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*DECK MCGABGR
SUBROUTINE MCGABGR(IPRINT,LFORW,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND,
1 NGINDV,NCONV,KPSYS,JPMACR,NZON,IPERM,IM,MCU,JU,
2 EPSM,MAXM,RHS,F,FAC,LC0,IM0,MCU0)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solve the ACA corrective system (in a rebalancing form) using
* BICGSTAB.
*
*Reference: (p382)
* MEURANT, G. 1999. "Computer Solution of Large Linear Systems".
* Studies in Mathematics and its Applications vol.28. North Holland.
* 776p.
*
*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): R. Le Tellier
*
*Parameters: input
* IPRINT print parameter.
* LFORW flag set to .false. to transpose the coefficient matrix.
* PACA type of preconditioner to solve the ACA corrective system.
* N number of unknowns per group.
* NG total number of groups.
* NFIRST first group to proceed.
* NGEFF number of unconverged groups.
* M number of material mixtures.
* LC dimension of profiled matrices MCU and CQ.
* NGIND index of the groups to process.
* NGINDV index to pass from "NGEFF format" to "NG format".
* NCONV logical array of convergence status for each group (.TRUE.:
* not converged).
* KPSYS pointer array for each group properties.
* JPMACR pointer to the macrolib LCM object ('GROUP' directory).
* NZON index-number of the mixture type assigned to each volume.
* IPERM permutation array for ACA.
* IM connection matrix.
* MCU connection matrix.
* JU used for ilu0 preconditioner.
* EPSM stopping criterion.
* MAXM maximum number of iterations allowed.
* RHS right hand-side of the corrective system (already
* preconditioned).
* FAC scaling factor for precision.
* LC0 used in ILU0-ACA acceleration.
* IM0 used in ILU0-ACA acceleration.
* MCU0 used in ILU0-ACA acceleration.
*
*Parameters: output
* F corrective fluxes and currents.
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IPRINT,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND(NGEFF),
1 NGINDV(NG),KPSYS(NGEFF),JPMACR,NZON(N),IPERM(N),IM(N+1),MCU(LC),
2 JU(N),MAXM,LC0,IM0(*),MCU0(*)
REAL EPSM,FAC
DOUBLE PRECISION RHS(N,NGEFF),F(N,NGEFF)
LOGICAL LFORW,NCONV(NGEFF)
*----
* LOCAL VARIABLE
*----
REAL EPSMAX,EPSINF,EPS2
PARAMETER (EPSMAX=1E-7)
INTEGER I,II,J,ITER
DOUBLE PRECISION R,BI,WI,RT1,ASIN,ASIN2,SQ2
DOUBLE PRECISION DDOT,AUX(2),EPS,FNORM,RHSN
LOGICAL DEBUG
INTRINSIC SQRT,ABS
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:,:) :: PI,RI,SI,ROT,API,
1 ASI
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(PI(N,NGEFF),RI(N,NGEFF),SI(N,NGEFF),ROT(N,NGEFF),
1 API(N,NGEFF),ASI(N,NGEFF))
*
SQ2=1.D0/SQRT(2.D0)
*---
DEBUG=.FALSE.
EPSINF=EPSMAX*FAC
ITER=0
*
RHSN=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO I=1,N
RHSN=MAX(RHSN,ABS(RHS(I,II)))
ENDDO
ENDIF
ENDDO
IF (RHSN.LT.EPSINF) THEN
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO I=1,N
F(I,II)=0.0D0
ENDDO
ENDIF
ENDDO
IF (DEBUG) WRITE(6,200) RHSN,EPSINF
GO TO 40
ENDIF
EPS2=EPSMAX*REAL(RHSN)
EPS2=EPS2*EPS2
*---
* initial corrective flux is set to rhs
* calculate (P times (D times RHS)) -> RI
CALL MCGACA(LFORW,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND,NGINDV,NCONV,
1 KPSYS,JPMACR,NZON,IPERM,IM,MCU,JU,RHS(1,1),LC0,IM0,MCU0,RI)
R=0.0
FNORM=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO I=1,N
F(I,II)=RHS(I,II)
RI(I,II)=RHS(I,II)-RI(I,II)
PI(I,II)=RI(I,II)
ROT(I,II)=RI(I,II)
ENDDO
R=R+DDOT(N,RI(1,II),1,RI(1,II),1)
FNORM=FNORM+DDOT(N,F(1,II),1,F(1,II),1)
ENDIF
ENDDO
EPS=SQRT(R/FNORM)
IF (DEBUG) WRITE(6,100) ITER,EPS,EPSM
IF (EPS.LE.EPSM) GO TO 40
AUX(1)=R !!DDOT(N,RI,1,ROT,1)
*
DO WHILE (ITER.LT.MAXM)
* BiCGSTAB iterations
ITER=ITER+1
* calculate (P times (D times PI)) -> API
CALL MCGACA(LFORW,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND,NGINDV,
1 NCONV,KPSYS,JPMACR,NZON,IPERM,IM,MCU,JU,PI(1,1),LC0,IM0,
2 MCU0,API)
*
AUX(2)=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
AUX(2)=AUX(2)+DDOT(N,API(1,II),1,ROT(1,II),1)
ENDIF
ENDDO
AUX(2)=AUX(1)/AUX(2)
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO J=1,N
SI(J,II)=RI(J,II)-AUX(2)*API(J,II)
ENDDO
ENDIF
ENDDO
ITER=ITER+1
* calculate (P times (D times SI)) -> ASI
CALL MCGACA(LFORW,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND,NGINDV,
1 NCONV,KPSYS,JPMACR,NZON,IPERM,IM,MCU,JU,SI(1,1),LC0,IM0,
2 MCU0,ASI)
*
ASIN2=0.0
ASIN=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
ASIN2=ASIN2+DDOT(N,ASI(1,II),1,SI(1,II),1)
ASIN=ASIN+DDOT(N,ASI(1,II),1,ASI(1,II),1)
ENDIF
ENDDO
IF (ASIN.GT.EPSMAX*ASIN2) THEN
WI=ASIN2/ASIN
ELSE
* assuming lucky breakdown
WI=1.0
ENDIF
!!!!* Modification proposed by Sleijpen and Van der Vorst
!!!!* (Numerical Algorithms, 10:203-223, 1995)
!!!! ASIN2=0.0
!!!! ASIN=0.0
!!!! SIN=0.0
!!!! DO II=NFIRST,NGEFF
!!!! IF (NCONV(II)) THEN
!!!! ASIN2=ASIN2+DDOT(N,ASI(1,II),1,SI(1,II),1)
!!!! ASIN=ASIN+DDOT(N,ASI(1,II),1,ASI(1,II),1)
!!!! SIN=SIN+DDOT(N,SI(1,II),1,SI(1,II),1)
!!!! ENDIF
!!!! ENDDO
!!!! ASIN=SQRT(ASIN)
!!!! SIN=SQRT(SIN)
!!!! CN=ASIN*SIN
!!!! IF (CN.GT.EPSMAX*ASIN2) THEN
!!!! CN=ASIN2/CN
!!!! WI=MAX(ABS(CN),SQ2)*SIN/ASIN
!!!! WI=SIGN(WI,CN)
!!!! ELSE
!!!!* assuming lucky breakdown
!!!! WI=1.0
!!!! ENDIF
* calculate new iterate
R=0.0
FNORM=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO J=1,N
F(J,II)=F(J,II)+AUX(2)*PI(J,II)+WI*SI(J,II)
RI(J,II)=SI(J,II)-WI*ASI(J,II)
ENDDO
R=R+DDOT(N,RI(1,II),1,RI(1,II),1)
FNORM=FNORM+DDOT(N,F(1,II),1,F(1,II),1)
ENDIF
ENDDO
IF (FNORM.LT.EPS2) GOTO 30
EPS=SQRT(R/FNORM)
IF (DEBUG) WRITE(6,100) ITER,EPS,EPSM
IF (EPS.LE.EPSM) GO TO 20
RT1=AUX(1)
AUX(1)=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
AUX(1)=AUX(1)+DDOT(N,RI(1,II),1,ROT(1,II),1)
ENDIF
ENDDO
BI=AUX(1)/RT1*AUX(2)/WI
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO J=1,N
PI(J,II)=RI(J,II)+BI*(PI(J,II)-WI*API(J,II))
ENDDO
ENDIF
ENDDO
ENDDO
20 CONTINUE
* determine final residual norm
ITER=ITER+1
* calculate (P times (D times F)) -> RI
CALL MCGACA(LFORW,PACA,N,NG,NFIRST,NGEFF,M,LC,NGIND,NGINDV,NCONV,
1 KPSYS,JPMACR,NZON,IPERM,IM,MCU,JU,F(1,1),LC0,IM0,MCU0,RI)
*
R=0.0
FNORM=0.0
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO I=1,N
RI(I,II)=RHS(I,II)-RI(I,II)
ENDDO
R=R+DDOT(N,RI(1,II),1,RI(1,II),1)
FNORM=FNORM+DDOT(N,F(1,II),1,F(1,II),1)
ENDIF
ENDDO
IF (FNORM.LT.EPS2) GOTO 30
EPS=SQRT(R/FNORM)
IF (IPRINT.GT.0) WRITE(6,400) EPS,ITER
!!!! R=0.0
!!!! FNORM=0.0
!!!! EPS=0.0
!!!! DO II=NFIRST,NGEFF
!!!! IF (NCONV(II)) THEN
!!!! DO I=1,N
!!!! R=MAX(R,ABS(RI(I,II)))
!!!! FNORM=MAX(FNORM,ABS(F(I,II)))
!!!! ENDDO
!!!! EPS=MAX(EPS,R/FNORM)
!!!! ENDIF
!!!! ENDDO
!!!! WRITE(*,*) ' PRC=',EPS
GO TO 40
*
30 IF (DEBUG) WRITE(6,300) ITER,FNORM,EPS2
DO II=NFIRST,NGEFF
IF (NCONV(II)) THEN
DO I=1,N
F(I,II)=0.0
ENDDO
ENDIF
ENDDO
*----
* SCRATCH STORAGE DEALLOCATION
*----
40 DEALLOCATE(ASI,API,ROT,SI,RI,PI)
RETURN
*
100 FORMAT(9X,14H MCGABGR:ITER=,I3,5H EPS=,E9.2,5H TAR=,E9.2)
200 FORMAT(9X,27H MCGABGR:RHS INFINITE NORM=,E9.2,5H LIM=,E9.2/
1 9X,33H -> ACA CORRECTION IS SET TO ZERO)
300 FORMAT(9X,14H MCGABGR:ITER=,I3,7H FNORM=,E9.2,5H LIM=,E9.2)
400 FORMAT(10X,48HACA: UP-SCATTE. GROUPS: MULTIGROUP BICGSTAB: PRC:,
1 E9.2,2H (,I4,12H ITERATIONS))
END
|
