Acceleration of nonlinear solvers for natural convection problems

DOI10.1515/jnma-2020-0067zbMath1495.65174arXiv2004.06471OpenAlexW3107641740MaRDI QIDQ2070271

Leo G. Rebholz, Mengying Xiao, Sara Pollock

Publication date: 24 January 2022

Published in: Journal of Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.06471

zbMATH Keywords

finite element methodBoussinesq equationsPicard iterationAnderson acceleration

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Numerical computation of solutions to systems of equations (65H10) Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Extrapolation to the limit, deferred corrections (65B05) Free convection (76R10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (4)

Anderson acceleration for a regularized Bingham model ⋮ Efficient and effective algebraic splitting‐based solvers for nonlinear saddle point problems ⋮ Enabling convergence of the iterated penalty Picard iteration with \(O ( 1 )\) penalty parameter for incompressible Navier-Stokes via Anderson acceleration ⋮ Improved convergence of the Arrow-Hurwicz iteration for the Navier-Stokes equation via grad-div stabilization and Anderson acceleration

Uses Software

• Anderson

Cites Work

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• A projection-based stabilized finite element method for steady-state natural convection problem
• Anderson acceleration and application to the three-temperature energy equations
• Benchmarking results for the Newton-Anderson method
• A stable finite element for the Stokes equations
• The rate of convergence of Newton's process
• A comparative study on methods for convergence acceleration of iterative vector sequences
• Finite Elements and Fast Iterative Solvers
• Two classes of multisecant methods for nonlinear acceleration
• Anderson Acceleration for Fixed-Point Iterations
• Numerical solution of saddle point problems
• A Family of $Q_{k+1,k}\timesQ_{k,k+1}$ Divergence-Free Finite Elements on Rectangular Grids
• Anderson-Accelerated Convergence of Picard Iterations for Incompressible Navier--Stokes Equations
• A new family of stable mixed finite elements for the 3D Stokes equations
• Anderson acceleration for contractive and noncontractive operators
• Exact smooth piecewise polynomial sequences on Alfeld splits
• A Proof That Anderson Acceleration Improves the Convergence Rate in Linearly Converging Fixed-Point Methods (But Not in Those Converging Quadratically)
• Numerical methods for nonlinear equations
• Convergence Analysis for Anderson Acceleration
• On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
• An Augmented Lagrangian‐Based Approach to the Oseen Problem
• The Mathematical Theory of Finite Element Methods
• Iterative Procedures for Nonlinear Integral Equations

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