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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Proceedings ArticleDOI
Pod-galerkin-reduced model predictive control for radiative drying of coatings
Xiaoqing Cao,Beshah Ayalew +1 more
TL;DR: In this article, a control scheme for infrared drying of waterborne coatings is outlined and demonstrated, which is described by a coupled system of a nonlinear partial differential equation for moisture content and an nonlinear ordinary differential equation (ODE) for coating temperature.
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A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection–Diffusion Equation
TL;DR: In this article , the authors proposed a new scheme for the fractional stochastic advection-diffusion equation (FSA-DE) in time where fractional term is expressed in Caputo sence of order.
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Parabolic inverse convection-diffusion-reaction problem solved using an adaptive parametrization
Giulia Deolmi,Fabio Marcuzzi +1 more
TL;DR: In this article, the authors investigated the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution.
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Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
TL;DR: In this article , a weakly symplectic deep convolutional autoencoder is proposed to approximate a nonlinear symplectic trial manifold, which is then used for model order teduction on manifolds.
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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