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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Numerical Techniques for Optimization Problems with PDE Constraints
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The Reduced-Order Extrapolating Method about the Crank-Nicolson Finite Element Solution Coefficient Vectors for Parabolic Type Equation
TL;DR: In this paper, a reduced-order extrapolating technique about the unknown solution coefficient vectors in the Crank-Nicolson finite element (CNFE) method for the parabolic type partial differential equation (PDE) was derived.
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Commutation error in reduced order modeling of fluid flows
TL;DR: In this paper, the authors investigate whether the commutation error has a significant effect on ROM development for high viscosities, but not so much for low viscoities, when the CE is nonzero.
Posted Content
Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion Equations
Traian Iliescu,Zhu Wang +1 more
TL;DR: In this paper, a variational multiscale closure model was proposed for numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated convectiondiffusion equations.
Journal ArticleDOI
Reactor power distribution detection and estimation via a stabilized gappy proper orthogonal decomposition method
Helin Gong,Yingrui Yu,Qing Li +2 more
TL;DR: A stabilized gappy POD method is proposed within the data assimilation framework, which involves the preknowledge of the manifold structure of the physical states and the L-curve for setting regularization parameter, which is applied to simulate the power distribution during the control rods movement process for the HPR1000 reactor core.
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
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