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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Relative impact of advective and dispersive processes on the eciency of POD-based model reduction for solute transport in porous media
TL;DR: The applicability of a model order reduction technique to the cost-eective solution of transport of passive scalars in porous media and the way the selection of these time scales is linked to the Proper Orthogonal Decomposition (POD) is explored.
Optimality conditions and POD a-posteriori error estimates for a semilinear parabolic optimal control
TL;DR: An optimal control problem for a parametrized nonlinear parabolic differential equation, which is motivated by lithium-ion battery models, is considered, and a reduced-order modelling based on proper orthogonal decomposition (POD) is applied.
An Operator Inference Oriented Approach for Mechanical Systems
TL;DR: This work presents an extension of operator inference for mechanical systems, preserving the second-order structure, and focuses on a recent data-driven methodology, namely operator inference, that aims at inferring the reduced operators using only trajectories of high-fidelity models.
Journal ArticleDOI
Simulation of the interaction of light with 3‐D metallic nanostructures using a proper orthogonal decomposition‐Galerkin reduced‐order discontinuous Galerkin time‐domain method
Kun Li,Lin Li,Stéphane Lanteri +2 more
TL;DR: In this paper , a reduced-order model based on the proper orthogonal decomposition (POD) technique for the system of 3D time-domain Maxwell's equations coupled to a Drude dispersion model is employed to describe the interaction of light with nanometer scale metallic structures.
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Calibrated Filtered Reduced Order Modeling
TL;DR: In this paper, a calibrated filtered reduced order model (CF-ROM) framework is proposed for numerical simulation of general nonlinear PDEs that are amenable to reduced order modeling.
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