We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial steps are obtained using one of several Krylov subspace methods. The algorithm is implemented in a Fortran solver called NITSOL that is robust yet easy to use and provides a number of useful options and features. The structure offers the user great flexibility in addressing problem specificity through preconditioning and other means and allows easy adaptation to parallel environments. Features and capabilities are illustrated in numerical experiments.

References in zbMATH (referenced in 97 articles , 1 standard article )

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  1. Reisner, Jon; Wyszogrodzki, Andrzej; Mousseau, Vincent; Knoll, Dana: An efficient physics-based preconditioner for the fully implicit solution of small-scale thermally driven atmospheric flows. (2003)
  2. Syamsudhuha; Silvester, David J.: Efficient solution of the steady-state Navier-Stokes equations using a multigrid preconditioned Newton-Krylov method (2003)
  3. Keyes, David E.: Terascale implicit methods for partial differential equations (2002)
  4. Tuminaro, Raymond S.; Walker, Homer F.; Shadid, John N.: On backtracking failure in Newton-GMRES methods with a demonstration for the Navier-Stokes equations (2002)
  5. Ascher, U. M.; Haber, E.: Grid refinement and scaling for distributed parameter estimation problems (2001)
  6. Bellavia, Stefania; Macconi, Maria; Morini, Benedetta: A hybrid Newton-GMRES method for solving nonlinear equations (2001)
  7. Bellavia, Stefania; Morini, Benedetta: A globally convergent Newton-GMRES subspace method for systems of nonlinear equations (2001)
  8. Deng, G. B.; Piquet, J.; Vasseur, X.; Visonneau, M.: A new fully coupled method for computing turbulent flows (2001)
  9. Pernice, M.; Tocci, M. D.: A multigrid-preconditioned Newton--Krylov method for the incompressible Navier--Stokes equations (2001)
  10. Ford, Judith; Chen, Ke; Scales, Laurence: A new wavelet transform preconditioner for iterative solution of elastohydrodynamic lubrication problems (2000)
  11. Gasparo, M. G.; Morini, B.: Inexact methods: Forcing terms and conditioning (2000)
  12. Nash, Stephen G.: A survey of truncated-Newton methods (2000)
  13. Pernice, Michael: A hybrid multigrid method for the steady-state incompressible Navier-Stokes equations (2000)
  14. Booth, Michael J.; Schlijper, A. G.; Scales, L. E.; Haymet, A. D. J.: Efficient solution of liquid state integral equations using the Newton-GMRES algorithm (1999)
  15. Pernice, Michael; Walker, Homer F.: NITSOL: A Newton iterative solver for nonlinear systems (1998)
  16. Tocci, Michael D.; Kelley, C. T.; Miller, Cass T.; Kees, Christopher E.: Inexact Newton methods and the method of lines for solving Richards’ equation in two space dimensions (1998)
  17. Shadid, John N.; Tuminaro, Ray S.; Walker, Homer F.: An inexact Newton method for fully coupled solution of the Navier-Stokes equations with heat and mass transport (1997)

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