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|
*DECK FLDMON
SUBROUTINE FLDMON (IPTRK,IPSYS,IPFLUX,LL4,ITY,NUN,NGRP,LMOD,ICL1,
1 ICL2,IMPX,IMPH,TITR,EPS2,NADI,MAXOUT,MAXINR,EPSINR,RAND,FKEFF,
2 EVECT,ADECT)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solution of multigroup eigenvalue systems for the calculation of the
* LMOD first bi-orthogonal harmonics of the diffusion equation in
* Trivac. Use the preconditionned power method with Hotelling deflation
* and a two-parameter SVAT acceleration technique.
*
*Copyright:
* Copyright (C) 2002 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
* IPTRK L_TRACK pointer to the tracking information.
* IPSYS L_SYSTEM pointer to system matrices.
* IPFLUX L_FLUX pointer to the solution.
* LL4 order of the system matrices.
* ITY type of solution (2: classical Trivac; 3: Thomas-Raviart).
* NUN number of unknowns in each energy group.
* NGRP number of energy groups.
* LMOD number of bi-orthogonal harmonics to compute.
* ICL1 number of free iterations in one cycle of the inverse power
* method.
* ICL2 number of accelerated iterations in one cycle.
* IMPX print parameter: =0: no print ; =1: minimum printing;
* =2: iteration history is printed; =3: solution is printed.
* IMPH type of histogram processing:
* =0: no action is taken;
* =1: the flux is compared to a reference flux stored on LCM
* =2: the convergence histogram is printed;
* =3: the convergence histogram is printed with axis and
* titles. The plotting file is completed;
* =4: the convergence histogram is printed with axis, acce-
* leration factors and titles. The plotting file is
* completed.
* TITR title.
* EPS2 convergence criteria for the flux.
* NADI number of inner ADI iterations per outer iteration.
* MAXOUT maximum number of outer iterations.
* MAXINR maximum number of thermal iterations.
* EPSINR thermal iteration epsilon.
* RAND initialization flag:
* =.true. use an initial random flux; =.false. use a flat flux.
*
*Parameters: output
* FKEFF effective multiplication factor of each harmonic.
* EVECT converged direct harmonic vector.
* ADECT converged adjoint harmonic vector.
*
*References:
* A. H\'ebert, 'Preconditioning the power method for reactor
* calculations', Nucl. Sci. Eng., 94, 1 (1986).
* J. H. Wilkinson, "The algebraic eigenvalue problem", Clarendon
* Press, Oxford, p. 584, 1965.
*
*-----------------------------------------------------------------------
*
USE GANLIB
*----
* SUBROUTINE ARGUMENTS
*----
TYPE(C_PTR) IPTRK,IPSYS,IPFLUX
CHARACTER TITR*72
INTEGER LL4,ITY,NUN,NGRP,LMOD,ICL1,ICL2,IMPX,IMPH,NADI,MAXOUT,
1 MAXINR
REAL EPS2,EPSINR,FKEFF(LMOD),EVECT(NUN,NGRP,LMOD),
1 ADECT(NUN,NGRP,LMOD)
LOGICAL RAND
*----
* LOCAL VARIABLES
*----
PARAMETER (MMAXX=250,EPS1=1.0E-5)
PARAMETER (IM=714025,ID=1366,IC=150889,RM=1.4005112E-6)
CHARACTER*12 TEXT12
LOGICAL LOGTES
DOUBLE PRECISION 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,Z1,
3 FMIN
TYPE(C_PTR) JPFLUX,KPFLUX,MPFLUX,NPFLUX
REAL ERR(MMAXX),ALPH(MMAXX),BETA(MMAXX)
DOUBLE PRECISION, 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 /)
DOUBLE PRECISION, 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, DIMENSION(:), ALLOCATABLE :: AGAR
REAL, DIMENSION(:,:), ALLOCATABLE :: GRAD1,GRAD2,VEA1,VEA2,VEA3,
1 VEB1,VEB2,VEB3
REAL, DIMENSION(:), POINTER :: AGARM
TYPE(C_PTR) AGARM_PTR
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(AGAR(LL4),GRAD1(NUN,NGRP),GRAD2(NUN,NGRP),VEA1(NUN,NGRP),
1 VEA2(NUN,NGRP),VEA3(NUN,NGRP),VEB1(NUN,NGRP),VEB2(NUN,NGRP),
2 VEB3(NUN,NGRP))
*
* TKT : CPU TIME FOR THE SOLUTION OF LINEAR SYSTEMS.
* TKB : CPU TIME FOR BILINEAR PRODUCT EVALUATIONS.
TKT=0.0
TKB=0.0
CALL MTOPEN(IMPX,IPTRK,LL4)
IF(LL4.GT.NUN) CALL XABORT('FLDMON: INVALID NUMBER OF UNKNOWNS.')
*
DO 390 IMOD=1,LMOD
CALL KDRCPU(TK1)
IF(IMPX.GE.1) WRITE (6,'(1H1//13H HARMONIC NB.,I3//)') IMOD
CALL LCMLEN(IPFLUX,'MODE',ILONG,ITYLCM)
IF((ILONG.NE.0).AND.(IMPH.EQ.0)) THEN
JPFLUX=LCMGID(IPFLUX,'MODE')
KPFLUX=LCMGIL(JPFLUX,IMOD)
MPFLUX=LCMGID(KPFLUX,'FLUX')
NPFLUX=LCMGID(KPFLUX,'AFLUX')
DO 10 IGR=1,NGRP
CALL LCMGDL(MPFLUX,IGR,EVECT(1,IGR,IMOD))
CALL LCMGDL(NPFLUX,IGR,ADECT(1,IGR,IMOD))
10 CONTINUE
ELSE IF((IMOD.EQ.1).OR.(.NOT.RAND)) THEN
* UNIFORM UNKNOWN VECTOR.
DO 25 IGR=1,NGRP
DO 20 I=1,NUN
EVECT(I,IGR,IMOD)=1.0
ADECT(I,IGR,IMOD)=1.0
20 CONTINUE
25 CONTINUE
ELSE
* RANDOM UNKNOWN VECTOR.
ISEED=0
DO 35 IGR=1,NGRP
DO 30 I=1,NUN
ISEED=MOD(ISEED*ID+IC,IM)
RAN=REAL(ISEED)*RM
EVECT(I,IGR,IMOD)=RAN
ADECT(I,IGR,IMOD)=RAN
30 CONTINUE
35 CONTINUE
ENDIF
*----
* PRECONDITIONED POWER METHOD FOR THE DIRECT PROBLEM
*----
EVAL=1.0D0
VVV=0.0
ISTART=1
NNADI=NADI
TEST=0.0
IF(IMPX.GE.1) WRITE (6,600) NADI,'DIRECT'
IF(IMPX.GE.2) WRITE (6,610)
CALL FLDDEF(NUN,IPTRK,IPSYS,LL4,ITY,NGRP,IMOD,LMOD,EVECT,ADECT,
1 EVECT(1,1,IMOD),1,VEA1,VEB1)
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
M=0
50 M=M+1
*----
* EIGENVALUE EVALUATION
*----
CALL KDRCPU(TK1)
AEBE=0.0D0
BEBE=0.0D0
DO 65 IGR=1,NGRP
DO 60 I=1,LL4
AEBE=AEBE+VEA1(I,IGR)*VEB1(I,IGR)
BEBE=BEBE+VEB1(I,IGR)**2
60 CONTINUE
65 CONTINUE
EVAL=AEBE/BEBE
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*----
* DIRECTION EVALUATION
*----
DO 110 IGR=1,NGRP
CALL KDRCPU(TK1)
DO 70 I=1,LL4
GRAD1(I,IGR)=REAL(EVAL)*VEB1(I,IGR)-VEA1(I,IGR)
70 CONTINUE
DO 100 JGR=1,IGR-1
WRITE(TEXT12,'(1HA,2I3.3)') IGR,JGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 100
IF(ITY.EQ.13) THEN
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,JGR),AGAR)
DO 80 I=1,LL4
GRAD1(I,IGR)=GRAD1(I,IGR)+AGAR(I)
80 CONTINUE
ELSE
CALL LCMGPD(IPSYS,TEXT12,AGARM_PTR)
CALL C_F_POINTER(AGARM_PTR,AGARM,(/ ILONG /))
DO 90 I=1,ILONG
GRAD1(I,IGR)=GRAD1(I,IGR)+AGARM(I)*GRAD1(I,JGR)
90 CONTINUE
ENDIF
100 CONTINUE
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*
CALL KDRCPU(TK1)
WRITE(TEXT12,'(1HA,2I3.3)') IGR,IGR
CALL FLDADI(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,IGR),NNADI)
CALL KDRCPU(TK2)
TKT=TKT+(TK2-TK1)
110 CONTINUE
*----
* PERFORM THERMAL (UP-SCATTERING) ITERATIONS
*----
IF(MAXINR.GT.1) THEN
CALL FLDTHR(IPTRK,IPSYS,IPFLUX,.FALSE.,LL4,ITY,NUN,NGRP,ICL1,
1 ICL2,IMPX,NNADI,0,MAXINR,EPSINR,ITER,TKT,TKB,GRAD1)
ENDIF
*----
* DISPLACEMENT EVALUATION
*----
CALL KDRCPU(TK1)
F=0.0D0
DELS=ABS(REAL((EVAL-VVV)/EVAL))
VVV=REAL(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 FLDDEF(NUN,IPTRK,IPSYS,LL4,ITY,NGRP,IMOD,LMOD,EVECT,ADECT,
1 GRAD1(1,1),1,VEA2,VEB2)
IF(1+MOD(M-ISTART,ICL1+ICL2).GT.ICL1) THEN
DO 125 IGR=1,NGRP
DO 120 I=1,LL4
* COMPUTE (A ,A )
AEAE=AEAE+VEA1(I,IGR)**2
AEAG=AEAG+VEA1(I,IGR)*VEA2(I,IGR)
AEAH=AEAH+VEA1(I,IGR)*VEA3(I,IGR)
AGAG=AGAG+VEA2(I,IGR)**2
AGAH=AGAH+VEA2(I,IGR)*VEA3(I,IGR)
AHAH=AHAH+VEA3(I,IGR)**2
* COMPUTE (B ,B )
BEBG=BEBG+VEB1(I,IGR)*VEB2(I,IGR)
BEBH=BEBH+VEB1(I,IGR)*VEB3(I,IGR)
BGBG=BGBG+VEB2(I,IGR)**2
BGBH=BGBH+VEB2(I,IGR)*VEB3(I,IGR)
BHBH=BHBH+VEB3(I,IGR)**2
* COMPUTE (A ,B )
AEBG=AEBG+VEA1(I,IGR)*VEB2(I,IGR)
AEBH=AEBH+VEA1(I,IGR)*VEB3(I,IGR)
AGBE=AGBE+VEA2(I,IGR)*VEB1(I,IGR)
AGBG=AGBG+VEA2(I,IGR)*VEB2(I,IGR)
AGBH=AGBH+VEA2(I,IGR)*VEB3(I,IGR)
AHBE=AHBE+VEA3(I,IGR)*VEB1(I,IGR)
AHBG=AHBG+VEA3(I,IGR)*VEB2(I,IGR)
AHBH=AHBH+VEA3(I,IGR)*VEB3(I,IGR)
120 CONTINUE
125 CONTINUE
*
130 N=N+1
IF(N.GT.10) GO TO 135
* COMPUTE X(M+1)
X=BEBE+ALP*ALP*BGBG+BET*BET*BHBH+2.0D0*(ALP*BEBG+BET*BEBH
1 +ALP*BET*BGBH)
DXDA=2.0D0*(BEBG+ALP*BGBG+BET*BGBH)
DXDB=2.0D0*(BEBH+ALP*BGBH+BET*BHBH)
* COMPUTE Y(M+1)
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
1 +ALP*BET*AGAH)
DYDA=2.0D0*(AEAG+ALP*AGAG+BET*AGAH)
DYDB=2.0D0*(AEAH+ALP*AGAH+BET*AHAH)
* COMPUTE Z(M+1)
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
1 +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(M+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
1 -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 135
ALP=ALP-D2F(1,3)
BET=BET-D2F(2,3)
IF(ALP.GT.100.0) GO TO 135
IF((ABS(D2F(1,3)).LE.1.0D-4).AND.(ABS(D2F(2,3)).LE.1.0D-4))
1 GO TO 140
GO TO 130
*
* alternative algorithm in case of Newton-Raphton failure
135 IF(IMPX.GT.0) WRITE(6,'(/30H FLDMON: FAILURE OF THE NEWTON,
1 55H-RAPHTON ALGORIHTHM FOR COMPUTING THE OVERRELAXATION PA,
2 12HRAMETERS(1).)')
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
1 +ALP*BET*BGBH)
* COMPUTE Y
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
1 +ALP*BET*AGAH)
* COMPUTE Z
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
1 +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)
140 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=M+1
ALP=1.0D0
BET=0.0D0
ENDIF
DO 155 IGR=1,NGRP
DO 150 I=1,LL4
GRAD1(I,IGR)=REAL(ALP)*(GRAD1(I,IGR)+REAL(BET)*GRAD2(I,IGR))
VEA2(I,IGR)=REAL(ALP)*(VEA2(I,IGR)+REAL(BET)*VEA3(I,IGR))
VEB2(I,IGR)=REAL(ALP)*(VEB2(I,IGR)+REAL(BET)*VEB3(I,IGR))
150 CONTINUE
155 CONTINUE
ENDIF
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*
LOGTES=(M.LT.ICL1).OR.(MOD(M-ISTART,ICL1+ICL2).EQ.ICL1-1)
IF(LOGTES.AND.(DELS.LE.EPS1)) THEN
DELT=0.0
DO 170 IGR=1,NGRP
DELN=0.0
DELD=0.0
DO 160 I=1,LL4
EVECT(I,IGR,IMOD)=EVECT(I,IGR,IMOD)+GRAD1(I,IGR)
VEA1(I,IGR)=VEA1(I,IGR)+VEA2(I,IGR)
VEB1(I,IGR)=VEB1(I,IGR)+VEB2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
VEA3(I,IGR)=VEA2(I,IGR)
VEB3(I,IGR)=VEB2(I,IGR)
DELN=MAX(DELN,ABS(VEB2(I,IGR)))
DELD=MAX(DELD,ABS(VEB1(I,IGR)))
160 CONTINUE
IF(DELD.NE.0.0) DELT=MAX(DELT,DELN/DELD)
170 CONTINUE
IF(IMPX.GE.2) WRITE (6,615) M,AEAE,AEAG,AEAH,AGAG,AGAH,AHAH,
1 BEBE,ALP,BET,EVAL,F,DELS,DELT,N,BEBG,BEBH,BGBG,BGBH,BHBH,
2 AEBE,AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
* COMPUTE THE CONVERGENCE HISTOGRAM.
IF((IMPH.GE.1).AND.(M.LE.MMAXX)) THEN
JPFLUX=LCMGID(IPFLUX,'MODE')
KPFLUX=LCMGIL(JPFLUX,IMOD)
CALL FLDXCO(KPFLUX,LL4,NUN,EVECT(1,NGRP,IMOD),.TRUE.,ERR(M))
ALPH(M)=REAL(ALP)
BETA(M)=REAL(BET)
ENDIF
IF(DELT.LE.EPS2) GO TO 190
ELSE
DO 185 IGR=1,NGRP
DO 180 I=1,LL4
EVECT(I,IGR,IMOD)=EVECT(I,IGR,IMOD)+GRAD1(I,IGR)
VEA1(I,IGR)=VEA1(I,IGR)+VEA2(I,IGR)
VEB1(I,IGR)=VEB1(I,IGR)+VEB2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
VEA3(I,IGR)=VEA2(I,IGR)
VEB3(I,IGR)=VEB2(I,IGR)
180 CONTINUE
185 CONTINUE
IF(IMPX.GE.2) WRITE (6,620) M,AEAE,AEAG,AEAH,AGAG,AGAH,AHAH,
1 BEBE,ALP,BET,EVAL,F,DELS,N,BEBG,BEBH,BGBG,BGBH,BHBH,AEBE,
2 AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
* COMPUTE THE CONVERGENCE HISTOGRAM.
IF((IMPH.GE.1).AND.(M.LE.MMAXX)) THEN
JPFLUX=LCMGID(IPFLUX,'MODE')
KPFLUX=LCMGIL(JPFLUX,IMOD)
CALL FLDXCO(KPFLUX,LL4,NUN,EVECT(1,NGRP,IMOD),.TRUE.,ERR(M))
ALPH(M)=REAL(ALP)
BETA(M)=REAL(BET)
ENDIF
ENDIF
*
IF(M.EQ.1) TEST=DELS
IF((M.GT.5).AND.(DELS.GT.TEST)) CALL XABORT('FLDMON: CONVERGENCE'
1 //' FAILURE.')
IF(M.GE.MAXOUT) THEN
WRITE (6,'(/46H FLDMON: ***WARNING*** MAXIMUM NUMBER OF ITERA,
1 17HTIONS IS REACHED.)')
GO TO 190
ENDIF
IF(MOD(M,36).EQ.0) THEN
ISTART=M+1
NNADI=NNADI+1
IF(IMPX.GE.1) WRITE (6,700) NNADI
ENDIF
GO TO 50
*----
* DIRECT SOLUTION EDITION
*----
190 Z1=1.0D0/EVAL
IF(IMPX.GE.1) WRITE (6,630) 1.0D0/EVAL
IF(IMPX.EQ.1) WRITE (6,640) M
IF(IMPX.EQ.3) THEN
DO 210 IGR=1,NGRP
WRITE (6,660) 'DIRECT',IGR,(EVECT(I,IGR,IMOD),I=1,LL4)
210 CONTINUE
ENDIF
IF(IMPH.EQ.1) THEN
JPFLUX=LCMGID(IPFLUX,'MODE')
KPFLUX=LCMGIL(JPFLUX,IMOD)
CALL LCMLEN(KPFLUX,'REF',ILONG,ITYLCM)
IF(ILONG.EQ.0) THEN
WRITE(6,'(44H FLDMON: STORE A REFERENCE THERMAL HARMONIC.)')
CALL LCMPUT(KPFLUX,'REF',NUN,2,EVECT(1,NGRP,IMOD))
ENDIF
ELSE IF(IMPH.GE.2) THEN
JPFLUX=LCMGID(IPFLUX,'MODE')
KPFLUX=LCMGIL(JPFLUX,IMOD)
IGRAPH=0
215 IGRAPH=IGRAPH+1
WRITE (TEXT12,'(5HHISTO,I3)') IGRAPH
CALL LCMLEN (KPFLUX,TEXT12,ILENG,ITYLCM)
IF(ILENG.EQ.0) THEN
MM=MIN(M,MMAXX)
CALL LCMSIX (KPFLUX,TEXT12,1)
CALL LCMPTC (KPFLUX,'HTITLE',72,TITR)
CALL LCMPUT (KPFLUX,'ALPHA',MM,2,ALPH)
CALL LCMPUT (KPFLUX,'BETA',MM,2,BETA)
CALL LCMPUT (KPFLUX,'ERROR',MM,2,ERR)
CALL LCMPUT (KPFLUX,'IMPH',1,1,IMPH)
CALL LCMSIX (KPFLUX,' ',2)
ELSE
GO TO 215
ENDIF
ENDIF
*----
* PRECONDITIONED POWER METHOD FOR THE ADJOINT PROBLEM
*----
CALL KDRCPU(TK1)
EVAL=1.0D0
VVV=0.0
ISTART=1
NNADI=NADI
TEST=0.0
IF(IMPX.GE.1) WRITE (6,600) NADI,'ADJOINT'
IF(IMPX.GE.2) WRITE (6,610)
CALL FLDDEF(NUN,IPTRK,IPSYS,LL4,ITY,NGRP,IMOD,LMOD,EVECT,ADECT,
1 ADECT(1,1,IMOD),2,VEA1,VEB1)
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
M=0
220 M=M+1
*----
* EIGENVALUE CALCULATION
*----
CALL KDRCPU(TK1)
AEBE=0.0D0
BEBE=0.0D0
DO 235 IGR=1,NGRP
DO 230 I=1,LL4
AEBE=AEBE+VEA1(I,IGR)*VEB1(I,IGR)
BEBE=BEBE+VEB1(I,IGR)**2
230 CONTINUE
235 CONTINUE
EVAL=AEBE/BEBE
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*----
* DIRECTION EVALUATION
*----
DO 280 IGR=NGRP,1,-1
CALL KDRCPU(TK1)
DO 240 I=1,LL4
GRAD1(I,IGR)=REAL(EVAL)*VEB1(I,IGR)-VEA1(I,IGR)
240 CONTINUE
DO 270 JGR=NGRP,IGR+1,-1
WRITE(TEXT12,'(1HA,2I3.3)') JGR,IGR
CALL LCMLEN(IPSYS,TEXT12,ILONG,ITYLCM)
IF(ILONG.EQ.0) GO TO 270
IF(ITY.EQ.13) THEN
CALL MTLDLM(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,JGR),AGAR)
DO 250 I=1,LL4
GRAD1(I,IGR)=GRAD1(I,IGR)+AGAR(I)
250 CONTINUE
ELSE
CALL LCMGPD(IPSYS,TEXT12,AGARM_PTR)
CALL C_F_POINTER(AGARM_PTR,AGARM,(/ ILONG /))
DO 260 I=1,ILONG
GRAD1(I,IGR)=GRAD1(I,IGR)+AGARM(I)*GRAD1(I,JGR)
260 CONTINUE
ENDIF
270 CONTINUE
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*
CALL KDRCPU(TK1)
WRITE(TEXT12,'(1HA,2I3.3)') IGR,IGR
CALL FLDADI(TEXT12,IPTRK,IPSYS,LL4,ITY,GRAD1(1,IGR),NNADI)
CALL KDRCPU(TK2)
TKT=TKT+(TK2-TK1)
280 CONTINUE
*----
* PERFORM THERMAL (UP-SCATTERING) ITERATIONS
*----
IF(MAXINR.GT.1) THEN
CALL FLDTHR(IPTRK,IPSYS,IPFLUX,.TRUE.,LL4,ITY,NUN,NGRP,ICL1,
1 ICL2,IMPX,NNADI,0,MAXINR,EPSINR,ITER,TKT,TKB,GRAD1)
ENDIF
*----
* DISPLACEMENT EVALUATION
*----
CALL KDRCPU(TK1)
F=0.0D0
DELS=ABS(REAL((EVAL-VVV)/EVAL))
VVV=REAL(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 FLDDEF(NUN,IPTRK,IPSYS,LL4,ITY,NGRP,IMOD,LMOD,EVECT,ADECT,
1 GRAD1(1,1),2,VEA2,VEB2)
IF(1+MOD(M-ISTART,ICL1+ICL2).GT.ICL1) THEN
DO 295 IGR=1,NGRP
DO 290 I=1,LL4
* COMPUTE (A ,A )
AEAE=AEAE+VEA1(I,IGR)**2
AEAG=AEAG+VEA1(I,IGR)*VEA2(I,IGR)
AEAH=AEAH+VEA1(I,IGR)*VEA3(I,IGR)
AGAG=AGAG+VEA2(I,IGR)**2
AGAH=AGAH+VEA2(I,IGR)*VEA3(I,IGR)
AHAH=AHAH+VEA3(I,IGR)**2
* COMPUTE (B ,B )
BEBG=BEBG+VEB1(I,IGR)*VEB2(I,IGR)
BEBH=BEBH+VEB1(I,IGR)*VEB3(I,IGR)
BGBG=BGBG+VEB2(I,IGR)**2
BGBH=BGBH+VEB2(I,IGR)*VEB3(I,IGR)
BHBH=BHBH+VEB3(I,IGR)**2
* COMPUTE (A ,B )
AEBG=AEBG+VEA1(I,IGR)*VEB2(I,IGR)
AEBH=AEBH+VEA1(I,IGR)*VEB3(I,IGR)
AGBE=AGBE+VEA2(I,IGR)*VEB1(I,IGR)
AGBG=AGBG+VEA2(I,IGR)*VEB2(I,IGR)
AGBH=AGBH+VEA2(I,IGR)*VEB3(I,IGR)
AHBE=AHBE+VEA3(I,IGR)*VEB1(I,IGR)
AHBG=AHBG+VEA3(I,IGR)*VEB2(I,IGR)
AHBH=AHBH+VEA3(I,IGR)*VEB3(I,IGR)
290 CONTINUE
295 CONTINUE
*
300 N=N+1
IF(N.GT.10) GO TO 305
* COMPUTE X(M+1)
X=BEBE+ALP*ALP*BGBG+BET*BET*BHBH+2.0D0*(ALP*BEBG+BET*BEBH
1 +ALP*BET*BGBH)
DXDA=2.0D0*(BEBG+ALP*BGBG+BET*BGBH)
DXDB=2.0D0*(BEBH+ALP*BGBH+BET*BHBH)
* COMPUTE Y(M+1)
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
1 +ALP*BET*AGAH)
DYDA=2.0D0*(AEAG+ALP*AGAG+BET*AGAH)
DYDB=2.0D0*(AEAH+ALP*AGAH+BET*AHAH)
* COMPUTE Z(M+1)
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
1 +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(M+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
1 -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 305
ALP=ALP-D2F(1,3)
BET=BET-D2F(2,3)
IF(ALP.GT.100.0) GO TO 305
IF((ABS(D2F(1,3)).LE.1.0D-4).AND.(ABS(D2F(2,3)).LE.1.0D-4))
1 GO TO 310
GO TO 300
*
* alternative algorithm in case of Newton-Raphton failure
305 IF(IMPX.GT.0) WRITE(6,'(/30H FLDMON: FAILURE OF THE NEWTON,
1 55H-RAPHTON ALGORIHTHM FOR COMPUTING THE OVERRELAXATION PA,
2 12HRAMETERS(2).)')
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
1 +ALP*BET*BGBH)
* COMPUTE Y
Y=AEAE+ALP*ALP*AGAG+BET*BET*AHAH+2.0D0*(ALP*AEAG+BET*AEAH
1 +ALP*BET*AGAH)
* COMPUTE Z
Z=AEBE+ALP*ALP*AGBG+BET*BET*AHBH+ALP*(AEBG+AGBE)
1 +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)
310 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=M+1
ALP=1.0D0
BET=0.0D0
ENDIF
DO 325 IGR=1,NGRP
DO 320 I=1,LL4
GRAD1(I,IGR)=REAL(ALP)*(GRAD1(I,IGR)+REAL(BET)*GRAD2(I,IGR))
VEA2(I,IGR)=REAL(ALP)*(VEA2(I,IGR)+REAL(BET)*VEA3(I,IGR))
VEB2(I,IGR)=REAL(ALP)*(VEB2(I,IGR)+REAL(BET)*VEB3(I,IGR))
320 CONTINUE
325 CONTINUE
ENDIF
CALL KDRCPU(TK2)
TKB=TKB+(TK2-TK1)
*
LOGTES=(M.LT.ICL1).OR.(MOD(M-ISTART,ICL1+ICL2).EQ.ICL1-1)
IF(LOGTES.AND.(DELS.LE.EPS1))THEN
DELT=0.0
DO 340 IGR=1,NGRP
DELN=0.0
DELD=0.0
DO 330 I=1,LL4
ADECT(I,IGR,IMOD)=ADECT(I,IGR,IMOD)+GRAD1(I,IGR)
VEA1(I,IGR)=VEA1(I,IGR)+VEA2(I,IGR)
VEB1(I,IGR)=VEB1(I,IGR)+VEB2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
VEA3(I,IGR)=VEA2(I,IGR)
VEB3(I,IGR)=VEB2(I,IGR)
DELN=MAX(DELN,ABS(VEB2(I,IGR)))
DELD=MAX(DELD,ABS(VEB1(I,IGR)))
330 CONTINUE
IF(DELD.NE.0.0) DELT=MAX(DELT,DELN/DELD)
340 CONTINUE
IF(IMPX.GE.2) WRITE (6,615) M,AEAE,AEAG,AEAH,AGAG,AGAH,AHAH,
1 BEBE,ALP,BET,EVAL,F,DELS,DELT,N,BEBG,BEBH,BGBG,BGBH,BHBH,AEBE,
2 AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
IF(DELT.LE.EPS2) GO TO 360
ELSE
DO 355 IGR=1,NGRP
DO 350 I=1,LL4
ADECT(I,IGR,IMOD)=ADECT(I,IGR,IMOD)+GRAD1(I,IGR)
VEA1(I,IGR)=VEA1(I,IGR)+VEA2(I,IGR)
VEB1(I,IGR)=VEB1(I,IGR)+VEB2(I,IGR)
GRAD2(I,IGR)=GRAD1(I,IGR)
VEA3(I,IGR)=VEA2(I,IGR)
VEB3(I,IGR)=VEB2(I,IGR)
350 CONTINUE
355 CONTINUE
IF(IMPX.GE.2) WRITE (6,620) M,AEAE,AEAG,AEAH,AGAG,AGAH,AHAH,
1 BEBE,ALP,BET,EVAL,F,DELS,N,BEBG,BEBH,BGBG,BGBH,BHBH,AEBE,
2 AEBG,AEBH,AGBE,AGBG,AGBH,AHBE,AHBG,AHBH
ENDIF
IF(M.EQ.1) TEST=DELS
IF((M.GT.5).AND.(DELS.GT.TEST)) CALL XABORT('FLDMON: CONVERGENCE'
1 //' FAILURE.')
IF(M.GE.MAXOUT) THEN
WRITE (6,'(/46H FLDMON: ***WARNING*** MAXIMUM NUMBER OF ITERA,
1 17HTIONS IS REACHED.)')
GO TO 360
ENDIF
IF(MOD(M,36).EQ.0) THEN
ISTART=M+1
NNADI=NNADI+1
IF(IMPX.GE.1) WRITE (6,700) NNADI
ENDIF
GO TO 220
*----
* ADJOINT SOLUTION EDITION
*----
360 IF(IMPX.GE.1) WRITE (6,630) 1.0D0/EVAL
IF(IMPX.EQ.1) WRITE (6,640) M
IF(IMPX.EQ.3) THEN
DO 380 IGR=1,NGRP
WRITE (6,660) 'ADJOINT',IGR,(ADECT(I,IGR,IMOD),I=1,LL4)
380 CONTINUE
ENDIF
*
IF(ABS(Z1-1.0D0/EVAL).GT.1.0E-4) CALL XABORT('FLDMON: FAILURE O'
1 //'F HARMONIC COMPUTATION.')
FKEFF(IMOD)=REAL(0.5D0*(Z1+1.0D0/EVAL))
390 CONTINUE
IF(IMPX.GE.1) THEN
WRITE (6,650) TKT,TKB,TKT+TKB
WRITE (6,670) (FKEFF(IMOD),IMOD=1,LMOD)
ENDIF
*----
* SCRATCH STORAGE DEALLOCATION
*----
DEALLOCATE(AGAR,GRAD1,GRAD2,VEA1,VEA2,VEA3,VEB1,VEB2,VEB3)
RETURN
*
600 FORMAT(1H1/50H FLDMON: ITERATIVE PROCEDURE BASED ON PRECONDITION,
1 17HED POWER METHOD (,I2,37H ADI ITERATIONS PER OUTER ITERATION)./
2 9X,A7,10H EQUATION.)
610 FORMAT(//5X,17HBILINEAR PRODUCTS,48X,5HALPHA,3X,4HBETA,3X,
1 12HEIGENVALUE..,12X,8HACCURACY,11(1H.),2X,1HN)
615 FORMAT(1X,I3,1P,7E9.1,0P,2F8.3,E14.6,3E10.2,I4/(4X,1P,7E9.1))
620 FORMAT(1X,I3,1P,7E9.1,0P,2F8.3,E14.6,2E10.2,10X,I4/(4X,1P,7E9.1))
630 FORMAT(/42H FLDMON: EFFECTIVE MULTIPLICATION FACTOR =,1P,D17.10/)
640 FORMAT(/23H FLDMON: CONVERGENCE IN,I5,12H ITERATIONS.)
650 FORMAT(/53H FLDMON: CPU TIME USED TO SOLVE THE TRIANGULAR LINEAR,
1 10H SYSTEMS =,F10.3/23X,34HTO COMPUTE THE BILINEAR PRODUCTS =,
2 F10.3,20X,16HTOTAL CPU TIME =,F10.3)
660 FORMAT(//9H FLDMON: ,A7,37H EIGENVECTOR CORRESPONDING TO THE GRO,
1 2HUP,I4//(5X,1P,8E14.5))
670 FORMAT(//21H FLDMON: EIGENVALUES:/(5X,1P,E17.10))
700 FORMAT(/53H FLDMON: INCREASING THE NUMBER OF INNER ITERATIONS TO,
1 I3,36H ADI ITERATIONS PER OUTER ITERATION./)
END
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