Jacobian-free Newton-Krylov methods: a survey of approaches and applications.

DOI10.1016/j.jcp.2003.08.010zbMath1036.65045OpenAlexW2171303908MaRDI QIDQ1419825

Publication date: 26 January 2004

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2003.08.010

zbMATH Keywords

convergence integro-differential equations numerical examples preconditioning boundary value problems initial value problems survey paper partial differential equations Jacobian-free Newton-Krylov methods nonlinear fixed point method

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Numerical methods for integral equations (65R20) PDEs in connection with fluid mechanics (35Q35) Other nonlinear integral equations (45G10) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical computation of matrix norms, conditioning, scaling (65F35) Applications to the sciences (65Z05)

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communication-avoiding implicit-explicit method for a free-surface ocean model, Fully-implicit orthogonal reconstructed discontinuous Galerkin method for fluid dynamics with phase change, An assessment of coupling algorithms for nuclear reactor core physics simulations, Conservative tightly-coupled simulations of stochastic multiscale systems, A Legendre-Fourier spectral method with exact conservation laws for the Vlasov-Poisson system, Extendible and efficient Python framework for solving evolution equations with stabilized discontinuous Galerkin methods, Development of a balanced adaptive time-stepping strategy based on an implicit JFNK-DG compressible flow solver, New smoother to enhance multigrid-based methods for Bratu problem, A three-dimensional finite volume method based on radial basis functions for the accurate computational modelling of nonlinear diffusion equations, Application of implicit-explicit high order Runge-Kutta methods to discontinuous-Galerkin schemes, A numerical method for solving the 3D unsteady incompressible Navier-Stokes equations in curvilinear domains with complex immersed boundaries, A uniparametric LU-SGS method for systems of nonlinear equations, Scalable semismooth Newton methods with multilevel domain decomposition for subsurface flow and reactive transport in porous media, A numerical framework for integrating deferred correction methods to solve high order collocation formulations of ODEs, A Fourier-accelerated volume integral method for elastoplastic contact, Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation, Data-driven modelling of the Reynolds stress tensor using random forests with invariance, The nested block preconditioning technique for the incompressible Navier-Stokes equations with emphasis on hemodynamic simulations, Nonlinearly preconditioned constraint-preserving algorithms for subsurface three-phase flow with capillarity, Comparison of ROW, ESDIRK, and BDF2 for unsteady flows with the high-order flux reconstruction formulation, Method of hyperelastic nodal forces for deformation of nonlinear membranes, Bivariate gamma model, An investigation of nonlinear time-fractional anomalous diffusion models for simulating transport processes in heterogeneous binary media, A gradient descent method for solving a system of nonlinear equations, Newton method for stationary and quasi-stationary problems for Smoluchowski-type equations, The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems, Operator-based preconditioning for the 2-D 3-T energy equations in radiation hydrodynamics simulations, Nektar++: design and implementation of an implicit, spectral/\(hp\) element, compressible flow solver using a Jacobian-free Newton Krylov approach, A truly forward semi-Lagrangian WENO scheme for the Vlasov-Poisson system, A class of domain decomposition based nonlinear explicit-implicit iteration algorithms for solving diffusion equations with discontinuous coefficient, A Jacobian-free approximate Newton-Krylov startup strategy for RANS simulations, IMEX and exact sequence discretization of the multi-fluid plasma model, Preconditioning a Newton-Krylov solver for all-speed melt pool flow physics, The compact gradient recovery discontinuous Galerkin method for diffusion problems, 3D global optimal forcing and response of the supersonic boundary layer, Asymptotic and positivity preserving methods for Kerr-Debye model with Lorentz dispersion in one dimension, A robust approach for stability analysis of complex flows using high-order Navier-Stokes solvers, High-performance implementation of discontinuous Galerkin methods with application in fluid flow, A review of nonlinear FFT-based computational homogenization methods, Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations, Two new effective iteration methods for nonlinear systems with complex symmetric Jacobian matrices, \(p\)-multigrid matrix-free discontinuous Galerkin solution strategies for the under-resolved simulation of incompressible turbulent flows, A residual smoothing strategy for accelerating Newton method continuation, Output-based adaptive aerodynamic simulations using convolutional neural networks, Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows, Convergence analysis of the modified Newton-HSS method under the Hölder continuous condition, The preconditioned Jacobian-free Newton-Krylov methods for nonequilibrium radiation diffusion equations, An enhanced parareal algorithm based on the deferred correction methods for a stiff system, Adjoint code generator, A novel coupled level set and volume of fluid method for sharp interface capturing on 3D tetrahedral grids, DPMHSS-based iteration methods for solving weakly nonlinear systems with complex coefficient matrices, A brief survey of methods for solving nonlinear least-squares problems, A high accuracy method for long-time evolution of acoustic wave equation, Wavelet preconditioned Newton-Krylov method for elastohydrodynamic lubrication of line contact problems, On the efficiency of combining different methods for acceleration of iterations at the solution of PDEs by the method of collocations and least residuals, Shear decoupled parallel scalable preconditioners for nonlinear thermo-mechanical coupled contact applications, PetIGA: a framework for high-performance isogeometric analysis, An FFT-based spectral solver for interface decohesion modelling using a gradient damage approach, A scalable fully implicit framework for reservoir simulation on parallel computers, Integrated heart -- coupling multiscale and multiphysics models for the simulation of the cardiac function, The generalized finite difference method for long-time transient heat conduction in 3D anisotropic composite materials, A fully implicit, conservative, non-linear, electromagnetic hybrid particle-ion/fluid-electron algorithm, Entropy stable space-time discontinuous Galerkin schemes with summation-by-parts property for hyperbolic conservation laws, A distributed and parallel unite and conquer method to solve sequences of non-Hermitian linear systems, Parallel multilevel domain decomposition preconditioners for monolithic solution of non-isothermal flow in reservoir simulation, Parallel fully coupled methods for bound-preserving solution of subsurface flow and transport in porous media, Modified Newton-PSBTS method for solving complex nonlinear systems with symmetric Jacobian matrices, Multiscale modeling of polycrystalline materials with Jacobian-free multiscale method (JFMM), A semi-implicit meshless method for incompressible flows in complex geometries, Pseudospectral methods and iterative solvers for optimization problems from multiscale particle dynamics, Nonlinear \(p\)-multigrid preconditioner for implicit time integration of compressible Navier-Stokes equations with \(p\)-adaptive flux reconstruction, A minimum-type nonlinear complementarity simulator with constrained pressure residual (CPR) methods for wormhole propagation in carbonate acidization, Inexact Hessian-vector products in reduced-space differential-equation constrained optimization

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