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
A POD-based reduced-order FD extrapolating algorithm for traffic flow
Zhendong Luo,Di Xie,Fei Teng +2 more
TL;DR: In this article, a traffic flow Lighthill, Whitham, and Richards (LWR) model is studied by means of a proper orthogonal decomposition (POD) technique.
Journal ArticleDOI
Adaptive POD model reduction for solute transport in heterogeneous porous media
TL;DR: It is found that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing Pe, which suggests that the effects of local-scale dispersive processes facilitate the P OD method to capture the salient features of the system dynamics embedded in the selected snapshots.
Proceedings ArticleDOI
Nonlinear model order reduction of Burgers' Equation using proper orthogonal decomposition
TL;DR: The proper orthogonal decomposition (POD) method is employed here that provides a reliable and accurate modeling approach, while the temporal discretization of the continuous error function leads to a more accurate estimation of the defined cost function.
Journal ArticleDOI
Long-time Reynolds averaging of reduced order models for fluid flows: Preliminary results
Luigi C. Berselli,Traian Iliescu,Birgul Koc,Roger Lewandowski,Roger Lewandowski,Roger Lewandowski +5 more
TL;DR: In this paper, GNAMPA of INdAM, University of Pisa, Italy, and National Science Foundation (NSF) proposed a method to solve the problem of genetic sequencing.
Journal ArticleDOI
A reduced-order DG formulation based on POD method for the time-domain Maxwell’s equations in dispersive media
TL;DR: A POD–DGTD formulation with lower dimension and sufficiently high accuracy is established, together with the description of the POD reduced-order basis, its construction from a snapshot set, and its application to the solution of the time-domain Maxwell’s equations.
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