136 citations · 549 across the 44 of their papers we have counts for
46 papers
Continuous data assimilation in steady Navier-Stokes equations with unknown viscosity: robust and efficient solvers and fast parameter recovery
L. Rebholz, J. Reyes, J. Whitehead
Recent advances in equation discovery methods such as SINDy have highlighted the growing interest in identifying governing parameters and models directly from data. In this work, w…
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…
On a blended Anderson / NGMRES acceleration for the Navier-Stokes Picard iteration: convergence analysis and adaptive depth selection
Yunhui He, Leo Rebholz
Anderson acceleration (AA) and nonlinear GMRES (NGMRES) have been successfully applied to improve the efficiency and robustness of many nonlinear solvers, with each being shown to…
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…