nitsol Interface

input(1) = nnimax = maximum number of nonlinear iterations (default 200).

input(2) = ijacv = flag for determining the method of J*v evaluation:
             0 => finite-difference evaluation (default) 
             1 => analytic evaluation

input(3) = ikrysl = flag for determining the Krylov solver: 
             0 => GMRES (default)
             1 => BiCGSTAB
             2 => TFQMR

           For brief descriptions of the solvers plus references, 
           see the subroutines nitgm, nitstb, and nittfq.

input(4) = kdmax = maximum Krylov subspace dimension when GMRES is used 
           (default 20).

input(5) = irpre = flag for right preconditioning: 
             0 => no right preconditioning
             1 => right preconditioning

input(6) = iksmax = maximum allowable number of iterations per call 
           to the Krylov solver routine (default 1000).

input(7) = iresup = residual update flag when GMRES is used; on 
           restarts, the residual is updated as follows: 
             0 => linear combination (default) 
             1 => direct evaluation
           The first is cheap (one n-vector saxpy) but may lose 
           accuracy with extreme residual reduction; the second 
           retains accuracy better but costs one J*v product per 
           restart.

input(8) = ifdord = order of the finite-difference formula (sometimes) 
           used when input(2) = ijacv = 0. When input(2) = ijacv = 0, 
           this must be 0, 1, 2, or 4 on input; otherwise, it is 
           irrelevant. With input(2) = ijacv = 0, the precise 
           meaning is as follows:

           If GMRES is used, then ifdord matters only if input(7) = 
           iresup = 1, in which case it determines the order of 
           the finite-difference formula used in evaluating the 
           initial residual at each GMRES restart (default 2); if 
           ifdord = 0 on input, then it is set to 2 below. NOTE: This 
           only affects initial residuals at restarts; first-order 
           differences are always used within each GMRES cycle. Using 
           higher-order differences at restarts only should give 
           the same accuracy as if higher-order differences were 
           used throughout; see K. Turner and H. F. Walker, "Efficient 
           high accuracy solutions with GMRES(m)," SIAM J. Sci. 
           Stat. Comput., 13 (1992), pp. 815--825.

           If BiCGSTAB or TFQMR is used, then ifdord determines the 
           order of the finite-difference formula used at each 
           iteration (default 1); if ifdord = 0 on input, then it 
           is set to 1 below.

input(9) = ibtmax = maximum allowable number of backtracks (step 
           reductions) per call to nitbt (default 10).

           USAGE NOTE: Backtracking can be turned off by setting 
              ibtmax = -1. Other negative values of ibtmax are not 
           valid.

input(10) = ieta = flag determining the forcing term eta as follows: 
             0 => abs( ||fcur|| - ||fprev+Jprev*sprev|| )/||fprev||
                  (default) 
             1 => (||fcur||/||fprev||)**2 
             2 => gamma*(||fcur||/||fprev||)**alpha 
                  for user-supplied gamma in (0,1] and alpha in (1,2] 
             3 => fixed (constant) eta in (0,1), either 0.1 (default) 
                     or specified by the user (see USAGE NOTE below) 
           Here, fcur = current f, fprev = previous f, etc. The Krylov 
           iterations are terminated when an iterate s satisfies 
           an inexact Newton condition ||F + J*s|| .le. eta*||F||.

           USAGE NOTE: If input(10) = ieta = 2, then alpha and gamma 
           must be set in common block nitparam.h as described below. 
              If input(10) = ieta = 3, then the desired constant eta may 
              be similarly set in nitparam.h if a value other than the 
              default of 0.1 is desired.

           The first three expressions above are from S. C. Eisenstat 
           and H. F. Walker, "Choosing the forcing terms in an inexact 
           Newton method", SIAM J. Scientific Computing, 17 (1996), 
           pp. 16--32. (They may be modified according to certain 
           safeguards in subroutine nitdrv.) The first gives convergence 
           that is q-superlinear and of r-order (1+sqrt(5))/2. The 
           second gives convergence that is r-quadratic and of q-order 
           p for every p in [1,2). The third gives convergence that is 
           of q-order alpha when gamma < 1 and, when gamma = 1, of 
           r-order alpha and q-order p for every p in [1,alpha). The 
           fourth gives q-linear convergence with asymptotic rate 
           constant eta in a certain norm; see R. S. Dembo, S. C. 
              Eisenstat, and T. Steihaug, "Inexact Newton methods", 
           SIAM J. Numer. Anal., 18 (1982), pp. 400-408.

           Of these four choices, the 1st is usually satisfactory, 
           the 2nd or 3rd is sometimes preferred, and the 4th may be 
           useful in some situations, e.g., it may be desirable to 
           choose a fairly large fixed eta in (0,1), such as eta = .1, 
           when numerical inaccuracy prevents the Krylov solver 
           from obtaining much residual reduction.

 info(1)   = nfe (number of function evaluations)
 info(2)   = njve (number of J*v evaluations)
 info(3)   = nrpre (number of P(inverse)*v evaluations)
 info(4)   = nli (number of linear iterations)
 info(5)   = nni (number of nonlinear iterations)
 info(6)   = nbt (number of backtracks)