Zobrazeno 1 - 10
of 362
pro vyhledávání: '"REBHOLZ, LEO G."'
This paper considers continuous data assimilation (CDA) in partial differential equation (PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove that long-time optimally accurate solutions are obtained for such paramet
Externí odkaz:
http://arxiv.org/abs/2408.00396
Autor:
Olshanskii, Maxim A., Rebholz, Leo G.
This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations. Additionally, it enhan
Externí odkaz:
http://arxiv.org/abs/2405.03796
The purpose of this paper is to develop a practical strategy to accelerate Newton's method in the vicinity of singular points. We present an adaptive safeguarding scheme with a tunable parameter, which we call adaptive gamma-safeguarding, that one ca
Externí odkaz:
http://arxiv.org/abs/2402.09295
Autor:
Olshanskii, Maxim A., Rebholz, Leo G.
Publikováno v:
Computer Methods in Applied Mechanics and Engineering 418 (2024): 116583
We consider local balances of momentum and angular momentum for the incompressible Navier-Stokes equations. First, we formulate new weak forms of the physical balances (conservation laws) of these quantities, and prove they are equivalent to the usua
Externí odkaz:
http://arxiv.org/abs/2309.05585
This paper considers improving the Picard and Newton iterative solvers for the Navier-Stokes equations in the setting where data measurements or solution observations are available. We construct adapted iterations that use continuous data assimilatio
Externí odkaz:
http://arxiv.org/abs/2306.01172
We study continuous data assimilation (CDA) applied to projection and penalty methods for the Navier-Stokes (NS) equations. Penalty and projection methods are more efficient than consistent NS discretizations, however are less accurate due to modelin
Externí odkaz:
http://arxiv.org/abs/2302.05962
Autor:
Pollock, Sara, Rebholz, Leo G.
This work introduces, analyzes and demonstrates an efficient and theoretically sound filtering strategy to ensure the condition of the least-squares problem solved at each iteration of Anderson acceleration. The filtering strategy consists of two ste
Externí odkaz:
http://arxiv.org/abs/2211.12953
We consider two modifications of the Arrow-Hurwicz (AH) iteration for solving the incompressible steady Navier-Stokes equations for the purpose of accelerating the algorithm: grad-div stabilization, and Anderson acceleration. AH is a classical iterat
Externí odkaz:
http://arxiv.org/abs/2203.01534
We investigate both theoretically and numerically the consistency between the nonlinear discretization in full order models (FOMs) and reduced order models (ROMs) for incompressible flows. To this end, we consider two cases: (i) FOM-ROM consistency,
Externí odkaz:
http://arxiv.org/abs/2111.06749
This paper studies a finite element discretization of the regularized Bingham equations that describe viscoplastic flow. An efficient nonlinear solver for the discrete model is then proposed and analyzed. The solver is based on Anderson acceleration
Externí odkaz:
http://arxiv.org/abs/2108.08945