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
Remarks on the efficiency of POD for model reduction in non-linear dynamics of continuous elastic systems
Rubens Sampaio,Christian Soize +1 more
TL;DR: In this paper, the efficiency of the reduced models constructed using the proper orthogonal decomposition (POD)-basis and the LIN-basis in non-linear dynamics for continuous elastic systems is analyzed.
Posted Content
An Ensemble-Proper Orthogonal Decomposition Method for the Nonstationary Navier-Stokes Equations
TL;DR: This work incorporates a proper orthogonal decomposition (POD) reduced-order model into the ensemble-based method for the efficient determination of the multiple solutions corresponding to many parameter sets of the time-dependent Navier-Stokes equations.
Journal ArticleDOI
Computation of POD basis functions for fluid flows with lanczos methods
TL;DR: The proper orthogonal decomposition (POD) approach allows us to construct low-order models for fluid flows by computed via a truncated singular value decomposition of the data matrix given by the snapshots.
Book ChapterDOI
Reduced Order Modelling Approaches to PDE-Constrained Optimization Based on Proper Orthogonal Decomposition
TL;DR: This paper discusses some relevant topics arising from the POD based reduced order modelling approach and suggests that specific modelling issues should be taken into account such that sufficiently accurate gradient information is obtained during the optimization process.
Dissertation
Dimension reduction for unsteady nonlinear partial differential equations via empirical interpolation methods
TL;DR: In this article, a Rice University thesis/dissertation was published as a paper entitled "Rice University thesis and dissertations" with the title: "RICE this article.
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.
Related Papers (5)
Galerkin Proper Orthogonal Decomposition Methods for a General Equation in Fluid Dynamics
Karl Kunisch,Stefan Volkwein +1 more