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*DECK MCGABG
SUBROUTINE MCGABG(IPRINT,LFORW,PACA,N,LC,EPSM,MAXM,IM,MCU,JU,
1 DIAGF,CF,ILUDF,ILUCF,RHS,F,FAC,LC0,IM0,MCU0)
*
*-----------------------------------------------------------------------
*
*Purpose:
* Solve the ACA corrective system 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 dimension of the corrective system.
* LC dimension of profiled matrices MCU and CQ.
* IM connection matrix.
* MCU connection matrix.
* DIAGF diagonal elements of the matrix to inverse.
* CF non-diagonal elements of the matrix to inverse.
* 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.
* EPSM stopping criterion.
* MAXM maximum number of iterations allowed.
*
*Parameters: output
* F corrective fluxes and currents.
*
*Parameters: scratch
* JU undefined.
* ILUDF undefined.
* ILUCF undefined.
*
*-----------------------------------------------------------------------
*
IMPLICIT NONE
*----
* SUBROUTINE ARGUMENTS
*----
INTEGER IPRINT,PACA,N,LC,IM(N+1),MCU(LC),JU(N),MAXM,LC0,IM0(*),
1 MCU0(*)
REAL DIAGF(N),CF(LC),ILUDF(N),ILUCF(LC),EPSM,FAC
DOUBLE PRECISION RHS(N),F(N)
LOGICAL LFORW
*----
* LOCAL VARIABLE
*----
REAL EPSMAX,EPSINF,EPS2
PARAMETER (EPSMAX=1E-7)
INTEGER I,J,ITER
DOUBLE PRECISION R,BI,WI,RT1
DOUBLE PRECISION DDOT,AUX(2),EPS,FNORM,RHSN,ASIN,ASIN2,SIN,CN,SQ2
LOGICAL DEBUG
INTRINSIC SQRT,ABS,SIGN
DOUBLE PRECISION, ALLOCATABLE, DIMENSION(:) :: PI,RI,SI,ROT,API,
1 ASI
*----
* SCRATCH STORAGE ALLOCATION
*----
ALLOCATE(PI(N),RI(N),SI(N),ROT(N),API(N),ASI(N))
*
SQ2=1.D0/SQRT(2.D0)
*----
DEBUG=.FALSE.
EPSINF=EPSMAX*FAC
ITER=0
*
RHSN=0.0
DO I=1,N
RHSN=MAX(RHSN,ABS(RHS(I)))
ENDDO
IF(RHSN.LT.EPSINF) THEN
DO I=1,N
F(I)=0.0
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 MCGPRA(LFORW,3,PACA,.FALSE.,N,LC,IM,MCU,JU,DIAGF,CF,ILUDF,
1 ILUCF,DIAGF,RHS(1),RI,LC0,IM0,MCU0,CF)
DO I=1,N
F(I)=RHS(I)
RI(I)=RHS(I)-RI(I)
PI(I)=RI(I)
ROT(I)=RI(I)
ENDDO
R=DDOT(N,RI,1,RI,1)
FNORM=DDOT(N,F,1,F,1)
EPS=SQRT(R/FNORM)
IF(DEBUG) WRITE(6,100) ITER,EPS,EPSM
IF(EPS.LE.EPSM) THEN
IF(IPRINT.GT.2) WRITE(6,100) ITER,EPS,EPSM
GO TO 40
ENDIF
AUX(1)=R
*
DO WHILE (ITER.LT.MAXM)
* BiCGSTAB iterations
ITER=ITER+1
* calculate (P times (D times PI)) -> API
CALL MCGPRA(LFORW,3,PACA,.FALSE.,N,LC,IM,MCU,JU,DIAGF,CF,
1 ILUDF,ILUCF,DIAGF,PI(1),API,LC0,IM0,MCU0,CF)
*
AUX(2)=AUX(1)/DDOT(N,API,1,ROT,1)
DO J=1,N
SI(J)=RI(J)-AUX(2)*API(J)
ENDDO
ITER=ITER+1
* calculate (P times (D times SI)) -> ASI
CALL MCGPRA(LFORW,3,PACA,.FALSE.,N,LC,IM,MCU,JU,DIAGF,CF,
1 ILUDF,ILUCF,DIAGF,SI(1),ASI,LC0,IM0,MCU0,CF)
*
!!!! ASIN=DDOT(N,ASI,1,ASI,1)
!!!! ASIN2=DDOT(N,ASI,1,SI,1)
!!!! 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=DDOT(N,ASI,1,SI,1)
ASIN=SQRT(DDOT(N,ASI,1,ASI,1))
SIN=SQRT(DDOT(N,SI,1,SI,1))
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
DO J=1,N
F(J)=F(J)+AUX(2)*PI(J)+WI*SI(J)
RI(J)=SI(J)-WI*ASI(J)
ENDDO
R=DDOT(N,RI,1,RI,1)
FNORM=DDOT(N,F,1,F,1)
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)=DDOT(N,RI,1,ROT,1)
BI=AUX(1)/RT1*AUX(2)/WI
DO J=1,N
PI(J)=RI(J)+BI*(PI(J)-WI*API(J))
ENDDO
ENDDO
20 CONTINUE
* determine final residual norm
ITER=ITER+1
* calculate (P times (D times F)) -> RI
CALL MCGPRA(LFORW,3,PACA,.FALSE.,N,LC,IM,MCU,JU,DIAGF,CF,ILUDF,
1 ILUCF,DIAGF,F(1),RI,LC0,IM0,MCU0,CF)
DO I=1,N
RI(I)=RHS(I)-RI(I)
ENDDO
*
R=DDOT(N,RI,1,RI,1)
FNORM=DDOT(N,F,1,F,1)
IF(FNORM.LT.EPS2) GOTO 30
EPS=SQRT(R/FNORM)
IF(IPRINT.GT.2) WRITE(6,100) ITER,EPS,EPSM
!!!! IF(EPS.GT.EPSM) THEN
!!!! DO I=1,N
!!!! PI(I)=RI(I)
!!!! ROT(I)=RI(I)
!!!! ENDDO
!!!! GO TO 10
!!!! ENDIF
GO TO 40
*
30 IF(DEBUG) WRITE(6,300) ITER,FNORM,EPS2
F(:N)=0.0
*----
* SCRATCH STORAGE DEALLOCATION
*----
40 DEALLOCATE(ASI,API,ROT,SI,RI,PI)
RETURN
*
100 FORMAT(12X,14H MCGABG: ITER=,I3,5H EPS=,E9.2,5H TAR=,E9.2)
200 FORMAT(12X,27H MCGABG: RHS INFINITE NORM=,E9.2,5H LIM=,E9.2/
1 12X,33H -> ACA CORRECTION IS SET TO ZERO)
300 FORMAT(12X,14H MCGABG: ITER=,I3,7H FNORM=,E9.2,5H LIM=,E9.2)
END
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