Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems

DOI10.1016/j.jcp.2023.112548OpenAlexW4387747360MaRDI QIDQ6202131

Han Yu, Lulu Liu, Weiguo Gao, David E. Keyes

Publication date: 21 February 2024

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

Full work available at URL: https://doi.org/10.1016/j.jcp.2023.112548

zbMATH Keywords

Schwarz methodsnonlinear preconditioningNewton methods for nonlinear algebraic systems

Mathematics Subject Classification ID

Numerical linear algebra (65Fxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Nonlinear algebraic or transcendental equations (65Hxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-level nonlinear elimination based preconditioners for inexact Newton methods with application in shocked duct flow calculation
• Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media
• On the nonlinear domain decomposition method
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• A parallel adaptive nonlinear elimination preconditioned inexact Newton method for transonic full potential equation
• An adaptive nonlinear elimination preconditioned inexact Newton algorithm for highly local nonlinear multicomponent PDE systems
• Linear and nonlinear substructured restricted additive Schwarz iterations and preconditioning
• Sequential-implicit Newton method for multiphysics simulation
• A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis
• An explicit formulation of the multiplicative Schwarz preconditioner
• Composing Scalable Nonlinear Algebraic Solvers
• A Nonlinearly Preconditioned Inexact Newton Algorithm for Steady State Lattice Boltzmann Equations
• Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm
• Nonlinear Preconditioning: How to Use a Nonlinear Schwarz Method to Precondition Newton's Method
• Nonlinear FETI-DP and BDDC Methods
• An Optimal Block Iterative Method and Preconditioner for Banded Matrices with Applications to PDEs on Irregular Domains
• A User’s View of Solving Stiff Ordinary Differential Equations
• Inexact Newton Methods with Restricted Additive Schwarz Based Nonlinear Elimination for Problems with High Local Nonlinearity
• Anderson Acceleration for Fixed-Point Iterations
• Multiplicative Schwarz Algorithms for Some Nonsymmetric and Indefinite Problems
• Active-Set Reduced-Space Methods with Nonlinear Elimination for Two-Phase Flow Problems in Porous Media
• A steepest gradient method for optimum structural design
• Toward Extremely Scalable Nonlinear Domain Decomposition Methods for Elliptic Partial Differential Equations
• Parallel Multilevel Preconditioners
• A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
• Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• Globally Convergent Inexact Newton Methods
• Pseudotransient Continuation and Differential-Algebraic Equations
• Convergence Theory of Restricted Multiplicative Schwarz Methods
• A Note on Adaptive Nonlinear Preconditioning Techniques
• Nonlinearly Preconditioned Inexact Newton Algorithms
• Non‐linear additive Schwarz preconditioners and application in computational fluid dynamics
• Choosing the Forcing Terms in an Inexact Newton Method
• A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
• Approximate Error Bounds on Solutions of Nonlinearly Preconditioned PDEs
• A Nonlinear Elimination Preconditioned Inexact Newton Algorithm
• Additive and Hybrid Nonlinear Two-Level Schwarz Methods and Energy Minimizing Coarse Spaces for Unstructured Grids
• A Multilayer Nonlinear Elimination Preconditioned Inexact Newton Method for Steady-State Incompressible Flow Problems in Three Dimensions
• Nonlinear Preconditioning Strategies for Two-Phase Flows in Porous Media Discretized by a Fully Implicit Discontinuous Galerkin Method
• Field-Split Preconditioned Inexact Newton Algorithms
• Nonlinear Multiplicative Schwarz Preconditioning in Natural Convection Cavity Flow
• Newton additive and multiplicative Schwarz iterative methods
• On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method
• \(\text{PIN}^{\mathcal L}\)  : Preconditioned Inexact Newton with Learning Capability for Nonlinear System of Equations
• Asynchronous domain decomposition methods for nonlinear PDEs

This page was built for publication: Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems