From the 1 of 11 linked papers with an AI index.
11 papers
NGMRES convergence analysis and proof of acceleration for contractive and noncontractive iterations
Y. He, L. Rebholz, M. Xiao
The paper provides the first theoretical convergence analysis of nonlinear GMRES (NGMRES) for both contractive and noncontractive fixed‑point iterations, identifying the ratio‑gain…
A modified Anderson acceleration with sharp linear convergence rate predictions and application to incompressible flows
Yunhui He, Leo Rebholz
In this work, we extend a modified Anderson acceleration proposed in [Y. He, arXiv:2603.25983, 2026] to accelerate the Picard iteration for the Navier-Stokes equations. In this var…
Convergence analysis and proof of acceleration for NGMRES applied to the Picard iteration for Navier-Stokes equations
Yunhui He, Leo G Rebholz
We consider nonlinear GMRES (NGMRES) as an acceleration technique for the Navier-Stokes Picard iteration, a direction that has not previously been explored. We identify the optimal…
Continuous-data-assimilation-enabled fast and robust convergence of an Uzawa-based solver for Navier-Stokes equations with large Reynolds number
Victoria Luongo Fisher, Jessica C. Franklin, Leo G. Rebholz
This paper shows how continuous data assimilation (CDA) can be used to provably enable and accelerate convergence of a (efficient at each iteration due to a physics-splitting, but…
An efficient splitting iteration for a CDA-accelerated solver for incompressible flow problems
Victoria L. Fisher, Leo G. Rebholz, Duygu Vargun
We propose, analyze, and test an efficient splitting iteration for solving the incompressible, steady Navier-Stokes equations in the setting where partial solution data is known. T…
Benchmark stress tests for flow past a cylinder at higher Reynolds numbers using EMAC
Henry von Wahl, Leo G. Rebholz, L. Ridgway Scott
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder at Reynolds numbers 500 and 1000, where the solution is observed to be periodic when the pr…