Matrix-free methods for stiff systems of ODE's
SIAM Journal on Numerical Analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A local convergence theory for combined inexact-Newton/finite-difference projection methods
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
Hybrid Krylov methods for nonlinear systems of equations
SIAM Journal on Scientific and Statistical Computing
Viscous computations using a direct solver
Computers and Fluids
Multilevel projection methods for partial differential equations
Multilevel projection methods for partial differential equations
SIAM Journal on Scientific and Statistical Computing
Efficient high accuracy solutions with GMRES(m)
SIAM Journal on Scientific and Statistical Computing
How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
A flexible inner-outer preconditioned GMRES algorithm
SIAM Journal on Scientific Computing
A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems
SIAM Journal on Scientific Computing
A direct Newton solver for the two-dimensional tokamak edge plasma fluid equations
Journal of Computational Physics
Towards polyalgorithmic linear system solvers for nonlinear elliptic problems
SIAM Journal on Scientific Computing
A comparison of preconditioned nonsymmetric Krylov methods on a large-scale MIMD machine
SIAM Journal on Scientific Computing
An implicit upwind algorithm for computing turbulent flows on unstructured grids
Computers and Fluids
Implicit and conservative difference scheme for the Fokker-Planck equation
Journal of Computational Physics
Journal of Computational Physics
A two-dimensional finite element model of the edge plasma
Journal of Computational Physics
Iterative solution methods
Choosing the forcing terms in an inexact Newton method
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
A multigrid preconditioner for the semiconductor equations
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Implicit/multigrid algorithms for incompressible turbulent flows on unstructured grids
Journal of Computational Physics
Preconditioning techniques for the Newton-Krylov solution of compressible flows
Journal of Computational Physics
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Fully implicit kinetic solution of collisional plasmas
Journal of Computational Physics
ADIC: an extensible automatic differentiation tool for ANSI-C
Software—Practice & Experience
Journal of Computational Physics
Efficient parallel computation of unstructured finite element reacting flow solutions
Parallel Computing - Special issue on applications: parallel computing methods in applied fluid mechanics
Advanced finite element modeling of the tokamak plasma edge
Journal of Computational Physics
Convergence Analysis of Pseudo-Transient Continuation
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Parallel Newton--Krylov--Schwarz Algorithms for the Transonic Full Potential Equation
SIAM Journal on Scientific Computing
Enhanced Nonlinear Iterative Techniques Applied to a Nonequilibrium Plasma Flow
SIAM Journal on Scientific Computing
NITSOL: A Newton Iterative Solver for Nonlinear Systems
SIAM Journal on Scientific Computing
An improved convection scheme applied to recombining divertor plasma flows
Journal of Computational Physics
Multigrid strategies for viscous flow solvers on anisotropic unstructured meshes
Journal of Computational Physics
SIAM Journal on Scientific Computing
A multilevel iterative field solver for implicit, kinetic, plasma simulation
Journal of Computational Physics
A multgrid Newton-Krylov method for multimaterial equilibrium radiation diffusion
Journal of Computational Physics
Time step size selection for radiation diffusion calculations
Journal of Computational Physics
Parallel Newton-Krylov methods for PDE-constrained optimization
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
A Multigrid Preconditioned Newton--Krylov Method
SIAM Journal on Scientific Computing
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
An implicit energy-conservative 2D Fokker-Planck algorithm: II. Jacobian-free Newton—Krylov solver
Journal of Computational Physics
A discretization scheme for an extended drift-diffusion model including trap-assisted phenomena
Journal of Computational Physics
Physics-based preconditioning and the Newton-Krylov method for non-equilibrium radiation diffusion
Journal of Computational Physics
On Newton-Krylov multigrid methods for the imcompressible Navier-Stokes equations
Journal of Computational Physics
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Journal of Computational Physics
Multigrid
High-performacne parallel implicit CFD
Parallel Computing - Special issue on parallel computing in aerospace
Parallel simulation of compressible flow using automatic differentiation and PETSc
Parallel Computing - Special issue on parallel computing in aerospace
An efficient implicit discontinuous spectral Galerkin method
Journal of Computational Physics
Parallel Computer Architecture: A Hardware/Software Approach
Parallel Computer Architecture: A Hardware/Software Approach
Using automatic differentiation for second-order matrix-free methods in PDE-constrained optimization
Automatic differentiation of algorithms
Numerical Modeling in Applied Physics and Astrophysics
Numerical Modeling in Applied Physics and Astrophysics
Application of parallel implicit methods to edge-plasma numerical simulations
Journal of Computational Physics
An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers
Journal of Computational Physics
An implicit, nonlinear reduced resistive MHD solver
Journal of Computational Physics
A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
An Aggregation-Based Domain Decomposition Preconditioner for Groundwater Flow
SIAM Journal on Scientific Computing
On Preconditioning Newton--Krylov Methods in Solidifying Flow Applications
SIAM Journal on Scientific Computing
Preconditioning Strategies for Fully Implicit Radiation Diffusion with Material-Energy Transfer
SIAM Journal on Scientific Computing
Nonlinearly Preconditioned Inexact Newton Algorithms
SIAM Journal on Scientific Computing
Creating Simulation Capabilities
IEEE Computational Science & Engineering
An implicit particle-in-cell method for granular materials
Journal of Computational Physics
On backtracking failure in newton-GMRES methods with a demonstration for the navier-stokes equations
Journal of Computational Physics
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
On balanced approximations for time integration of multiple time scale systems
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
SCHWARZ-BASED ALGORITHMS FOR COMPRESSIBLE FLOWS
SCHWARZ-BASED ALGORITHMS FOR COMPRESSIBLE FLOWS
A 2D high-ß Hall MHD implicit nonlinear solver
Journal of Computational Physics
Journal of Computational Physics
New physics-based preconditioning of implicit methods for non-equilibrium radiation diffusion
Journal of Computational Physics
Pseudotransient Continuation and Differential-Algebraic Equations
SIAM Journal on Scientific Computing
International Journal of High Performance Computing Applications
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
International Journal of High Performance Computing Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Implicitly balanced solution of the two-phase flow equations coupled to nonlinear heat conduction
Journal of Computational Physics
Jacobian---Free Newton---Krylov Methods for the Accurate Time Integration of Stiff Wave Systems
Journal of Scientific Computing
High Performance Computing of Compressible Flows
HPCASIA '05 Proceedings of the Eighth International Conference on High-Performance Computing in Asia-Pacific Region
ASP-DAC '06 Proceedings of the 2006 Asia and South Pacific Design Automation Conference
Newton's method for steady and unsteady reacting flows
Proceedings of the 44th annual Southeast regional conference
A parallel explicit/implicit time stepping scheme on block-adaptive grids
Journal of Computational Physics
A choice of forcing terms in inexact Newton method
Journal of Computational and Applied Mathematics
Second-order accurate projective integrators for multiscale problems
Journal of Computational and Applied Mathematics
A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations
Applied Numerical Mathematics
Journal of Computational Physics
A fully implicit numerical method for single-fluid resistive magnetohydrodynamics
Journal of Computational Physics
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
Fourierization of the Legendre--Galerkin method and a new space--time spectral method
Applied Numerical Mathematics
An iterative matrix-free method in implicit immersed boundary/continuum methods
Computers and Structures
Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes
Journal of Computational Physics
Krylov deferred correction accelerated method of lines transpose for parabolic problems
Journal of Computational Physics
Journal of Computational Physics
Numerical prediction of interfacial instabilities: Sharp interface method (SIM)
Journal of Computational Physics
An iterative semi-implicit scheme with robust damping
Journal of Computational Physics
Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids
Computers & Mathematics with Applications
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
Journal of Computational Physics
Variable Relaxation Solve for Nonlinear Thermal Conduction
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
On computational issues of immersed finite element methods
Journal of Computational Physics
On the linear convergence of Newton-Krylov methods
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
On choosing a nonlinear initial iterate for solving the 2-D 3-T heat conduction equations
Journal of Computational Physics
A Jacobian-free Newton-Krylov algorithm for compressible turbulent fluid flows
Journal of Computational Physics
Preconditioning methods for discontinuous Galerkin solutions of the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
A Scalable and Adaptable Solution Framework within Components of the Community Climate System Model
ICCS 2009 Proceedings of the 9th International Conference on Computational Science
Semi-implicit Krylov deferred correction methods for ordinary differential equations
AMATH'09 Proceedings of the 15th american conference on Applied mathematics
Journal of Computational Physics
Self-consistent solution of cosmological radiation-hydrodynamics and chemical ionization
Journal of Computational Physics
Newton-conjugate-gradient methods for solitary wave computations
Journal of Computational Physics
An implicit immersed boundary method for three-dimensional fluid-membrane interactions
Journal of Computational Physics
Journal of Computational Physics
On physics-based preconditioning of the Navier-Stokes equations
Journal of Computational Physics
Journal of Computational Physics
Fluid-structure interaction in blood flows on geometries based on medical imaging
Computers and Structures
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Large deformation of liquid capsules enclosed by thin shells immersed in the fluid
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Analysis of a mixed semi-implicit/implicit algorithm for low-frequency two-fluid plasma modeling
Journal of Computational Physics
An adaptive implicit-explicit scheme for the DNS and LES of compressible flows on unstructured grids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D
Journal of Scientific Computing
A second order self-consistent IMEX method for radiation hydrodynamics
Journal of Computational Physics
Fast unsteady flow computations with a Jacobian-free Newton-Krylov algorithm
Journal of Computational Physics
Nonlinear variants of the TR/BDF2 method for thermal radiative diffusion
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Accelerated non-linear finite volume method for diffusion
Journal of Computational Physics
An Analysis of Equivalent Operator Preconditioning for Equation-Free Newton-Krylov Methods
SIAM Journal on Numerical Analysis
Operator-Based Preconditioning of Stiff Hyperbolic Systems
SIAM Journal on Scientific Computing
Marker Redistancing/Level Set Method for High-Fidelity Implicit Interface Tracking
SIAM Journal on Scientific Computing
A Fully Implicit Domain Decomposition Algorithm for Shallow Water Equations on the Cubed-Sphere
SIAM Journal on Scientific Computing
A Simplified and Flexible Variant of GCROT for Solving Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Long-time integration methods for mesoscopic models of pattern-forming systems
Journal of Computational Physics
Hybrid programming model for implicit PDE simulations on multicore architectures
IWOMP'11 Proceedings of the 7th international conference on OpenMP in the Petascale era
Journal of Computational and Applied Mathematics
Review of implicit methods for the magnetohydrodynamic description of magnetically confined plasmas
Journal of Computational Physics
Estimating Computational Noise
SIAM Journal on Scientific Computing
Anderson Acceleration for Fixed-Point Iterations
SIAM Journal on Numerical Analysis
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
SIAM Journal on Scientific Computing
Predictor-Corrector preconditioned newton-krylov method for cavity flow
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Estimating Derivatives of Noisy Simulations
ACM Transactions on Mathematical Software (TOMS)
A relaxation method for large eigenvalue problems, with an application to flow stability analysis
Journal of Computational Physics
Journal of Computational Physics
Semi-implicit formulation of the immersed finite element method
Computational Mechanics
Numerical solution of diffusion models in biomedical imaging on multicore processors
Journal of Biomedical Imaging - Special issue on Parallel Computation in Medical Imaging Applications
Mathematical and Computer Modelling: An International Journal
Compact and Stable Discontinuous Galerkin Methods for Convection-Diffusion Problems
SIAM Journal on Scientific Computing
Efficient evaluation of the direct and adjoint linearized dynamics from compressible flow solvers
Journal of Computational Physics
ACM Transactions on Mathematical Software (TOMS)
Adaptive mesh, finite volume modeling of marine ice sheets
Journal of Computational Physics
Comparative performance of exponential, implicit, and explicit integrators for stiff systems of ODEs
Journal of Computational and Applied Mathematics
An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg-Landau problem
Journal of Computational Physics
Crystal plasticity with Jacobian-Free Newton---Krylov
Computational Mechanics
Multigrid in energy preconditioner for Krylov solvers
Journal of Computational Physics
A parallel adaptive newton-krylov-schwarz method for 3D compressible inviscid flow simulations
Modelling and Simulation in Engineering
A banded preconditioner for the two-sided, nonlinear space-fractional diffusion equation
Computers & Mathematics with Applications
A steady-state solver and stability calculator for nonlinear internal wave flows
Journal of Computational Physics
Journal of Computational Physics
CUDA acceleration of a matrix-free Rosenbrock-K method applied to the shallow water equations
ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
Journal of Computational and Applied Mathematics
An enhanced parareal algorithm based on the deferred correction methods for a stiff system
Journal of Computational and Applied Mathematics
Energy-conserving discontinuous Galerkin methods for the Vlasov-Ampère system
Journal of Computational Physics
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
A parallel Jacobian-free Newton-Krylov solver for a coupled sea ice-ocean model
Journal of Computational Physics
Skew-symmetric convection form and secondary conservative finite difference methods for moving grids
Journal of Computational Physics
Journal of Computational Physics
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
Journal of Computational Physics
Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition
Journal of Computational and Applied Mathematics
A second-order accurate in time IMplicit-EXplicit (IMEX) integration scheme for sea ice dynamics
Journal of Computational Physics
PyTrilinos: Recent advances in the Python interface to Trilinos
Scientific Programming
Hi-index | 31.76 |
Jacobian-free Newton-Krylov (JFNK) methods are synergistic combinations of Newton-type methods for superlinearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations. The link between the two methods is the Jacobian-vector product, which may be probed approximately without forming and storing the elements of the true Jacobian, through a variety of means. Various approximations to the Jacobian matrix may still be required for preconditioning the resulting Krylov iteration. As with Krylov methods for linear problems, successful application of the JFNK method to any given problem is dependent on adequate preconditioning. JFNK has potential for application throughout problems governed by nonlinear partial differential equations and integro-differential equations. In this survey paper, we place JFNK in context with other nonlinear solution algorithms for both boundary value problems (BVPs) and initial value problems (IVPs). We provide an overview of the mechanics of JFNK and attempt to illustrate the wide variety of preconditioning options available. It is emphasized that JFNK can be wrapped (as an accelerator) around another nonlinear fixed point method (interpreted as a preconditioning process, potentially with significant code reuse). The aim of this paper is not to trace fully the evolution of JFNK, nor to provide proofs of accuracy or optimal convergence for all of the constituent methods, but rather to present the reader with a perspective on how JFNK may be applicable to applications of interest and to provide sources of further practical information.