Journal ArticleDOI
Galerkin proper orthogonal decomposition methods for parabolic problems
Karl Kunisch,Stefan Volkwein +1 more
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In this article, error bounds for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved and the resulting error bounds depend on the number of POD basis functions and on the time discretization.Abstract:
In this work error estimates for Galerkin proper orthogonal decomposition (POD) methods for linear and certain non-linear parabolic systems are proved. The resulting error bounds depend on the number of POD basis functions and on the time discretization. Numerical examples are included.read more
Citations
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Journal ArticleDOI
Application of local improvements to reduced-order models to sampling methods for nonlinear PDEs with noise
TL;DR: This work extends upon the results of Raissi and Seshaiyer (2014) and achieves local improvements to reduced-order models using sensitivity analysis of the proper orthogonal decomposition.
Proceedings ArticleDOI
Closed-loop tracking control of poloidal magnetic flux profile in tokamaks
TL;DR: This paper proposes a framework to solve a closed-loop, finite-time, optimal tracking control problem for the poloidal magnetic flux profile via diffusivity, interior, and boundary actuation through reduced order modeling via proper orthogonal decomposition (POD) and successive optimal control computation for a bilinear system.
Book ChapterDOI
Fully Adaptive and Integrated Numerical Methods for the Simulation and Control of Variable Density Multiphase Flows Governed by Diffuse Interface Models
TL;DR: A dual weighted residual concept for spatial mesh adaptivity which is based on the newly derived stationarity conditions is proposed which addresses future research directions, including closed-loop control concepts and model order reduction techniques for simulation and control of variable density multiphase flows.
Posted Content
An Analysis of Galerkin Proper Orthogonal Decomposition for Subdiffusion
Bangti Jin,Zhi Zhou +1 more
TL;DR: In this paper, a Galerkin-L1-POD scheme for the subdiffusion model with a Caputo fractional derivative of order α in (0, 1)$ in time was developed.
Posted Content
A nudged hybrid analysis and modeling approach for realtime wake-vortex transport and decay prediction
TL;DR: In this article, a long short-term memory (LSTM) nudging framework was proposed for the enhancement of reduced order models of fluid flows utilizing noisy measurements for air traffic improvements.
References
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Book
Infinite-Dimensional Dynamical Systems in Mechanics and Physics
TL;DR: In this article, the authors give bounds on the number of degrees of freedom and the dimension of attractors of some physical systems, including inertial manifolds and slow manifolds.
Book
Turbulence, Coherent Structures, Dynamical Systems and Symmetry
TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Book
Galerkin Finite Element Methods for Parabolic Problems
TL;DR: The standard Galerkin method is based on more general approximations of the elliptic problem as discussed by the authors, and is used to solve problems in algebraic systems at the time level.
Journal ArticleDOI
Control of the Burgers equation by a reduced-order approach using proper orthogonal decomposition
Karl Kunisch,Stefan Volkwein +1 more
TL;DR: POD is utilized to solve open-loop and closed-loop optimal control problems for the Burgers equation to comparison of POD-based algorithms with numerical results obtained from finite-element discretization of the optimality system.
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Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
Karl Kunisch,Stefan Volkwein +1 more