The effect of Anderson acceleration on superlinear and sublinear convergence

LG Rebholz, M Xiao - Journal of Scientific Computing, 2023 - Springer
This paper considers the effect of Anderson acceleration (AA) on the convergence order of
nonlinear solvers in fixed point form xk+ 1= g (xk), that are looking for a fixed point x∗ of g …

Enabling convergence of the iterated penalty Picard iteration with O (1) penalty parameter for incompressible Navier–Stokes via Anderson acceleration

LG Rebholz, D Vargun, M Xiao - Computer Methods in Applied Mechanics …, 2021 - Elsevier
This paper considers an enhancement of the classical iterated penalty Picard (IPP) method
for the incompressible Navier–Stokes equations, where we restrict our attention to O (1) …

Efficient and effective algebraic splitting‐based solvers for nonlinear saddle point problems

J Liu, LG Rebholz, M Xiao - Mathematical Methods in the …, 2024 - Wiley Online Library
The incremental Picard Yosida (IPY) method has recently been developed as an iteration for
nonlinear saddle point problems that is as effective as Picard but more efficient. By …

Improved convergence of the Arrow–Hurwicz iteration for the Navier–Stokes equation via grad–div stabilization and Anderson acceleration

PG Geredeli, LG Rebholz, D Vargun… - Journal of Computational …, 2023 - Elsevier
We consider two modifications of the Arrow–Hurwicz (AH) iteration for solving the
incompressible steady Navier–Stokes equations for the purpose of accelerating the …

Anderson acceleration for nonlinear PDEs discretized by space–time spectral methods

S Nataj, Y He - Computers & Mathematics with Applications, 2024 - Elsevier
In this work, we consider Anderson acceleration for numerical solutions of nonlinear time
dependent partial differential equations discretized by space–time spectral methods, where …

[HTML][HTML] A highly accurate family of stable and convergent numerical solvers based on Daftardar–Gejji and Jafari decomposition technique for systems of nonlinear …

S Qureshi, IK Argyros, H Jafari, A Soomro, K Gdawiec - MethodsX, 2024 - Elsevier
This study introduces a family of root-solvers for systems of nonlinear equations, leveraging
the Daftardar–Gejji and Jafari Decomposition Technique coupled with the midpoint …

Anderson acceleration for a regularized Bingham model

S Pollock, LG Rebholz, D Vargun - Numerical Methods for …, 2023 - Wiley Online Library
This article studies a finite element discretization of the regularized Bingham equations that
describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then …

Anderson acceleration for degenerate and nondegenerate problems

S Pollock - Deterministic and Stochastic Optimal Control and …, 2021 - taylorfrancis.com
This chapter discusses the Anderson acceleration (AA) algorithm, and the basic
assumptions used in the theory, including the degeneracy and nondegeneracy conditions. It …

[PDF][PDF] Anderson acceleration of nonlinear solvers for the stationary Gross-Pitaevskii equation

D Forbes, L Rebholz - Advances in Applied Mathematics and Mechanics, 2021 - par.nsf.gov
We consider Anderson acceleration (AA) applied to two nonlinear solvers for the stationary
Gross-Pitaevskii equation: a Picard type nonlinear iterative solver and a normalized gradient …

Acceleration Methods for Nonlinear Solvers and Application to Fluid Flow Simulations

D Vargun - 2023 - search.proquest.com
This thesis studies nonlinear iterative solvers for the simulation of Newtonian and non-
Newtonian fluid models with two different approaches: Anderson acceleration (AA), an …