On backtracking failure in newton-GMRES methods with a demonstration for the navier-stokes equations
Journal of Computational Physics
A Hybrid Newton-GMRES Method for Solving Nonlinear Equations
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Journal of Computational Physics
Hybrid (OpenMP and MPI) parallelization of MFIX: a multiphase CFD code for modeling fluidized beds
Proceedings of the 2003 ACM symposium on Applied computing
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited
ACM Transactions on Mathematical Software (TOMS)
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
A fast solver for the Ornstein-Zernike equations
Journal of Computational Physics
A choice of forcing terms in inexact Newton method
Journal of Computational and Applied Mathematics
BiCGStab, VPAStab and an adaptation to mildly nonlinear systems
Journal of Computational and Applied Mathematics
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Advances in Engineering Software
Choice of initial guess in iterative solution of series of systems arising in fluid flow simulations
Journal of Computational Physics
Development of a 2-D algorithm to simulate convection and phase transition efficiently
Journal of Computational Physics
Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions
Journal of Computational Physics
Nonmonotone derivative-free methods for nonlinear equations
Computational Optimization and Applications
Journal of Computational Physics
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids
Computers & Mathematics with Applications
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
Algorithm 896: LSA: Algorithms for large-scale optimization
ACM Transactions on Mathematical Software (TOMS)
On physics-based preconditioning of the Navier-Stokes equations
Journal of Computational Physics
Reduced-dissipation remapping of velocity in staggered arbitrary Lagrangian-Eulerian methods
Journal of Computational and Applied Mathematics
Accelerating an inexact Newton/GMRES scheme by subspace decomposition
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
SIAM Journal on Scientific Computing
Anderson Acceleration for Fixed-Point Iterations
SIAM Journal on Numerical Analysis
Efficient Preconditioner Updates for Shifted Linear Systems
SIAM Journal on Scientific Computing
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
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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.