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
A posteriori error estimation for nonlinear parabolic boundary control
Eileen Kammann,Fredi Tröltzsch +1 more
TL;DR: This work applies the technique of error estimation for the optimal control of nonlinear parabolic partial differential equations to a model reduced optimal control problem obtained by proper orthogonal decomposition (POD).
Journal ArticleDOI
HJB-POD feeback control of advection-diffusion equation with a model predictive control snapshot sampling
Alessandro Alla,Michael Hinze +1 more
TL;DR: In this article, the authors presented an approximation of an infinite horizon optimal control problem for evolutive advection-diffusion equations based on a model reduction technique, using a Proper Orthogonal Decomposition (POD) approximation, coupled with a Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function of the corresponding control problem.
Journal ArticleDOI
Radiation, Frequency Averaging and Proper Orthogonal Decomposition
René Pinnau,Alexander Schulze +1 more
TL;DR: The method of snapshots is employed to devise an automated a posteriori algorithm, which helps to reduce significantly the dimensionality for further simulations in proper orthogonal decomposition for frequency averaging in radiative heat transfer.
Journal ArticleDOI
A Broadband Enhanced Nodal-Order Reduction Methodology for Large-Scale Equation Sets of 3-D Transient Field Problems
TL;DR: In this article, a broadband enhanced nodal-order reduction (ENOR) methodology is proposed to reduce the order of equation sets of 3-D transient field problems, which is validated by using the numerical results on a thermal problem of a classic 7-layer insulated-gate bipolar transistor (IGBT) module in terms of computation times and accuracies.
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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