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+++ b/Dragon/src/SNTT2D.f
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+*DECK SNTT2D
+ SUBROUTINE SNTT2D (IGE,IMPX,LX,LY,SIDE,IELEM,NLF,NPQ,NSCT,IQUAD,
+ 1 NCODE,ZCODE,MAT,XXX,YYY,VOL,IDL,DU,DE,W,MRM,MRMY,DB,DA,DAL,PL,
+ 2 LL4,NUN,EELEM,WX,WE,CST,IBFP,ISCHM,ESCHM,IGLK,MN,DN,IL,IM,ISCAT)
+*
+*-----------------------------------------------------------------------
+*
+*Purpose:
+* Numbering corresponding to a 2-D Cartesian or R-Z geometry with
+* discrete ordinates approximation of the flux.
+*
+*Copyright:
+* Copyright (C) 2005 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 and C. Bienvenue
+*
+*Parameters: input
+* IGE type of 2D geometry (=0 Cartesian; =1 R-Z; =2 Hexagonal).
+* IMPX print parameter.
+* LX number of elements along the X axis.
+* LY number of elements along the Y axis.
+* SIDE side of an hexagon.
+* IELEM measure of order of the spatial approximation polynomial:
+* =1 constant - only for HODD, classical diamond scheme
+* (default for HODD);
+* =2 linear - default for DG;
+* =3 parabolic;
+* =4 cubic - only for DG.
+* NLF SN order for the flux (even number).
+* NPQ number of SN directions in four octants (including zero-weight
+* directions).
+* NSCT maximum number of spherical harmonics moments of the flux.
+* IQUAD type of SN quadrature (1 Level symmetric, type IQUAD;
+* 4 Legendre-Chebyshev; 5 symmetric Legendre-Chebyshev;
+* 6 quadruple range).
+* NCODE type of boundary condition applied on each side
+* (i=1 X-; i=2 X+; i=3 Y-; i=4 Y+):
+* =1: VOID; =2: REFL; =4: TRAN.
+* ZCODE ZCODE(I) is the albedo corresponding to boundary condition
+* 'VOID' on each side (ZCODE(I)=0.0 by default).
+* MAT mixture index assigned to each element.
+* XXX Cartesian coordinates along the X axis.
+* YYY Cartesian coordinates along the Y axis.
+* EELEM measure of order of the energy approximation polynomial:
+* =1 constant - default for HODD;
+* =2 linear - default for DG;
+* >3 higher orders.
+* IBFP type of energy proparation relation:
+* =0 no Fokker-Planck term;
+* =1 Galerkin type;
+* =2 heuristic Przybylski and Ligou type.
+* ISCHM method of spatial discretisation:
+* =1 High-Order Diamond Differencing (HODD) - default;
+* =2 Discontinuous Galerkin finite element method (DG);
+* =3 Adaptive weighted method (AWD).
+* ESCHM method of energy discretisation:
+* =1 High-Order Diamond Differencing (HODD) - default;
+* =2 Discontinuous Galerkin finite element method (DG);
+* =3 Adaptive weighted method (AWD).
+* IGLK angular interpolation type:
+* =0 classical SN method.
+* =1 Galerkin quadrature method (M = inv(D))
+* =2 Galerkin quadrature method (D = inv(M))
+* ISCAT maximum number of spherical harmonics moments of the flux.
+*
+*Parameters: output
+* VOL volume of each element.
+* IDL isotropic flux indices.
+* DU first direction cosines ($\\mu$).
+* DE second direction cosines ($\\eta$).
+* W weights.
+* MRM quadrature index.
+* MRMY quadrature index.
+* DB diamond-scheme parameter.
+* DA diamond-scheme parameter.
+* DAL diamond-scheme angular redistribution parameter.
+* PL discrete values of the spherical harmonics corresponding
+* to the 2D SN quadrature.
+* LL4 number of unknowns being solved for, over the domain. This
+* includes the various moments of the isotropic (and if present,
+* anisotropic) flux.
+* NUN total number of unknowns stored in the FLUX vector per group.
+* This includes LL4 (see above) as well as any surface boundary
+* fluxes, if present.
+* WX spatial closure relation weighting factors.
+* WE energy closure relation weighting factors.
+* CST constants for the polynomial approximations.
+* MN moment-to-discrete matrix.
+* DN discrete-to-moment matrix.
+* IL indexes (l) of each spherical harmonics in the
+* interpolation basis.
+* IM indexes (m) of each spherical harmonics in the
+* interpolation basis.
+*
+*-----------------------------------------------------------------------
+*
+*----
+* SUBROUTINE ARGUMENTS
+*----
+ INTEGER IGE,IMPX,LX,LY,IELEM,NLF,NPQ,NSCT,IQUAD,NCODE(4),
+ 1 MAT(LX,LY),IDL(LX*LY),MRM(NPQ),MRMY(NPQ),LL4,NUN,EELEM,IBFP,
+ 2 ISCHM,ESCHM,IL(NSCT),IM(NSCT),ISCAT,IGLK
+ REAL ZCODE(4),VOL(LX,LY),XXX(LX+1),YYY(LY+1),DU(NPQ),DE(NPQ),
+ 1 W(NPQ),DB(LX,NPQ),DA(LX,LY,NPQ),DAL(LX,LY,NPQ),PL(NSCT,NPQ),
+ 2 WX(IELEM+1),WE(EELEM+1),CST(MAX(IELEM,EELEM)),MN(NPQ,NSCT),
+ 3 DN(NSCT,NPQ)
+*----
+* LOCAL VARIABLES
+*----
+ CHARACTER HSMG*131
+ LOGICAL L1,L2,L3,L4
+ PARAMETER(RLOG=1.0E-8,PI=3.141592654)
+ REAL PX,PE
+ DOUBLE PRECISION NORM,IPROD
+ INTEGER, ALLOCATABLE, DIMENSION(:) :: JOP
+ REAL, ALLOCATABLE, DIMENSION(:) :: XX,YY,UU,WW,TPQ,UPQ,VPQ,WPQ
+ DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: V,V2
+ DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: U,MND
+ DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:,:) :: RLM
+*----
+* SCRATCH STORAGE ALLOCATION
+*----
+ ALLOCATE(XX(LX),YY(LY))
+*----
+* UNFOLD FOUR-OCTANT QUADRATURES.
+*----
+ IF(MOD(NLF,2).EQ.1) CALL XABORT('SNTT2D: EVEN NLF EXPECTED.')
+ IF(IQUAD.EQ.10) THEN
+ NPQ0=NLF**2/4
+ ELSE
+ NPQ0=NLF*(NLF/2+1)/4
+ ENDIF
+ ALLOCATE(JOP(NLF/2),UU(NLF/2),WW(NLF/2),TPQ(NPQ0),UPQ(NPQ0),
+ 1 VPQ(NPQ0),WPQ(NPQ0))
+ IF(IQUAD.EQ.1) THEN
+ CALL SNQU01(NLF,JOP,UU,WW,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.2) THEN
+ CALL SNQU02(NLF,JOP,UU,WW,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.3) THEN
+ CALL SNQU03(NLF,JOP,UU,WW,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.4) THEN
+ CALL SNQU04(NLF,JOP,UU,WW,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.5) THEN
+ UU(:NLF/2)=0.0
+ CALL SNQU05(NLF,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.6) THEN
+ UU(:NLF/2)=0.0
+ CALL SNQU06(NLF,TPQ,UPQ,VPQ,WPQ)
+ ELSE IF(IQUAD.EQ.10) THEN
+ CALL SNQU10(NLF,JOP,UU,WW,TPQ,UPQ,VPQ,WPQ)
+ ELSE
+ CALL XABORT('SNTT2D: UNKNOWN QUADRATURE TYPE.')
+ ENDIF
+ N=0
+ IOF=0
+ DO 30 I=1,NLF/2
+ IF(IGLK.NE.0) THEN
+ JOF = NLF-2*I+2
+ KOF = (NLF+4)*NLF/4
+ ELSE
+ IOF=IOF+1
+ JOF=IOF+NLF-2*I+2
+ KOF=IOF+(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=-SQRT(1.0-UU(I)*UU(I))
+ DE(IOF)=-UU(I)
+ W(IOF)=0.0
+ ENDIF
+ DO 10 J=0,NLF/2-I
+ IOF=IOF+1
+ KOF=IOF+(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=-UPQ(N+J+1)
+ DE(IOF)=-VPQ(N+J+1)
+ W(IOF)=WPQ(N+J+1)
+ JOF=JOF-1
+ 10 CONTINUE
+ DO 20 J=NLF/2-I,0,-1
+ IOF=IOF+1
+ KOF=IOF+(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=UPQ(N+J+1)
+ DE(IOF)=-VPQ(N+J+1)
+ W(IOF)=WPQ(N+J+1)
+ JOF=JOF-1
+ 20 CONTINUE
+ N=N+NLF/2-I+1
+ 30 CONTINUE
+ N=0
+ DO 60 I=1,NLF/2
+ IF(IGLK.NE.0) THEN
+ JOF=NLF-2*I+2
+ KOF=-(NLF+4)*NLF/4
+ ELSE
+ IOF=IOF+1
+ JOF=IOF+NLF-2*I+2
+ KOF=IOF-(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=-SQRT(1.0-UU(I)*UU(I))
+ DE(IOF)=UU(I)
+ W(IOF)=0.0
+ ENDIF
+ DO 40 J=0,NLF/2-I
+ IOF=IOF+1
+ KOF=IOF-(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=-UPQ(N+J+1)
+ DE(IOF)=VPQ(N+J+1)
+ W(IOF)=WPQ(N+J+1)
+ JOF=JOF-1
+ 40 CONTINUE
+ DO 50 J=NLF/2-I,0,-1
+ IOF=IOF+1
+ KOF=IOF-(NLF+4)*NLF/4
+ MRM(IOF)=JOF
+ MRMY(IOF)=KOF
+ DU(IOF)=UPQ(N+J+1)
+ DE(IOF)=VPQ(N+J+1)
+ W(IOF)=WPQ(N+J+1)
+ JOF=JOF-1
+ 50 CONTINUE
+ N=N+NLF/2-I+1
+ 60 CONTINUE
+ DEALLOCATE(WPQ,VPQ,UPQ,TPQ,WW,UU,JOP)
+ IF(IMPX.GE.4) THEN
+ WRITE(6,'(/41H SNTT2D: FOUR-OCTANT ANGULAR QUADRATURES:/26X,
+ 1 2HMU,9X,3HETA,10X,2HXI,6X,6HWEIGHT)')
+ SUM=0.0
+ DO 70 N=1,NPQ
+ SUM=SUM+W(N)
+ ZI=SQRT(ABS(1.0-DU(N)**2-DE(N)**2))
+ IF(ZI.LT.1.0E-3) ZI=0.0
+ WRITE(6,'(1X,3I5,1P,4E12.4)') N,MRM(N),MRMY(N),DU(N),DE(N),ZI,
+ 1 W(N)
+ 70 CONTINUE
+ WRITE(6,'(54X,10(1H-)/52X,1P,E12.4)') SUM
+ ENDIF
+*----
+* IDENTIFICATION OF THE GEOMETRY.
+*----
+ IF(IGE.EQ.0) THEN
+* ----------
+* 2D CARTESIAN
+* ----------
+ DO 82 N=1,NPQ
+ VU=DU(N)
+ VE=DE(N)
+ DO 81 I=1,LX
+ XX(I)=XXX(I+1)-XXX(I)
+ DB(I,N)=VE*XX(I)
+ DO 80 J=1,LY
+ YY(J)=YYY(J+1)-YYY(J)
+ DA(I,J,N)=VU*YY(J)
+ DAL(I,J,N)=0.0
+ 80 CONTINUE
+ 81 CONTINUE
+ 82 CONTINUE
+ DO 91 I=1,LX
+ DO 90 J=1,LY
+ VOL(I,J)=XX(I)*YY(J)
+ 90 CONTINUE
+ 91 CONTINUE
+ ELSEIF(IGE.EQ.1) THEN
+* ----------
+* 2D TUBE
+* ----------
+ DO 95 J=1,LY
+ YY(J)=YYY(J+1)-YYY(J)
+ 95 CONTINUE
+ DO 102 N=1,NPQ
+ VU=DU(N)*PI
+ DO 101 I=1,LX
+ XX(I)=XXX(I+1)-XXX(I)
+ VE=(XXX(I)+XXX(I+1))*VU
+ DO 100 J=1,LY
+ DA(I,J,N)=VE*YY(J)
+ 100 CONTINUE
+ 101 CONTINUE
+ 102 CONTINUE
+ DB(:LX,:NPQ)=0.0
+ DAL(:LX,:LY,:NPQ)=0.0
+ DO 135 J=1,LY
+ DO 111 I=1,LX
+ VE=2.0*PI*(XXX(I+1)-XXX(I))*YY(J)
+ DO 110 N=2,NPQ
+ DB(I,N)=DB(I,N-1)-W(N)*DU(N)*VE
+ 110 CONTINUE
+ 111 CONTINUE
+ DO 130 N=2,NPQ
+ VE=W(N)
+ IF(VE.LE.RLOG) GOTO 130
+ DO 120 I=1,LX
+ DAL(I,J,N)=(DB(I,N)+DB(I,N-1))/VE
+ 120 CONTINUE
+ 130 CONTINUE
+ 135 CONTINUE
+ DO 155 I=1,LX
+ VE=PI*XX(I)*(XXX(I+1)+XXX(I))
+ DO 140 N=1,NPQ
+ DB(I,N)=VE*DE(N)
+ 140 CONTINUE
+ DO 150 J=1,LY
+ VOL(I,J)=YY(J)*VE
+ 150 CONTINUE
+ 155 CONTINUE
+ ELSEIF(IGE.EQ.2) THEN
+* ----------
+* 2D HEXAGONAL
+* ----------
+ DET = SQRT(3.0)*(SIDE**2)/2.0
+ DO 162 N=1,NPQ
+ VU=DU(N)
+ VE=DE(N)
+ DO 161 I=1,LX
+ DB(I,N)=VE
+ DO 160 J=1,LY
+ DA(I,J,N)=VU
+ VOL(I,J)=DET
+ 160 CONTINUE
+ 161 CONTINUE
+ 162 CONTINUE
+ ENDIF
+*----
+* GENERATE SPHERICAL HARMONICS FOR SCATTERING SOURCE.
+*----
+ IOF=0
+ DO 211 L=0,ISCAT-1
+ DO 210 M=-L,L
+ IF(MOD(L+M,2).EQ.1) GO TO 210
+ IOF=IOF+1
+ IF(IOF.GT.NSCT) GO TO 211
+ DO 200 N=1,NPQ
+ ZI=SQRT(ABS(1.0-DU(N)**2-DE(N)**2))
+ IF(ZI.LT.1.0E-3) ZI=0.0
+ PL(IOF,N)=PNSH(L,M,ZI,DU(N),DE(N))
+ 200 CONTINUE
+ 210 CONTINUE
+ 211 CONTINUE
+*----
+* GENERATE MAPPING MATRIX FOR GALERKIN QUADRATURE METHOD
+*----
+ MN(:NPQ,:NSCT)=0.0
+ DN(:NSCT,:NPQ)=0.0
+ IL(:NSCT)=0
+ IM(:NSCT)=0
+ IF(IGLK.NE.0) THEN
+ ALLOCATE(U(NPQ,NPQ),RLM(NPQ,ISCAT,2*ISCAT-1),V(NPQ),V2(NPQ),
+ 1 MND(NPQ,NPQ))
+ RLM(:NPQ,:ISCAT,:2*ISCAT-1)=0.0
+ DO L=0,ISCAT-1
+ DO M=-L,L
+ DO N=1,NPQ
+ ZI=SQRT(ABS(1.0-DU(N)**2-DE(N)**2))
+ IF(ZI.LT.1.0E-3) ZI=0.0
+ RLM(N,L+1,M+L+1)=PNSH(L,M,DU(N),DE(N),ZI)
+ ENDDO
+ ENDDO
+ ENDDO
+ ! GRAM-SCHMIDT PROCEDURE TO FIND INDEPENDANT SET
+ ! OF SPHERICAL HARMONICS WITH ANY QUADRATURE
+ U(:NPQ,:NPQ)=0.0D0
+ NORM=0.0D0
+ DO N=1,NPQ
+ NORM=NORM+RLM(N,1,1)**2
+ ENDDO
+ NORM=SQRT(NORM)
+ DO N=1,NPQ
+ IF(IGLK.EQ.1) THEN
+ MND(1,N)=2.0D0*W(N)*RLM(N,1,1)
+ ELSEIF(IGLK.EQ.2) THEN
+ MND(N,1)=(2.0*L+1.0)/(4.0*PI)*RLM(N,1,1)
+ ELSE
+ CALL XABORT('UNKNOWN GALERKIN QUADRATURE METHOD.')
+ ENDIF
+ U(N,1)=RLM(N,1,1)/NORM
+ ENDDO
+ IND=1
+ ! ITERATE OVER THE SPHERICAL HARMONICS
+ DO 212 L=1,ISCAT-1
+ DO 213 M=0,L
+ V2(:NPQ)=0.0D0
+ DO N=1,IND
+ IPROD=0.0D0
+ DO N2=1,NPQ
+ IPROD=IPROD+U(N2,N)*RLM(N2,L+1,M+L+1)
+ ENDDO
+ DO N2=1,NPQ
+ V2(N2)=V2(N2)+IPROD*U(N2,N)
+ ENDDO
+ ENDDO
+ V(:NPQ)=0.0D0
+ DO N=1,NPQ
+ V(N)=RLM(N,L+1,M+L+1)-V2(N)
+ ENDDO
+ NORM=0.0D0
+ DO N=1,NPQ
+ NORM=NORM+V(N)**2
+ ENDDO
+ NORM=SQRT(NORM)
+ ! KEEP THE SPHERICAL HARMONICS IF IT IS INDEPENDANT
+ IF(NORM.GE.1.0E-5) THEN
+ IND=IND+1
+ DO N=1,NPQ
+ U(N,IND)=V(N)/NORM
+ IF(IGLK.EQ.1) THEN
+ MND(IND,N)=2.0D0*W(N)*RLM(N,L+1,M+L+1)
+ ELSEIF(IGLK.EQ.2) THEN
+ MND(N,IND)=(2.0*L+1.0)/(4.0*PI)*RLM(N,L+1,M+L+1)
+ ELSE
+ CALL XABORT('UNKNOWN GALERKIN QUADRATURE METHOD.')
+ ENDIF
+ ENDDO
+ IL(IND)=L
+ IM(IND)=M
+ ENDIF
+ IF(IND.EQ.NPQ) GOTO 217
+ 213 ENDDO
+ 212 ENDDO
+ CALL XABORT('SNTT2D: THE'//
+ 1 ' GRAM-SCHMIDTH PROCEDURE TO FIND A SUITABLE INTERPOLATION'//
+ 2 ' BASIS REQUIRE HIGHER LEGENDRE ORDER.')
+ ! FIND INVERSE MATRIX
+ 217 IF(IGLK.EQ.1) THEN
+ DN=REAL(MND)
+ CALL ALINVD(NPQ,MND,NPQ,IER)
+ IF(IER.NE.0) CALL XABORT('SNTT2D: SINGULAR MATRIX.')
+ MN=REAL(MND)
+ ELSEIF(IGLK.EQ.2) THEN
+ MN=REAL(MND)
+ CALL ALINVD(NPQ,MND,NPQ,IER)
+ IF(IER.NE.0) CALL XABORT('SNTT2D: SINGULAR MATRIX.')
+ DN=REAL(MND)
+ ELSE
+ CALL XABORT('UNKNOWN GALERKIN QUADRATURE METHOD.')
+ ENDIF
+ DEALLOCATE(U,RLM,V,V2,MND)
+ ELSE
+ IND=1
+ DO L=0,ISCAT-1
+ DO 218 M=-L,L
+ IF(MOD(L+M,2).EQ.1) GO TO 218
+ IL(IND)=L
+ IM(IND)=M
+ DO N=1,NPQ
+ ZI=SQRT(ABS(1.0-DU(N)**2-DE(N)**2))
+ IF(ZI.LT.1.0E-3) ZI=0.0
+ DN(IND,N)=2.0*W(N)*PNSH(L,M,ZI,DU(N),DE(N))
+ MN(N,IND)=(2.0*L+1.0)/(4.0*PI)
+ 1 *PNSH(L,M,ZI,DU(N),DE(N))
+ ENDDO
+ IND=IND+1
+ 218 ENDDO
+ ENDDO
+ ENDIF
+*----
+* GENERATE THE WEIGHTING PARAMETERS OF THE CLOSURE RELATION.
+*----
+ PX=1
+ PE=1
+ IF(ISCHM.EQ.1.OR.ISCHM.EQ.3) THEN
+ PX=1
+ ELSEIF(ISCHM.EQ.2) THEN
+ PX=0
+ ELSE
+ CALL XABORT('SNTT2D: UNKNOWN TYPE OF SPATIAL CLOSURE RELATION.')
+ ENDIF
+ IF(MOD(IELEM,2).EQ.1) THEN
+ WX(1)=-PX
+ WX(2:IELEM+1:2)=1+PX
+ IF(IELEM.GE.2) WX(3:IELEM+1:2)=1-PX
+ ELSE
+ WX(1)=PX
+ WX(2:IELEM+1:2)=1-PX
+ IF(IELEM.GE.2) WX(3:IELEM+1:2)=1+PX
+ ENDIF
+ IF(IBFP.NE.0) THEN
+ IF(ESCHM.EQ.1.OR.ESCHM.EQ.3) THEN
+ PE=1
+ ELSEIF(ESCHM.EQ.2) THEN
+ PE=0
+ ELSE
+ CALL XABORT('SNTT2D: UNKNOWN TYPE OF ENERGY CLOSURE RELATION.')
+ ENDIF
+ IF(MOD(EELEM,2).EQ.1) THEN
+ WE(1)=-PE
+ WE(2:EELEM+1:2)=1+PE
+ IF(EELEM.GE.2) WE(3:EELEM+1:2)=1-PE
+ ELSE
+ WE(1)=PE
+ WE(2:EELEM+1:2)=1-PE
+ IF(EELEM.GE.2) WE(3:EELEM+1:2)=1+PE
+ ENDIF
+ ENDIF
+ ! NORMALIZED LEGENDRE POLYNOMIAL CONSTANTS
+ DO IEL=1,MAX(IELEM,EELEM)
+ CST(IEL)=SQRT(2.0*IEL-1.0)
+ ENDDO
+*----
+* COMPUTE ISOTROPIC FLUX INDICES.
+*----
+ NM=IELEM*IELEM*EELEM
+ NMX=IELEM*EELEM
+ NMY=IELEM*EELEM
+ NME=IELEM**2
+ LL4=LX*LY*NSCT*NM
+ IF(IGE.LT.2) THEN
+ NUN=LL4+(LX*NMY+LY*NMX)*NPQ
+ DO I=1,LX*LY
+ IDL(I)=(I-1)*NSCT*NM+1
+ ENDDO
+ ELSEIF(IGE.EQ.2) THEN
+ NUN=LL4
+ DO I=1,LX
+ IDL(I)=(I-1)*NSCT*NM+1
+ ENDDO
+ ELSE
+ CALL XABORT('SNTT2D: CHECK SPATIAL SCHEME DISCRETISATION '//
+ 1 'PARAMETER.')
+ ENDIF
+*----
+* SET BOUNDARY CONDITIONS.
+*----
+ DO 240 I=1,4
+ IF(NCODE(I).NE.1) ZCODE(I)=1.0
+ IF(NCODE(I).EQ.5) CALL XABORT('SNTT2D: SYME BC NOT ALLOWED.')
+ IF(NCODE(I).EQ.7) CALL XABORT('SNTT2D: ZERO FLUX BC NOT ALLOWED.')
+ 240 CONTINUE
+*----
+* CHECK FOR INVALID VIRTUAL ELEMENTS.
+*----
+ DO 295 I=2,LX-1
+ DO 290 J=2,LY-1
+ IF(MAT(I,J).EQ.0) THEN
+ L1=(NCODE(1).NE.1)
+ DO 250 J1=1,J-1
+ L1=L1.OR.(MAT(I,J1).NE.0)
+ 250 CONTINUE
+ L2=(NCODE(2).NE.1)
+ DO 260 J1=J+1,LY
+ L2=L2.OR.(MAT(I,J1).NE.0)
+ 260 CONTINUE
+ L3=(NCODE(3).NE.1)
+ DO 270 I1=1,I-1
+ L3=L3.OR.(MAT(I1,J).NE.0)
+ 270 CONTINUE
+ L4=(NCODE(4).NE.1)
+ DO 280 I1=I+1,LX
+ L4=L4.OR.(MAT(I1,J).NE.0)
+ 280 CONTINUE
+ IF(L1.AND.L2.AND.L3.AND.L4) THEN
+ WRITE(HSMG,'(17HSNTT2D: ELEMENT (,I3,1H,,I3,11H) CANNOT BE,
+ 1 9H VIRTUAL.)') I,J
+ CALL XABORT(HSMG)
+ ENDIF
+ ENDIF
+ 290 CONTINUE
+ 295 CONTINUE
+*----
+* SCRATCH STORAGE DEALLOCATION
+*----
+ DEALLOCATE(YY,XX)
+ RETURN
+ END
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