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. An, Heng-Bin; Bai, Zhong-Zhi: A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations (2007)
  2. An, Heng-Bin; Mo, Ze-Yao; Liu, Xing-Ping: A choice of forcing terms in inexact Newton method (2007)
  3. Bellavia, Stefania; Berrone, Stefano: Globalization strategies for Newton-Krylov methods for stabilized FEM discretization of Navier-Stokes equations (2007)
  4. Graves-Morris, P. R.: BiCGStab, VPAStab and an adaptation to mildly nonlinear systems (2007)
  5. Grippo, L.; Sciandrone, M.: Nonmonotone derivative-free methods for nonlinear equations (2007)
  6. Möller, M.: Efficient solution techniques for implicit finite element schemes with flux limiters (2007)
  7. Moore, Peter K.: Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions (2007)
  8. Moroney, T. J.; Turner, I. W.: A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations (2007)
  9. Tromeur-Dervout, D.; Vassilevski, Y.: POD acceleration of fully implicit solver for unsteady nonlinear flows and its application on grid architecture (2007)
  10. Bellavia, Stefania; Morini, Benedetta: Subspace trust-region methods for large bound-constrained nonlinear equations (2006)
  11. Catabriga, L.; Valli, A. M. P.; Melotti, B. Z.; Pessoa, L. M.; Coutinho, A. L. G. A.: Performance of LCD iterative method in the finite element and finite difference solution of convection-diffusion equations (2006)
  12. Evans, Katherine J.; Knoll, D. A.; Pernice, Michael: Development of a 2-D algorithm to simulate convection and phase transition efficiently (2006)
  13. Kaltenbacher, Barbara; Lahmer, Tom; Mohr, Marcus; Kaltenbacher, Manfred: PDE based determination of piezoelectric material tensors (2006)
  14. Tromeur-Dervout, Damien; Vassilevski, Yuri: Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations (2006)
  15. An, Heng-Bin: On convergence of the additive Schwarz preconditioned inexact Newton method (2005)
  16. Gould, Nicholas I. M.; Leyffer, Sven; Toint, Philippe L.: A multidimensional filter algorithm for nonlinear equations and nonlinear least-squares (2004)
  17. Kelley, C. T.; Pettitt, B. Montgomery: A fast solver for the Ornstein--Zernike equations (2004)
  18. Knoll, D. A.; Keyes, D. E.: Jacobian-free Newton-Krylov methods: a survey of approaches and applications. (2004)
  19. Debusschere, Bert J.; Najm, Habib N.; Matta, Alain; Knio, Omar M.; Ghanem, Roger G.; Le Maître, Olivier P.: Protein labeling reactions in electrochemical microchannel flow: numerical simulation and uncertainty propagation (2003)
  20. Gould, Nicholas I. M.; Orban, Dominique; Toint, Philippe L.: CUTEr and SifDec: a constrained and unconstrained testing environment, revisited (2003)