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.

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  1. Bonaldi, Francesco; Droniou, Jérôme; Masson, Roland; Pasteau, Antoine: Energy-stable discretization of two-phase flows in deformable porous media with frictional contact at matrix-fracture interfaces (2022)
  2. Ghosh, Supriyo; Newman, Christopher K.; Francois, Marianne M.: \textttTusas: a fully implicit parallel approach for coupled phase-field equations (2022)
  3. Bonaldi, Francesco; Brenner, Konstantin; Droniou, Jérôme; Masson, Roland; Pasteau, Antoine; Trenty, Laurent: Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces (2021)
  4. Brown, Jed; He, Yunhui; MacLachlan, Scott; Menickelly, Matt; Wild, Stefan M.: Tuning multigrid methods with robust optimization and local Fourier analysis (2021)
  5. Hien, Le Thi Khanh; Chua, Chek Beng: A global linear and local superlinear (quadratic) inexact non-interior continuation method for variational inequalities over general closed convex sets (2021)
  6. Jiang, Meng-Jiao; Guo, Xue-Ping: A new parameter-free method for Toeplitz systems of weakly nonlinear equations (2021)
  7. Mohammadi, Masoud; Vakilipour, Shidvash; Ormiston, Scott: Newton linearization of the Navier-Stokes equations for flow computations using a fully coupled finite volume method (2021)
  8. Franciolini, M.; Botti, L.; Colombo, A.; Crivellini, A.: (p)-multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows (2020)
  9. Frank, Florian; Rupp, Andreas; Kuzmin, Dmitri: Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation (2020)
  10. Gruzdev, A. P.; Melnikov, N. B.: Block Jacobi preconditioning for solving dynamic general equilibrium models (2020)
  11. Kong, Fande; Wang, Yaqi; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.; Lindsay, Alexander D.; DeHart, Mark D.; Martineau, Richard C.: A highly parallel multilevel Newton-Krylov-Schwarz method with subspace-based coarsening and partition-based balancing for the multigroup neutron transport equation on three-dimensional unstructured meshes (2020)
  12. Xie, Fang; Wu, Qing-Biao; Dai, Ping-Fei: Modified Newton-SHSS method for a class of systems of nonlinear equations (2019)
  13. Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.; Hittinger, Jeffrey A. F.: Kinetic simulation of collisional magnetized plasmas with semi-implicit time integration (2018)
  14. Liu, Lulu; Keyes, David E.; Krause, Rolf: A note on adaptive nonlinear preconditioning techniques (2018)
  15. Qin, Wanglong; Cai, Junwei; Lu, Hongqiang; Jimack, Peter K.; Walkley, M. A.: A study of preconditioned Jacobian-free Newton-Krylov discontinuous Galerkin method for compressible flows on 3D hexahedral grids (2018)
  16. Franciolini, Matteo; Crivellini, Andrea; Nigro, Alessandra: On the efficiency of a matrix-free linearly implicit time integration strategy for high-order discontinuous Galerkin solutions of incompressible turbulent flows (2017)
  17. Liu, Lulu; Zhang, Wei; Keyes, David E.: Nonlinear multiplicative Schwarz preconditioning in natural convection cavity flow (2017)
  18. Li, Yang; Guo, Xue-Ping: Semilocal convergence analysis for MMN-HSS methods under Hölder conditions (2017)
  19. Nigro, A.; de Bartolo, C.; Crivellini, A.; Bassi, F.: Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows (2017)
  20. Dalcin, L.; Collier, N.; Vignal, P.; Côrtes, A. M. A.; Calo, V. M.: PetIGA: a framework for high-performance isogeometric analysis (2016)

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