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|
*DECK NSSEIG
SUBROUTINE NSSEIG(NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,MAT,IDL,
> VOL,MUX,MUY,MUZ,IMAX,IMAY,IMAZ,IPY,IPZ,CHI,SIGF,SCAT,A11X,A11Y,
> A11Z,EPSTHR,MAXTHR,NADI,EPSOUT,MAXOUT,ICL1,ICL2,ITER,EVECT,
> FKEFF,IMPX)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solution of a multigroup eigenvalue system for the calculation of the
* direct neutron flux in Trivac. Use the preconditioned power method
* with a two-parameter SVAT acceleration technique. CMFD solution.
*
*Copyright:
* Copyright (C) 2023 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
* NMAX first dimension of array A11X.
* NMAY first dimension of array A11Y.
* NMAZ first dimension of array A11Z.
* LL4F number of unknowns per energy group.
* NDIM number of dimensions (1, 2 or 3).
* NEL number of nodes.
* NMIX number of mixtures in the nodal calculation.
* NG number of energy groups.
* MAT material mixtures.
* IDL position of averaged fluxes in unknown vector.
* VOL node volumes.
* MUX X-oriented compressed storage mode indices.
* MUY Y-oriented compressed storage mode indices.
* MUZ Z-oriented compressed storage mode indices.
* IMAX X-oriented position of each first non-zero column element.
* IMAY Y-oriented position of each first non-zero column element.
* IMAZ Z-oriented position of each first non-zero column element.
* IPY Y-oriented permutation matrices.
* IPZ Z-oriented permutation matrices.
* CHI fission spectra.
* SIGF nu times fission cross section.
* SCAT scattering cross section.
* A11X X-oriented sparse coefficient matrix.
* A11Y Y-oriented sparse coefficient matrix.
* A11Z Z-oriented sparse coefficient matrix.
* EPSTHR thermal iteration epsilon.
* MAXTHR maximum number of thermal iterations.
* NADI number of inner ADI iterations.
* EPSOUT convergence epsilon for the power method.
* MAXOUT maximum number of iterations for the power method.
* ICL1 number of free iretations in one cycle of the up-scattering
* iterations.
* ICL2 number of accelerated up-scattering iterations in one cycle.
* EVECT initial estimate of fundamental eigenvalue.
* IMPX print parameter.
* FKEFF initial estimate of fundamental eigenvalue.
*
*Parameters: output
* ITER number of iterations.
* EVECT corresponding eigenvector.
* FKEFF fundamental eigenvalue.
*
*-----------------------------------------------------------------------
*
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER, INTENT(IN) :: NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,
> MAT(NEL),IDL(NEL),MUX(LL4F),MUY(LL4F),MUZ(LL4F),IMAX(LL4F),
> IMAY(LL4F),IMAZ(LL4F),IPY(LL4F),IPZ(LL4F),MAXTHR,NADI,MAXOUT,
> ICL1,ICL2,IMPX
REAL, INTENT(IN) :: VOL(NEL),CHI(NMIX,NG),SIGF(NMIX,NG),
> SCAT(NMIX,NG,NG),A11X(NMAX,NG),A11Y(NMAY,NG),A11Z(NMAZ,NG)
INTEGER, INTENT(OUT) :: ITER
REAL, INTENT(IN) :: EPSTHR,EPSOUT
REAL, INTENT(INOUT) :: EVECT(LL4F,NG),FKEFF
*----
* LOCAL VARIABLES
*----
REAL, PARAMETER :: EPS1=1.0E-5
REAL(KIND=8), PARAMETER :: ALP_TAB(24) = (/ 0.2, 0.4, 0.6,
1 0.8, 1.0, 1.2, 1.5, 2.0, 10.0, 15.0, 20.0, 25.0, 30.0, 35.0,
2 40.0, 45.0, 50.0, 55.0, 60.0, 65.0, 70.0, 75.0, 80.0, 85.0 /)
REAL(KIND=8), PARAMETER :: BET_TAB(11) = (/ -1.0, -0.8, -0.6,
1 -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, 0.8, 1.0 /)
REAL(KIND=8) :: AEAE,AEAG,AEAH,AGAG,AGAH,AHAH,BEBE,BEBG,BEBH,
1 BGBG,BGBH,BHBH,AEBE,AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH,
2 X,DXDA,DXDB,Y,DYDA,DYDB,Z,DZDA,DZDB,F,D2F(2,3),EVAL,ALP,BET,
3 FMIN,VVV
LOGICAL LOGTES
CHARACTER(LEN=3) :: TEXT3
*----
* ALLOCATABLE ARRAYS
*----
REAL, ALLOCATABLE, DIMENSION(:) :: S2,F1,GARM1,GARM2
REAL, ALLOCATABLE, DIMENSION(:,:) :: S,GRAD1,GRAD2,GAR1,GAR2,
1 GAR3,GAF1,GAF2,GAF3
REAL, ALLOCATABLE, DIMENSION(:,:) :: IA11X,IA11Y,IA11Z
REAL, ALLOCATABLE, DIMENSION(:,:,:) :: WORK
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(S2(LL4F),S(LL4F,NG),GRAD1(LL4F,NG),GRAD2(LL4F,NG),
> GAR1(LL4F,NG),GAR2(LL4F,NG),GAR3(LL4F,NG),GAF1(LL4F,NG),
> GAF2(LL4F,NG),GAF3(LL4F,NG),WORK(LL4F,NG,3),IA11X(NMAX,NG),
> IA11Y(NMAY,NG),IA11Z(NMAZ,NG))
*----
* LU MATRIX FACTORIZATION
*----
IA11X(:NMAX,:NG)=A11X(:NMAX,:NG)
DO IG=1,NG
CALL ALLUF(LL4F,IA11X(1,IG),MUX,IMAX)
ENDDO
IF(NDIM.GT.1) THEN
IA11Y(:NMAY,:NG)=A11Y(:NMAY,:NG)
DO IG=1,NG
CALL ALLUF(LL4F,IA11Y(1,IG),MUY,IMAY)
ENDDO
ENDIF
IF(NDIM.EQ.3) THEN
IA11Z(:NMAZ,:NG)=A11Z(:NMAZ,:NG)
DO IG=1,NG
CALL ALLUF(LL4F,IA11Z(1,IG),MUZ,IMAZ)
ENDDO
ENDIF
*----
* POWER METHOD
*----
NCTOT=ICL1+ICL2
IF(ICL2.EQ.0) THEN
NCPTM=NCTOT+1
ELSE
NCPTM=ICL1
ENDIF
EVAL=1.0D0/FKEFF
VVV=0.0D0
ISTART=1
NNADI=NADI
TEST=0.0
IF(IMPX.GE.2) WRITE (6,600) NADI
ITER=0
DO
ITER=ITER+1
IF(ITER > MAXOUT) CALL XABORT('NSSEIG: OUTER ITER. FAILURE.')
*----
* EIGENVALUE EVALUATION
*----
CALL NSSMPA(NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,MAT,IDL,
> VOL,MUX,MUY,MUZ,IMAX,IMAY,IMAZ,IPY,IPZ,SCAT,A11X,A11Y,A11Z,
> EVECT,WORK(1,1,1))
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,EVECT,
> WORK(1,1,2))
AEBE=0.0D0
BEBE=0.0D0
DO IG=1,NG
DO I=1,LL4F
AEBE=AEBE+WORK(I,IG,1)*WORK(I,IG,2)
BEBE=BEBE+WORK(I,IG,2)**2
ENDDO
ENDDO
EVAL=AEBE/BEBE
S(:LL4F,:NG)=REAL(EVAL)*WORK(:LL4F,:NG,2)-WORK(:LL4F,:NG,1)
*----
* PERFORM THERMAL (UP-SCATTERING) ITERATIONS
*----
WORK(:LL4F,:NG,:3)=0.0D0
IGDEB=1
TEXT3='NO '
JTER=1
ALLOCATE(F1(LL4F),GARM1(LL4F),GARM2(LL4F))
DO
WORK(:LL4F,:NG,1)=WORK(:LL4F,:NG,2)
WORK(:LL4F,:NG,2)=WORK(:LL4F,:NG,3)
WORK(:LL4F,:NG,3)=0.0D0
GRAD1(:LL4F,:NG)=0.0D0
DO IG=IGDEB,NG
S2(:LL4F)=S(:LL4F,IG)
DO JG=1,NG
IF(JG.EQ.IG) CYCLE
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM.LE.0) CYCLE
IND=IDL(IEL)
IF(IND.EQ.0) CYCLE
S2(IND)=S2(IND)+VOL(IEL)*SCAT(IBM,IG,JG)*GRAD1(IND,JG)
ENDDO
ENDDO
*
WORK(:LL4F,IG,3)=0.0
DO IADI=1,NNADI
IF(IADI.EQ.1) THEN
F1(:LL4F)=S2(:LL4F)
ELSE
* scalar multiplication for a x-oriented matrix.
CALL ALLUM(LL4F,A11X(1,IG),WORK(1,IG,3),F1(1),MUX,
1 IMAX,1)
IF(NDIM.GE.2) THEN
* scalar multiplication for a y-oriented matrix.
GARM1(IPY(:LL4F))=WORK(:LL4F,IG,3)
GARM2(IPY(:LL4F))=F1(:LL4F)
CALL ALLUM(LL4F,A11Y(1,IG),GARM1(1),GARM2(1),MUY,
1 IMAY,2)
F1(:LL4F)=GARM2(IPY(:LL4F))
ENDIF
IF(NDIM.EQ.3) THEN
* scalar multiplication for a z-oriented matrix.
GARM1(IPZ(:LL4F))=WORK(:LL4F,IG,3)
GARM2(IPZ(:LL4F))=F1(:LL4F)
CALL ALLUM(LL4F,A11Z(1,IG),GARM1(1),GARM2(1),MUZ,
1 IMAZ,2)
F1(:LL4F)=GARM2(IPZ(:LL4F))
ENDIF
F1(:LL4F)=S2(:LL4F)-F1(:LL4F)
ENDIF
* scalar solution for a x-oriented linear system.
CALL ALLUS(LL4F,MUX,IMAX,IA11X(1,IG),F1)
IF(NDIM.GE.2) THEN
* scalar solution for a y-oriented linear system.
DO I=1,LL4F
II=IPY(I)
GARM1(II)=F1(I)*A11Y(MUY(II),IG)
ENDDO
CALL ALLUS(LL4F,MUY,IMAY,IA11Y(1,IG),GARM1)
F1(:LL4F)=GARM1(IPY(:LL4F))
ENDIF
IF(NDIM.EQ.3) THEN
* scalar solution for a z-oriented linear system.
DO I=1,LL4F
II=IPZ(I)
GARM1(II)=F1(I)*A11Z(MUZ(II),IG)
ENDDO
CALL ALLUS(LL4F,MUZ,IMAZ,IA11Z(1,IG),GARM1)
F1(:LL4F)=GARM1(IPZ(:LL4F))
ENDIF
WORK(:LL4F,IG,3)=WORK(:LL4F,IG,3)+F1(:LL4F)
GRAD1(:LL4F,IG)=WORK(:LL4F,IG,3)
ENDDO
ENDDO
IF(MAXTHR.EQ.0) EXIT
IF(MOD(JTER-1,NCTOT).GE.NCPTM) THEN
CALL NSS2AC(NG,LL4F,IGDEB,WORK,ZMU)
ELSE
ZMU=1.0D0
ENDIF
IGDEBO=IGDEB
DO IG=IGDEBO,NG
GINN=0.0D0
FINN=0.0D0
DO I=1,LL4F
GINN=MAX(GINN,ABS(WORK(I,IG,2)-WORK(I,IG,3)))
FINN=MAX(FINN,ABS(WORK(I,IG,3)))
ENDDO
GINN=GINN/FINN
IF((GINN.LT.EPSTHR).AND.(IGDEB.EQ.IG)) IGDEB=IGDEB+1
ENDDO
IF(GINN.LT.EPSTHR) TEXT3='YES'
IF(IMPX.GT.2) WRITE(6,610) JTER,GINN,EPSTHR,IGDEB,ZMU,TEXT3
IF((GINN.LT.EPSTHR).OR.(JTER.EQ.MAXTHR)) EXIT
JTER=JTER+1
ENDDO
DEALLOCATE(GARM2,GARM1,F1)
*----
* DISPLACEMENT EVALUATION
*----
F=0.0D0
DELS=ABS(REAL((EVAL-VVV)/EVAL))
VVV=EVAL
*----
* EVALUATION OF THE TWO ACCELERATION PARAMETERS ALP AND BET
*----
ALP=1.0D0
BET=0.0D0
N=0
AEAE=0.0D0
AEAG=0.0D0
AEAH=0.0D0
AGAG=0.0D0
AGAH=0.0D0
AHAH=0.0D0
BEBG=0.0D0
BEBH=0.0D0
BGBG=0.0D0
BGBH=0.0D0
BHBH=0.0D0
AEBG=0.0D0
AEBH=0.0D0
AGBE=0.0D0
AGBG=0.0D0
AGBH=0.0D0
AHBE=0.0D0
AHBG=0.0D0
AHBH=0.0D0
CALL NSSMPA(NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,MAT,IDL,VOL,
> MUX,MUY,MUZ,IMAX,IMAY,IMAZ,IPY,IPZ,SCAT,A11X,A11Y,A11Z,EVECT,
> GAR1)
CALL NSSMPA(NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,MAT,IDL,VOL,
> MUX,MUY,MUZ,IMAX,IMAY,IMAZ,IPY,IPZ,SCAT,A11X,A11Y,A11Z,GRAD1,
> GAR2)
IF(1+MOD(ITER-ISTART,ICL1+ICL2).GT.ICL1) THEN
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,EVECT,GAF1)
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,GRAD1,GAF2)
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,GRAD2,GAF3)
DO IG=1,NG
DO I=1,LL4F
* COMPUTE (A ,A )
AEAE=AEAE+GAR1(I,IG)**2
AEAG=AEAG+GAR1(I,IG)*GAR2(I,IG)
AEAH=AEAH+GAR1(I,IG)*GAR3(I,IG)
AGAG=AGAG+GAR2(I,IG)**2
AGAH=AGAH+GAR2(I,IG)*GAR3(I,IG)
AHAH=AHAH+GAR3(I,IG)**2
* COMPUTE (B ,B )
BEBG=BEBG+GAF1(I,IG)*GAF2(I,IG)
BEBH=BEBH+GAF1(I,IG)*GAF3(I,IG)
BGBG=BGBG+GAF2(I,IG)**2
BGBH=BGBH+GAF2(I,IG)*GAF3(I,IG)
BHBH=BHBH+GAF3(I,IG)**2
* COMPUTE (A ,B )
AEBG=AEBG+GAR1(I,IG)*GAF2(I,IG)
AEBH=AEBH+GAR1(I,IG)*GAF3(I,IG)
AGBE=AGBE+GAR2(I,IG)*GAF1(I,IG)
AGBG=AGBG+GAR2(I,IG)*GAF2(I,IG)
AGBH=AGBH+GAR2(I,IG)*GAF3(I,IG)
AHBE=AHBE+GAR3(I,IG)*GAF1(I,IG)
AHBG=AHBG+GAR3(I,IG)*GAF2(I,IG)
AHBH=AHBH+GAR3(I,IG)*GAF3(I,IG)
ENDDO
ENDDO
*
210 N=N+1
IF(N.GT.10) GO TO 215
* COMPUTE X(ITER+1)
X=BEBE+ALP*ALP*BGBG+BET*BET*BHBH+2.0D0*(ALP*BEBG+BET*BEBH
> +ALP*BET*BGBH)
DXDA=2.0D0*(BEBG+ALP*BGBG+BET*BGBH)
DXDB=2.0D0*(BEBH+ALP*BGBH+BET*BHBH)
* COMPUTE Y(ITER+1)
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
> +ALP*BET*AGAH)
DYDA=2.0D0*(AEAG+ALP*AGAG+BET*AGAH)
DYDB=2.0D0*(AEAH+ALP*AGAH+BET*AHAH)
* COMPUTE Z(ITER+1)
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
> +BET*(AEBH+AHBE)+ALP*BET*(AGBH+AHBG)
DZDA=AEBG+AGBE+2.0D0*ALP*AGBG+BET*(AGBH+AHBG)
DZDB=AEBH+AHBE+ALP*(AGBH+AHBG)+2.0D0*BET*AHBH
* COMPUTE F(ITER+1)
F=X*Y-Z*Z
D2F(1,1)=2.0D0*(BGBG*Y+DXDA*DYDA+X*AGAG-DZDA**2-2.0D0*Z*AGBG)
D2F(1,2)=2.0D0*BGBH*Y+DXDA*DYDB+DXDB*DYDA+2.0D0*X*AGAH
> -2.0D0*DZDA*DZDB-2.0D0*Z*(AGBH+AHBG)
D2F(2,2)=2.0D0*(BHBH*Y+DXDB*DYDB+X*AHAH-DZDB**2-2.0D0*Z*AHBH)
D2F(2,1)=D2F(1,2)
D2F(1,3)=DXDA*Y+X*DYDA-2.0D0*Z*DZDA
D2F(2,3)=DXDB*Y+X*DYDB-2.0D0*Z*DZDB
* SOLUTION OF A LINEAR SYSTEM.
CALL ALSBD(2,1,D2F,IER,2)
IF(IER.NE.0) GO TO 215
ALP=ALP-D2F(1,3)
BET=BET-D2F(2,3)
IF(ALP.GT.100.0D0) GO TO 215
IF((ABS(D2F(1,3)).LE.1.0D-4).AND.(ABS(D2F(2,3)).LE.1.0D-4))
> GO TO 220
GO TO 210
*
* alternative algorithm in case of Newton-Raphton failure
215 IF(IMPX.GT.0) WRITE(6,'(/30H NSSEIG: FAILURE OF THE NEWTON,
> 55H-RAPHTON ALGORIHTHM FOR COMPUTING THE OVERRELAXATION PA,
> 9HRAMETERS.)')
IAMIN=999
IBMIN=999
FMIN=HUGE(FMIN)
DO IA=1,SIZE(ALP_TAB)
ALP=ALP_TAB(IA)
DO IB=1,SIZE(BET_TAB)
BET=BET_TAB(IB)
* COMPUTE X
X=BEBE+ALP*ALP*BGBG+BET*BET*BHBH+2.0D0*(ALP*BEBG+BET*BEBH
> +ALP*BET*BGBH)
* COMPUTE Y
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
> +ALP*BET*AGAH)
* COMPUTE Z
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
> +BET*(AEBH+AHBE)+ALP*BET*(AGBH+AHBG)
* COMPUTE F
F=X*Y-Z*Z
IF(F.LT.FMIN) THEN
IAMIN=IA
IBMIN=IB
FMIN=F
ENDIF
ENDDO
ENDDO
ALP=ALP_TAB(IAMIN)
BET=BET_TAB(IBMIN)
220 BET=BET/ALP
IF((ALP.LT.1.0D0).AND.(ALP.GT.0.0D0)) THEN
ALP=1.0D0
BET=0.0D0
ELSE IF(ALP.LE.0.0D0) THEN
ISTART=ITER+1
ALP=1.0D0
BET=0.0D0
ENDIF
DO IG=1,NG
DO I=1,LL4F
GRAD1(I,IG)=REAL(ALP)*(GRAD1(I,IG)+REAL(BET)*GRAD2(I,IG))
GAR2(I,IG)=REAL(ALP)*(GAR2(I,IG)+REAL(BET)*GAR3(I,IG))
ENDDO
ENDDO
ENDIF
*
LOGTES=(ITER.LT.ICL1).OR.(MOD(ITER-ISTART,ICL1+ICL2).EQ.ICL1-1)
DELT=0.0D0
IF(LOGTES.AND.(DELS.LE.EPS1)) THEN
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,EVECT,GAF1)
CALL NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,GRAD1,GAF2)
DO IG=1,NG
DELN=0.0D0
DELD=0.0D0
DO I=1,LL4F
EVECT(I,IG)=EVECT(I,IG)+GRAD1(I,IG)
GAR1(I,IG)=GAR1(I,IG)+GAR2(I,IG)
GRAD2(I,IG)=GRAD1(I,IG)
GAR3(I,IG)=GAR2(I,IG)
DELN=MAX(DELN,ABS(GAF2(I,IG)))
DELD=MAX(DELD,ABS(GAF1(I,IG)))
ENDDO
IF(DELD.NE.0.0D0) DELT=MAX(DELT,DELN/DELD)
ENDDO
IF(IMPX.GE.2) WRITE (6,620) ITER,AEAE,AEAG,AEAH,AGAG,AGAH,
> AHAH,BEBE,ALP,BET,EVAL,F,DELS,DELT,N,BEBG,BEBH,BGBG,BGBH,
> BHBH,AEBE,AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
IF(DELT.LE.EPSOUT) EXIT
ELSE
DO IG=1,NG
DO I=1,LL4F
EVECT(I,IG)=EVECT(I,IG)+GRAD1(I,IG)
GAR1(I,IG)=GAR1(I,IG)+GAR2(I,IG)
GRAD2(I,IG)=GRAD1(I,IG)
GAR3(I,IG)=GAR2(I,IG)
ENDDO
ENDDO
IF(IMPX.GE.2) WRITE (6,620) ITER,AEAE,AEAG,AEAH,AGAG,AGAH,
> AHAH,BEBE,ALP,BET,EVAL,F,DELS,DELT,N,BEBG,BEBH,BGBG,BGBH,
> BHBH,AEBE,AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
ENDIF
*
IF(ITER.EQ.1) TEST=DELS
IF((ITER.GT.5).AND.(DELS.GT.TEST)) CALL XABORT('NSSEIG: CONVER'
> //'GENCE FAILURE.')
IF(ITER.GE.MAXOUT) THEN
WRITE (6,630)
EXIT
ENDIF
IF(MOD(ITER,36).EQ.0) THEN
ISTART=ITER+1
NNADI=NNADI+1
IF(IMPX.GE.1) WRITE (6,650) NNADI
ENDIF
ENDDO
*----
* FLUX NORMALIZATION
*----
FMAX=MAXVAL(EVECT(:LL4F,:NG))
EVECT(:LL4F,:NG)=EVECT(:LL4F,:NG)/FMAX
*----
* SOLUTION EDITION
*----
FKEFF=REAL(1.0D0/EVAL)
IF(IMPX.GE.1) WRITE (6,640) ITER,FKEFF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(IA11Z,IA11Y,IA11X)
DEALLOCATE(WORK,GAF3,GAF2,GAF1,GAR3,GAR2,GAR1,GRAD2,GRAD1,S,S2)
RETURN
*----
* FORMATS
*----
600 FORMAT(1H1/50H NSSEIG: ITERATIVE PROCEDURE BASED ON PRECONDITION,
> 17HED POWER METHOD (,I2,37H ADI ITERATIONS PER OUTER ITERATION)./
> 9X,16HDIRECT EQUATION.)
610 FORMAT (10X,3HIN(,I3,6H) FLX:,5H PRC=,1P,E9.2,5H TAR=,E9.2,
> 7H IGDEB=, I13,6H ACCE=,0P,F12.5,12H CONVERGED=,A3)
620 FORMAT(1X,I3,1P,7E9.1,0P,2F8.3,E14.6,3E10.2,I4/(4X,1P,7E9.1))
630 FORMAT(/53H NSSEIG: ***WARNING*** THE MAXIMUM NUMBER OF OUTER IT,
> 20HERATIONS IS REACHED.)
640 FORMAT(/23H NSSEIG: CONVERGENCE IN,I4,12H ITERATIONS.//
> 42H NSSEIG: EFFECTIVE MULTIPLICATION FACTOR =,1P,E17.10/)
650 FORMAT(/53H NSSEIG: INCREASING THE NUMBER OF INNER ITERATIONS TO,
1 I3,36H ADI ITERATIONS PER OUTER ITERATION./)
!
CONTAINS
SUBROUTINE NSSMPA(NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,MAT,IDL,
> VOL,MUX,MUY,MUZ,IMAX,IMAY,IMAZ,IPY,IPZ,SCAT,A11X,A11Y,A11Z,
> EVECT,S2)
!
! A*EVECT MULTIPLICATION
!
INTEGER, INTENT(IN) :: NMAX,NMAY,NMAZ,LL4F,NDIM,NEL,NMIX,NG,
> MAT(NEL),IDL(NEL),MUX(LL4F),MUY(LL4F),MUZ(LL4F),IMAX(LL4F),
> IMAY(LL4F),IMAZ(LL4F),IPY(LL4F),IPZ(LL4F)
REAL, INTENT(IN) :: VOL(NEL),SCAT(NMIX,NG,NG)
REAL, INTENT(IN) :: EVECT(LL4F,NG),A11X(NMAX,NG),A11Y(NMAY,NG),
> A11Z(NMAZ,NG)
REAL, INTENT(OUT) :: S2(LL4F,NG)
REAL, ALLOCATABLE, DIMENSION(:) :: GAR1,GAR2
!
ALLOCATE(GAR1(LL4F),GAR2(LL4F))
DO IG=1,NG
* scalar multiplication for a x-oriented matrix.
CALL ALLUM(LL4F,A11X(1,IG),EVECT(1,IG),S2(1,IG),MUX,IMAX,1)
IF(NDIM.GE.2) THEN
* scalar multiplication for a y-oriented matrix.
GAR1(IPY(:LL4F))=EVECT(:LL4F,IG)
GAR2(IPY(:LL4F))=S2(:LL4F,IG)
CALL ALLUM(LL4F,A11Y(1,IG),GAR1(1),GAR2(1),MUY,IMAY,2)
S2(:LL4F,IG)=GAR2(IPY(:LL4F))
ENDIF
IF(NDIM.EQ.3) THEN
* scalar multiplication for a z-oriented matrix.
GAR1(IPZ(:LL4F))=EVECT(:LL4F,IG)
GAR2(IPZ(:LL4F))=S2(:LL4F,IG)
CALL ALLUM(LL4F,A11Z(1,IG),GAR1(1),GAR2(1),MUZ,IMAZ,2)
S2(:LL4F,IG)=GAR2(IPZ(:LL4F))
ENDIF
DO JG=1,NG
IF(JG.EQ.IG) CYCLE
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM.LE.0) CYCLE
IND=IDL(IEL)
IF(IND.EQ.0) CYCLE
S2(IND,IG)=S2(IND,IG)-VOL(IEL)*SCAT(IBM,IG,JG)*
> EVECT(IND,JG)
ENDDO
ENDDO
ENDDO
DEALLOCATE(GAR2,GAR1)
END SUBROUTINE NSSMPA
!
SUBROUTINE NSSMPB(LL4F,NEL,NMIX,NG,MAT,IDL,VOL,CHI,SIGF,EVECT,
> S2)
!
! B*EVECT MULTIPLICATION
!
INTEGER, INTENT(IN) :: LL4F,NEL,NMIX,NG,MAT(NEL),IDL(NEL)
REAL, INTENT(IN) :: VOL(NEL),CHI(NMIX,NG),SIGF(NMIX,NG)
REAL, INTENT(IN) :: EVECT(LL4F,NG)
REAL, INTENT(OUT) :: S2(LL4F,NG)
!
S2(:LL4F,:NG)=0.0D0
DO IG=1,NG
DO JG=1,NG ! IG <-- JG
DO IEL=1,NEL
IBM=MAT(IEL)
IF(IBM.LE.0) CYCLE
IND=IDL(IEL)
IF(IND.EQ.0) CYCLE
S2(IND,IG)=S2(IND,IG)+VOL(IEL)*CHI(IBM,IG)*SIGF(IBM,JG)*
> EVECT(IND,JG)
ENDDO
ENDDO
ENDDO
END SUBROUTINE NSSMPB
END SUBROUTINE NSSEIG
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