ddasik.f

Go to the documentation of this file.

C Work perfored under the auspices of the U.S. Department of Energy
C by Lawrence Livermore National Laboratory under contract number
C W-7405-Eng-48.
C
      SUBROUTINE ddasik(X,Y,YPRIME,NEQ,ICOPT,ID,RES,JACK,PSOL,H,WT,
     *   jskip,rpar,ipar,savr,delta,r,yic,ypic,pwk,wm,iwm,cj,uround,
     *   epli,sqrtn,rsqrtn,epcon,ratemx,stptol,jflg,
     *   icnflg,icnstr,iernls)
C
C***BEGIN PROLOGUE  DDASIK
C***REFER TO  DDASPK
C***DATE WRITTEN   941026   (YYMMDD)
C***REVISION DATE  950808   (YYMMDD)
C***REVISION DATE  951110   Removed unreachable block 390.
C
C
C-----------------------------------------------------------------------
C***DESCRIPTION
C
C
C     DDASIK solves a nonlinear system of algebraic equations of the
C     form G(X,Y,YPRIME) = 0 for the unknown parts of Y and YPRIME in
C     the initial conditions.
C
C     An initial value for Y and initial guess for YPRIME are input.
C
C     The method used is a Newton scheme with Krylov iteration and a
C     linesearch algorithm.
C
C     The parameters represent
C
C     X         -- Independent variable.
C     Y         -- Solution vector at x.
C     YPRIME    -- Derivative of solution vector.
C     NEQ       -- Number of equations to be integrated.
C     ICOPT     -- Initial condition option chosen (1 or 2).
C     ID        -- Array of dimension NEQ, which must be initialized
C                  if ICOPT = 1.  See DDASIC.
C     RES       -- External user-supplied subroutine
C                  to evaluate the residual.  See RES description
C                  in DDASPK prologue.
C     JACK     --  External user-supplied routine to update
C                  the preconditioner.  (This is optional).
C                  See JAC description for the case
C                  INFO(12) = 1 in the DDASPK prologue.
C     PSOL      -- External user-supplied routine to solve
C                  a linear system using preconditioning.
C                  (This is optional).  See explanation inside DDASPK.
C     H         -- Scaling factor for this initial condition calc.
C     WT        -- Vector of weights for error criterion.
C     JSKIP     -- input flag to signal if initial JAC call is to be
C                  skipped.  1 => skip the call, 0 => do not skip call.
C     RPAR,IPAR -- Real and integer arrays used for communication
C                  between the calling program and external user
C                  routines.  They are not altered within DASPK.
C     SAVR      -- Work vector for DDASIK of length NEQ.
C     DELTA     -- Work vector for DDASIK of length NEQ.
C     R         -- Work vector for DDASIK of length NEQ.
C     YIC,YPIC  -- Work vectors for DDASIK, each of length NEQ.
C     PWK       -- Work vector for DDASIK of length NEQ.
C     WM,IWM    -- Real and integer arrays storing
C                  matrix information for linear system
C                  solvers, and various other information.
C     CJ        -- Matrix parameter = 1/H (ICOPT = 1) or 0 (ICOPT = 2).
C     UROUND    -- Unit roundoff.
C     EPLI      -- convergence test constant.
C                  See DDASPK prologue for more details.
C     SQRTN     -- Square root of NEQ.
C     RSQRTN    -- reciprical of square root of NEQ.
C     EPCON     -- Tolerance to test for convergence of the Newton
C                  iteration.
C     RATEMX    -- Maximum convergence rate for which Newton iteration
C                  is considered converging.
C     JFLG      -- Flag showing whether a Jacobian routine is supplied.
C     ICNFLG    -- Integer scalar.  If nonzero, then constraint
C                  violations in the proposed new approximate solution
C                  will be checked for, and the maximum step length
C                  will be adjusted accordingly.
C     ICNSTR    -- Integer array of length NEQ containing flags for
C                  checking constraints.
C     IERNLS    -- Error flag for nonlinear solver.
C                   0   ==> nonlinear solver converged.
C                   1,2 ==> recoverable error inside nonlinear solver.
C                           1 => retry with current Y, YPRIME
C                           2 => retry with original Y, YPRIME
C                  -1   ==> unrecoverable error in nonlinear solver.
C
C-----------------------------------------------------------------------
C
C***ROUTINES CALLED
C   RES, JACK, DNSIK, DCOPY
C
C***END PROLOGUE  DDASIK
C
C
      IMPLICIT DOUBLE PRECISION(a-h,o-z)
      dimension y(*),yprime(*),id(*),wt(*),icnstr(*)
      dimension savr(*),delta(*),r(*),yic(*),ypic(*),pwk(*)
      dimension wm(*),iwm(*), rpar(*),ipar(*)
      EXTERNAL res, jack, psol
C
      parameter(lnre=12, lnje=13, llocwp=29, llciwp=30)
      parameter(lmxnit=32, lmxnj=33)
C
C
C     Perform initializations.
C
      lwp = iwm(llocwp)
      liwp = iwm(llciwp)
      mxnit = iwm(lmxnit)
      mxnj = iwm(lmxnj)
      iernls = 0
      nj = 0
      eplin = epli*epcon
C
C     Call RES to initialize DELTA.
C
      ires = 0
      iwm(lnre) = iwm(lnre) + 1
      CALL res(x,y,yprime,cj,delta,ires,rpar,ipar)
      IF (ires .LT. 0) go to 370
C
C     Looping point for updating the preconditioner.
C
 300  CONTINUE
C
C     Initialize all error flags to zero.
C
      ierpj = 0
      ires = 0
      iernew = 0
C
C     If a Jacobian routine was supplied, call it.
C
      IF (jflg .EQ. 1 .AND. jskip .EQ. 0) THEN
        nj = nj + 1
        iwm(lnje)=iwm(lnje)+1
        CALL jack(res, ires, neq, x, y, yprime, wt, delta, r, h, cj,
     *     wm(lwp), iwm(liwp), ierpj, rpar, ipar)
        IF (ires .LT. 0 .OR. ierpj .NE. 0) go to 370
        ENDIF
      jskip = 0
C
C     Call the nonlinear Newton solver for up to MXNIT iterations.
C
      CALL dnsik(x,y,yprime,neq,icopt,id,res,psol,wt,rpar,ipar,
     *   savr,delta,r,yic,ypic,pwk,wm,iwm,cj,sqrtn,rsqrtn,
     *   eplin,epcon,ratemx,mxnit,stptol,icnflg,icnstr,iernew)
C
      IF (iernew .EQ. 1 .AND. nj .LT. mxnj .AND. jflg .EQ. 1) THEN
C
C       Up to MXNIT iterations were done, the convergence rate is < 1,
C       a Jacobian routine is supplied, and the number of JACK calls
C       is less than MXNJ.
C       Copy the residual SAVR to DELTA, call JACK, and try again.
C
        CALL dcopy(neq,  savr, 1, delta, 1)
        go to 300
        ENDIF
C
      IF (iernew .NE. 0) go to 380
      RETURN
C
C
C     Unsuccessful exits from nonlinear solver.
C     Set IERNLS accordingly.
C
 370  iernls = 2
      IF (ires .LE. -2) iernls = -1
      RETURN
C
 380  iernls = min(iernew,2)
      RETURN
C
C----------------------- END OF SUBROUTINE DDASIK-----------------------
      END