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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Reduced-order model in structural dynamics for high-modal density in the LF range. Applications to automotive vehicle and fuel assemblies.
TL;DR: A new approach is proposed for constructing a reduced-order model adapted to low-frequency range for dynamical structures which are made up of a stiff master structure and several flexible substructures and two industrial applications are presented.
Computational Parabolic Inverse Problems
TL;DR: In this paper, a general approach to solve numerically parabolic inverse problems is presented, whose underlying mathematical model is discretized using the Finite Element method, based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problems of pollution rate estimation.
Book ChapterDOI
Reduced Order Model Closures: A Brief Tutorial
TL;DR: In this article , the authors present a brief tutorial on reduced order model (ROM) closures in under-resolved simulations, which is aimed at first year graduate students and advanced undergraduate students.
Posted Content
An intrinsic Proper Generalized Decomposition for parametric symmetric elliptic problems
TL;DR: This paper applies a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the on-line step, and proves that the partial sums converge to the continuous solutions, in mean quadratic elliptic norm.
Posted Content
A Certified Two-Step Port-Reduced Reduced-Basis Component Method for Wave Equation and Time Domain Elastodynamic PDE.
TL;DR: A certified two-step parameterized Model Order Reduction (pMOR) technique for wave equation and elastodynamic Partial Differential Equations (PDE) and an a posteriori error estimate for the two- step PR-RBC approach based on the time-frequency duality are provided.
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