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. Brown, Jed; He, Yunhui; MacLachlan, Scott; Menickelly, Matt; Wild, Stefan M.: Tuning multigrid methods with robust optimization and local Fourier analysis (2021)
  2. 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)
  3. Gruzdev, A. P.; Melnikov, N. B.: Block Jacobi preconditioning for solving dynamic general equilibrium models (2020)
  4. 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)
  5. Xie, Fang; Wu, Qing-Biao; Dai, Ping-Fei: Modified Newton-SHSS method for a class of systems of nonlinear equations (2019)
  6. Ghosh, Debojyoti; Dorf, Mikhail A.; Dorr, Milo R.; Hittinger, Jeffrey A. F.: Kinetic simulation of collisional magnetized plasmas with semi-implicit time integration (2018)
  7. Liu, Lulu; Keyes, David E.; Krause, Rolf: A note on adaptive nonlinear preconditioning techniques (2018)
  8. 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)
  9. Liu, Lulu; Zhang, Wei; Keyes, David E.: Nonlinear multiplicative Schwarz preconditioning in natural convection cavity flow (2017)
  10. Li, Yang; Guo, Xue-Ping: Semilocal convergence analysis for MMN-HSS methods under Hölder conditions (2017)
  11. Nigro, A.; de Bartolo, C.; Crivellini, A.; Bassi, F.: Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows (2017)
  12. Dalcin, L.; Collier, N.; Vignal, P.; Côrtes, A. M. A.; Calo, V. M.: PetIGA: a framework for high-performance isogeometric analysis (2016)
  13. Liu, Lulu; Keyes, David E.: Convergence analysis for the multiplicative Schwarz preconditioned inexact Newton algorithm (2016)
  14. Liu, Shuang; Wang, Bofu; Wan, Zhenhua; Ma, Dongjun; Sun, Dejun: Bifurcation analysis of laminar isothermal planar opposed-jet flow (2016)
  15. Melnikov, Nikolai B.; Gruzdev, Arseniy P.; Dalton, Michael G.; O’Neill, Brian C.: Parallel algorithm for calculating general equilibrium in multiregion economic growth models (2016)
  16. Newman, Christopher; Womeldorff, Geoffrey; Knoll, Dana A.; Chacón, Luis: A communication-avoiding implicit-explicit method for a free-surface ocean model (2016)
  17. Abgrall, R.; De Santis, D.: Linear and non-linear high order accurate residual distribution schemes for the discretization of the steady compressible Navier-Stokes equations (2015)
  18. Gaul, André; Schlömer, Nico: Preconditioned recycling Krylov subspace methods for self-adjoint problems (2015)
  19. Liu, Lulu; Keyes, David E.: Field-split preconditioned inexact Newton algorithms (2015)
  20. Philip, Bobby; Berrill, Mark A.; Allu, Srikanth; Hamilton, Steven P.; Sampath, Rahul S.; Clarno, Kevin T.; Dilts, Gary A.: A parallel multi-domain solution methodology applied to nonlinear thermal transport problems in nuclear fuel pins (2015)

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