*DECK PNSZ2D SUBROUTINE PNSZ2D(ITY,NREG,IELEM,ICOL,XX,YY,MAT,VOL,NBMIX,NLF, 1 NVD,NAN,SIGT,SIGTI,L4,KN,QFR,LC,R,V,FUNKNO,SUNKNO) * *----------------------------------------------------------------------- * *Purpose: * Source calculation for a SPN approximation in BIVAC, including * neighbour Legendre and out-of-group contributions. * Raviart-Thomas method in 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. * NREG total number of regions. * 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). * XX X-directed mesh spacings. * YY Y-directed mesh spacings. * MAT index-number of the mixture type assigned to each volume. * VOL volumes. * 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 macroscopic cross sections ordered by mixture. * 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. * L4 order of the profiled system matrices. * KN element-ordered unknown list. * QFR element-ordered boundary conditions. * LC order of the unit matrices. * R unit Cartesian mass matrix. * V unit nodal coupling matrix. * FUNKNO initial fluxes. * SUNKNO initial sources. * *Parameters: output * SUNKNO modified sources. * *----------------------------------------------------------------------- * *---- * SUBROUTINE ARGUMENTS *---- INTEGER ITY,NREG,IELEM,ICOL,MAT(NREG),NBMIX,NLF,NVD,NAN,L4, 1 KN(5*NREG),LC REAL XX(NREG),YY(NREG),VOL(NREG),SIGT(NBMIX,NAN),SIGTI(NBMIX,NAN), 1 QFR(4*NREG),R(LC,LC),V(LC,LC-1),SUNKNO(L4*NLF/2),FUNKNO(L4*NLF/2) *---- * 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 DO 170 IL=0,NLF-1 IF((ITY.EQ.1).AND.(IL.GE.NAN)) GO TO 170 FACT=REAL(2*IL+1) *---- * COMPUTE THE SOURCE AT ORDER IL. *---- NUM1=0 NUM2=0 DO 160 K=1,NREG IBM=MAT(K) IF(IBM.EQ.0) GO TO 160 VOL0=VOL(K) GARS=SIGT(IBM,MIN(IL+1,NAN)) IF(MOD(IL,2).EQ.0) THEN DO 50 I0=1,IELEM DO 20 J0=1,IELEM JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 SUNKNO(JND1)=SUNKNO(JND1)+FACT*VOL0*GARS*FUNKNO(JND1) 20 CONTINUE IF(ITY.EQ.1) GO TO 50 * IND1=(IL/2)*L4+ABS(KN(NUM1+2))+I0-1 IND2=(IL/2)*L4+ABS(KN(NUM1+3))+I0-1 IND3=(IL/2)*L4+ABS(KN(NUM1+4))+I0-1 IND4=(IL/2)*L4+ABS(KN(NUM1+5))+I0-1 DO 30 J0=1,IELEM JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 IF(KN(NUM1+2).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+2))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL+1)*VOL0*V(1,J0)* 1 FUNKNO(IND1)/XX(K) ENDIF IF(KN(NUM1+3).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+3))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL+1)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(IND2)/XX(K) ENDIF JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 IF(KN(NUM1+4).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+4))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL+1)*VOL0*V(1,J0)* 1 FUNKNO(IND3)/YY(K) ENDIF IF(KN(NUM1+5).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+5))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL+1)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(IND4)/YY(K) ENDIF 30 CONTINUE IF(IL.GE.2) THEN IND1=((IL-2)/2)*L4+ABS(KN(NUM1+2))+I0-1 IND2=((IL-2)/2)*L4+ABS(KN(NUM1+3))+I0-1 IND3=((IL-2)/2)*L4+ABS(KN(NUM1+4))+I0-1 IND4=((IL-2)/2)*L4+ABS(KN(NUM1+5))+I0-1 DO 40 J0=1,IELEM JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 IF(KN(NUM1+2).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+2))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL)*VOL0*V(1,J0)* 1 FUNKNO(IND1)/XX(K) ENDIF IF(KN(NUM1+3).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+3))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(IND2)/XX(K) ENDIF JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 IF(KN(NUM1+4).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+4))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL)*VOL0*V(1,J0)* 1 FUNKNO(IND3)/YY(K) ENDIF IF(KN(NUM1+5).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+5))) SUNKNO(JND1)=SUNKNO(JND1)+SG*REAL(IL)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(IND4)/YY(K) ENDIF 40 CONTINUE ENDIF 50 CONTINUE ELSE IF(MOD(IL,2).EQ.1) THEN GARSI=SIGTI(IBM,MIN(IL+1,NAN)) DO 150 I0=1,IELEM * PARTIAL INVERSION OF THE ODD PARITY EQUATION. MODIFICATION OF * THE EVEN PARITY EQUATION. IF(IELEM.GT.1) THEN DO 65 J0=1,IELEM DO 60 K0=1,IELEM IF(QQ(J0,K0).EQ.0.0) GO TO 60 JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 KND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)**2)*VOL0*QQ(J0,K0)* 1 GARSI*FUNKNO(KND1)/(FACT*XX(K)*XX(K)) JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 KND1=(IL/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)**2)*VOL0*QQ(J0,K0)* 1 GARSI*FUNKNO(KND1)/(FACT*YY(K)*YY(K)) IF(IL.LE.NLF-3) THEN JND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 KND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*XX(K)*XX(K)) JND1=((IL+2)/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 KND1=(IL/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*YY(K)*YY(K)) JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 KND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*XX(K)*XX(K)) JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 KND1=((IL+2)/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*YY(K)*YY(K)) JND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 KND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+K0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL+1)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*XX(K)*XX(K)) JND1=((IL+2)/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 KND1=((IL+2)/2)*L4+KN(NUM1+1)+(K0-1)*IELEM+I0-1 SUNKNO(JND1)=SUNKNO(JND1)+(REAL(IL+1)*REAL(IL+1))*VOL0* 1 QQ(J0,K0)*GARSI*FUNKNO(KND1)/(FACT*YY(K)*YY(K)) ENDIF 60 CONTINUE 65 CONTINUE ENDIF * ODD PARITY EQUATION. DO 75 IC=1,2 IIC=1 IF(IC.EQ.2) IIC=IELEM+1 IND1=(IL/2)*L4+ABS(KN(NUM1+1+IC))+I0-1 S1=REAL(SIGN(1,KN(NUM1+1+IC))) DO 70 JC=1,2 JJC=1 IF(JC.EQ.2) JJC=IELEM+1 IND2=(IL/2)*L4+ABS(KN(NUM1+1+JC))+I0-1 IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0)) THEN S2=REAL(SIGN(1,KN(NUM1+1+JC))) SUNKNO(IND1)=SUNKNO(IND1)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS* 1 FUNKNO(IND2) ENDIF 70 CONTINUE 75 CONTINUE DO 85 IC=3,4 IF(IC.EQ.3) IIC=1 IF(IC.EQ.4) IIC=IELEM+1 IND1=(IL/2)*L4+ABS(KN(NUM1+1+IC))+I0-1 S1=REAL(SIGN(1,KN(NUM1+1+IC))) DO 80 JC=3,4 IF(JC.EQ.3) JJC=1 IF(JC.EQ.4) JJC=IELEM+1 IND2=(IL/2)*L4+ABS(KN(NUM1+1+JC))+I0-1 IF((KN(NUM1+1+IC).NE.0).AND.(KN(NUM1+1+JC).NE.0)) THEN S2=REAL(SIGN(1,KN(NUM1+1+JC))) SUNKNO(IND1)=SUNKNO(IND1)-S1*S2*FACT*R(IIC,JJC)*VOL0*GARS* 1 FUNKNO(IND2) ENDIF 80 CONTINUE 85 CONTINUE IF(ITY.EQ.1) GO TO 150 * IND1=(IL/2)*L4+ABS(KN(NUM1+2))+I0-1 IND2=(IL/2)*L4+ABS(KN(NUM1+3))+I0-1 IND3=(IL/2)*L4+ABS(KN(NUM1+4))+I0-1 IND4=(IL/2)*L4+ABS(KN(NUM1+5))+I0-1 IF((QFR(NUM2+1).NE.0.0).AND.(KN(NUM1+2).NE.0)) THEN * XINF SIDE. DO 90 IL2=1,NLF-1,2 ZMARS=PNMAR2(NZMAR,IL2,IL) IND5=(IL2/2)*L4+ABS(KN(NUM1+2))+I0-1 SUNKNO(IND1)=SUNKNO(IND1)-0.5*FACT*QFR(NUM2+1)*ZMARS* 1 FUNKNO(IND5) 90 CONTINUE ENDIF IF((QFR(NUM2+2).NE.0.0).AND.(KN(NUM1+3).NE.0)) THEN * XSUP SIDE. DO 100 IL2=1,NLF-1,2 ZMARS=PNMAR2(NZMAR,IL2,IL) IND5=(IL2/2)*L4+ABS(KN(NUM1+3))+I0-1 SUNKNO(IND2)=SUNKNO(IND2)-0.5*FACT*QFR(NUM2+2)*ZMARS* 1 FUNKNO(IND5) 100 CONTINUE ENDIF IF((QFR(NUM2+3).NE.0.0).AND.(KN(NUM1+4).NE.0)) THEN * YINF SIDE. DO 110 IL2=1,NLF-1,2 ZMARS=PNMAR2(NZMAR,IL2,IL) IND5=(IL2/2)*L4+ABS(KN(NUM1+4))+I0-1 SUNKNO(IND3)=SUNKNO(IND3)-0.5*FACT*QFR(NUM2+3)*ZMARS* 1 FUNKNO(IND5) 110 CONTINUE ENDIF IF((QFR(NUM2+4).NE.0.0).AND.(KN(NUM1+5).NE.0)) THEN * YSUP SIDE. DO 120 IL2=1,NLF-1,2 ZMARS=PNMAR2(NZMAR,IL2,IL) IND5=(IL2/2)*L4+ABS(KN(NUM1+5))+I0-1 SUNKNO(IND4)=SUNKNO(IND4)-0.5*FACT*QFR(NUM2+4)*ZMARS* 1 FUNKNO(IND5) 120 CONTINUE ENDIF * DO 130 J0=1,IELEM JND1=(IL/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 IF(KN(NUM1+2).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+2))) SUNKNO(IND1)=SUNKNO(IND1)+SG*REAL(IL)*VOL0*V(1,J0)* 1 FUNKNO(JND1)/XX(K) ENDIF IF(KN(NUM1+3).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+3))) SUNKNO(IND2)=SUNKNO(IND2)+SG*REAL(IL)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(JND1)/XX(K) ENDIF JND1=(IL/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 IF(KN(NUM1+4).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+4))) SUNKNO(IND3)=SUNKNO(IND3)+SG*REAL(IL)*VOL0*V(1,J0)* 1 FUNKNO(JND1)/YY(K) ENDIF IF(KN(NUM1+5).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+5))) SUNKNO(IND4)=SUNKNO(IND4)+SG*REAL(IL)*VOL0*V(IELEM+1,J0)* 1 FUNKNO(JND1)/YY(K) ENDIF 130 CONTINUE IF(IL.LE.NLF-3) THEN DO 140 J0=1,IELEM JND1=((IL+2)/2)*L4+KN(NUM1+1)+(I0-1)*IELEM+J0-1 IF(KN(NUM1+2).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+2))) SUNKNO(IND1)=SUNKNO(IND1)+SG*REAL(IL+1)*VOL0*V(1,J0)* 1 FUNKNO(JND1)/XX(K) ENDIF IF(KN(NUM1+3).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+3))) SUNKNO(IND2)=SUNKNO(IND2)+SG*REAL(IL+1)*VOL0* 1 V(IELEM+1,J0)*FUNKNO(JND1)/XX(K) ENDIF JND1=((IL+2)/2)*L4+KN(NUM1+1)+(J0-1)*IELEM+I0-1 IF(KN(NUM1+4).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+4))) SUNKNO(IND3)=SUNKNO(IND3)+SG*REAL(IL+1)*VOL0*V(1,J0)* 1 FUNKNO(JND1)/YY(K) ENDIF IF(KN(NUM1+5).NE.0) THEN SG=REAL(SIGN(1,KN(NUM1+5))) SUNKNO(IND4)=SUNKNO(IND4)+SG*REAL(IL+1)*VOL0* 1 V(IELEM+1,J0)*FUNKNO(JND1)/YY(K) ENDIF 140 CONTINUE ENDIF 150 CONTINUE ENDIF NUM1=NUM1+5 NUM2=NUM2+4 160 CONTINUE 170 CONTINUE RETURN END