5 citations · 11 across the 7 of their papers we have counts for
7 papers
NGMRES convergence analysis and proof of acceleration for contractive and noncontractive iterations
Y. He, L. Rebholz, M. Xiao
This paper gives the first convergence analysis and proof of acceleration for nonlinear GMRES (NGMRES) applied to contractive and noncontractive fixed point iterations (FPIs) for s…
Analysis of the Picard-Newton iteration for the Navier-Stokes equations: global stability and quadratic convergence
Sara Pollock, Leo Rebholz, Xuemin Tu +1
We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-Stokes equations that consists of first applying the Picard iteration and then applying t…
Superlinear convergence of Anderson accelerated Newton's method for solving stationary Navier-Stokes equations
Mengying Xiao
This paper studies the performance Newton's iteration applied with Anderson acceleration for solving the incompressible steady Navier-Stokes equations. We manifest that this method…
Enabling fast convergence of the iterated penalty Picard iteration with penalty parameter for incompressible Navier-Stokes via Anderson acceleration
Leo G. Rebholz, Duygu Vargun, Mengying Xiao
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 …
Acceleration of nonlinear solvers for natural convection problems
Sara Pollock, Leo G. Rebholz, Mengying Xiao
This paper develops an efficient and robust solution technique for the steady Boussinesq model of non-isothermal flow using Anderson acceleration applied to a Picard iteration. Aft…
Anderson-accelerated convergence of Picard iterations for incompressible Navier-Stokes equations
Sara Pollock, Leo G. Rebholz, Mengying Xiao
We propose, analyze and test Anderson-accelerated Picard iterations for solving the incompressible Navier-Stokes equations (NSE). Anderson acceleration has recently gained interest…
A proof that Anderson acceleration improves the convergence rate in linearly converging fixed point methods (but not in those converging quadratically)
Claire Evans, Sara Pollock, Leo G. Rebholz +1
This paper provides the first proof that Anderson acceleration (AA) improves the convergence rate of general fixed point iterations. AA has been used for decades to speed up nonlin…