Convergence Analysis for the Multiplicative Schwarz Preconditioned Inexact Newton Algorithm

DOI10.1137/15M1028182zbMath1352.65142OpenAlexW2540191835MaRDI QIDQ2829438

Lulu Liu, David E. Keyes

Publication date: 28 October 2016

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1028182

zbMATH Keywords

algorithmsystemnonlinear equationslocal convergencenonlinear preconditioningmultiplicative Schwarz

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Preconditioners for iterative methods (65F08)

Related Items (10)

A Nonlinear Elimination Preconditioned Inexact Newton Algorithm ⋮ An adaptive nonlinear elimination preconditioned inexact Newton algorithm for highly local nonlinear multicomponent PDE systems ⋮ \(\text{PIN}^{\mathcal L}\)  : Preconditioned Inexact Newton with Learning Capability for Nonlinear System of Equations ⋮ Nonlinearly Constrained Pressure Residual (NCPR) Algorithms for Fractured Reservoir Simulation ⋮ Overlapping multiplicative Schwarz preconditioning for linear and nonlinear systems ⋮ A nonlinear elimination preconditioned inexact Newton method for blood flow problems in human artery with stenosis ⋮ 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 ⋮ Nonlinear Preconditioning Strategies for Two-Phase Flows in Porous Media Discretized by a Fully Implicit Discontinuous Galerkin Method ⋮ Approximate Error Bounds on Solutions of Nonlinearly Preconditioned PDEs

Uses Software

• NITSOL

Cites Work

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• On the nonlinear domain decomposition method
• Jacobian-free Newton-Krylov methods: a survey of approaches and applications.
• A parallel nonlinear additive Schwarz preconditioned inexact Newton algorithm for incompressible Navier-Stokes equations
• A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Globally Convergent Inexact Newton Methods
• NITSOL: A Newton Iterative Solver for Nonlinear Systems
• 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
• Iterative Solution of Nonlinear Equations in Several Variables
• Field-Split Preconditioned Inexact Newton Algorithms
• On Convergence of the Additive Schwarz Preconditioned Inexact Newton Method

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