(5*NEL),
+     1 MU(L4),IIMAX,LC
+      REAL VOL(NEL),SIGT(NBMIX,NAN),SIGTI(NBMIX,NAN),XX(NEL),YY(NEL),
+     1 QFR(4*NEL),R(LC,LC),V(LC,LC-1),SYS(IIMAX)
+*----
+*  LOCAL VARIABLES
+*----
+      REAL QQ(5,5)
+*
+      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
+      ELSE
+         NZMAR=65
+      ENDIF
+      DO 12 I0=1,IELEM
+      DO 11 J0=1,IELEM
+      QQ(I0,J0)=0.0
+      DO 10 K0=2,IELEM
+      QQ(I0,J0)=QQ(I0,J0)+V(K0,I0)*V(K0,J0)/R(K0,K0)
+   10 CONTINUE
+   11 CONTINUE
+   12 CONTINUE
+      MUMAX=MU(L4)
+      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)
+*----
+*  ASSEMBLY OF THE MAIN COEFFICIENT MATRIX AT ORDER IL.
+*----
+      NUM1=0
+      NUM2=0
+      KEY=0
+      DO 90 K=1,NEL
+      IBM=MAT(K)
+      IF(IBM.EQ.0) GO TO 90
+      VOL0=VOL(K)
+      GARS=SIGT(IBM,MIN(IL+1,NAN))
+      IF(MOD(IL,2).EQ.0) THEN
+*        EVEN PARITY EQUATION.
+         DO 25 I0=1,IELEM
+         DO 20 J0=1,IELEM
+         JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
+         KEY=(IL/2)*MUMAX+MU(JND1)
+         SYS(KEY)=SYS(KEY)+FACT*VOL0*GARS
+   20    CONTINUE
+   25    CONTINUE
+      ELSE
+         GARSI=SIGTI(IBM,MIN(IL+1,NAN))
+         DO 80 I0=1,IELEM
+*        PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION OF
+*        THE EVEN PARITY EQUATION.
+         DO 45 J0=1,IELEM
+         JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
+         DO 30 K0=1,J0
+         IF(QQ(J0,K0).EQ.0.0) GO TO 30
+         KND1=KN(NUM1+1)+(I0-1)*IELEM+K0-1
+         KEY=(IL/2)*MUMAX+MU(JND1)-JND1+KND1
+         SYS(KEY)=SYS(KEY)+(REAL(IL)**2)*VOL0*QQ(J0,K0)*GARSI/(FACT*
+     1   XX(K)*XX(K))
+         IF(IL.LE.NLF-3) THEN
+            KEY=((IL+2)/2)*MUMAX+MU(JND1)-JND1+KND1
+            SYS(KEY)=SYS(KEY)+(REAL(IL+1)**2)*VOL0*QQ(J0,K0)*GARSI/
+     1      (FACT*XX(K)*XX(K))
+         ENDIF
+   30    CONTINUE
+         JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
+         DO 40 K0=1,J0
+         IF(QQ(J0,K0).EQ.0.0) GO TO 40
+         KND1=KN(NUM1+1)+(K0-1)*IELEM+I0-1
+         KEY=(IL/2)*MUMAX+MU(JND1)-JND1+KND1
+         SYS(KEY)=SYS(KEY)+(REAL(IL)**2)*VOL0*QQ(J0,K0)*GARSI/(FACT*
+     1   YY(K)*YY(K))
+         IF(IL.LE.NLF-3) THEN
+            KEY=((IL+2)/2)*MUMAX+MU(JND1)-JND1+KND1
+            SYS(KEY)=SYS(KEY)+(REAL(IL+1)**2)*VOL0*QQ(J0,K0)*GARSI/
+     1      (FACT*YY(K)*YY(K))
+         ENDIF
+   40    CONTINUE
+   45    CONTINUE
+*
+*        ODD PARITY EQUATION.
+         DO 55 IC=1,2
+         IIC=1
+         IF(IC.EQ.2) IIC=IELEM+1
+         IND1=ABS(KN(NUM1+1+IC))+I0-1
+         S1=REAL(SIGN(1,KN(NUM1+1+IC)))
+         DO 50 JC=1,2
+         JJC=1
+         IF(JC.EQ.2) JJC=IELEM+1
+         IND2=ABS(KN(NUM1+1+JC))+I0-1
+         IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0).AND.
+     1      (IND1.GE.IND2)) THEN
+            S2=REAL(SIGN(1,KN(NUM1+1+JC)))
+            KEY=(IL/2)*MUMAX+MU(IND1)-IND1+IND2
+            SYS(KEY)=SYS(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
+         ENDIF
+   50    CONTINUE
+   55    CONTINUE
+         DO 65 IC=3,4
+         IIC=1
+         IF(IC.EQ.4) IIC=IELEM+1
+         IND1=ABS(KN(NUM1+1+IC))+I0-1
+         S1=REAL(SIGN(1,KN(NUM1+1+IC)))
+         DO 60 JC=3,4
+         JJC=1
+         IF(JC.EQ.4) JJC=IELEM+1
+         IND2=ABS(KN(NUM1+1+JC))+I0-1
+         IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0).AND.
+     1      (IND1.GE.IND2)) THEN
+            S2=REAL(SIGN(1,KN(NUM1+1+JC)))
+            KEY=(IL/2)*MUMAX+MU(IND1)-IND1+IND2
+            SYS(KEY)=SYS(KEY)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS
+         ENDIF
+   60    CONTINUE
+   65    CONTINUE
+         IF(ITY.EQ.1) GO TO 80
+*
+         IND1=ABS(KN(NUM1+2))+I0-1
+         IND2=ABS(KN(NUM1+3))+I0-1
+         IND3=ABS(KN(NUM1+4))+I0-1
+         IND4=ABS(KN(NUM1+5))+I0-1
+         IF((QFR(NUM2+1).NE.0.0).AND.(KN(NUM1+2).NE.0)) THEN
+            KEY=(IL/2)*MUMAX+MU(IND1)
+            SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+1)*ZMARS
+         ENDIF
+         IF((QFR(NUM2+2).NE.0.0).AND.(KN(NUM1+3).NE.0)) THEN
+            KEY=(IL/2)*MUMAX+MU(IND2)
+            SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+2)*ZMARS
+         ENDIF
+         IF((QFR(NUM2+3).NE.0.0).AND.(KN(NUM1+4).NE.0)) THEN
+            KEY=(IL/2)*MUMAX+MU(IND3)
+            SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+3)*ZMARS
+         ENDIF
+         IF((QFR(NUM2+4).NE.0.0).AND.(KN(NUM1+5).NE.0)) THEN
+            KEY=(IL/2)*MUMAX+MU(IND4)
+            SYS(KEY)=SYS(KEY)-0.5*FACT*QFR(NUM2+4)*ZMARS
+         ENDIF
+*
+         DO 70 J0=1,IELEM
+         JND1=KN(NUM1+1)+(I0-1)*IELEM+J0-1
+         IF(KN(NUM1+2).NE.0) THEN
+            S1=REAL(SIGN(1,KN(NUM1+2)))
+            IF(JND1.GT.IND1) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND1
+            IF(JND1.LT.IND1) KEY=(IL/2)*MUMAX+MU(IND1)-IND1+JND1
+            SYS(KEY)=SYS(KEY)+S1*REAL(IL)*VOL0*V(1,J0)/XX(K)
+         ENDIF
+         IF(KN(NUM1+3).NE.0) THEN
+            S2=REAL(SIGN(1,KN(NUM1+3)))
+            IF(JND1.GT.IND2) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND2
+            IF(JND1.LT.IND2) KEY=(IL/2)*MUMAX+MU(IND2)-IND2+JND1
+            SYS(KEY)=SYS(KEY)+S2*REAL(IL)*VOL0*V(IELEM+1,J0)/XX(K)
+         ENDIF
+         JND1=KN(NUM1+1)+(J0-1)*IELEM+I0-1
+         IF(KN(NUM1+4).NE.0) THEN
+            S3=REAL(SIGN(1,KN(NUM1+4)))
+            IF(JND1.GT.IND3) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND3
+            IF(JND1.LT.IND3) KEY=(IL/2)*MUMAX+MU(IND3)-IND3+JND1
+            SYS(KEY)=SYS(KEY)+S3*REAL(IL)*VOL0*V(1,J0)/YY(K)
+         ENDIF
+         IF(KN(NUM1+5).NE.0) THEN
+            S4=REAL(SIGN(1,KN(NUM1+5)))
+            IF(JND1.GT.IND4) KEY=(IL/2)*MUMAX+MU(JND1)-JND1+IND4
+            IF(JND1.LT.IND4) KEY=(IL/2)*MUMAX+MU(IND4)-IND4+JND1
+            SYS(KEY)=SYS(KEY)+S4*REAL(IL)*VOL0*V(IELEM+1,J0)/YY(K)
+         ENDIF
+   70    CONTINUE
+   80    CONTINUE
+      ENDIF
+      NUM1=NUM1+5
+      NUM2=NUM2+4
+   90 CONTINUE
+  100 CONTINUE
+      RETURN
+      END