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
Space–time POD based computational vademecums for parametric studies: application to thermo-mechanical problems
TL;DR: This paper proposes a non-intrusive strategy for building computational vademecums dedicated to real-time simulations of nonlinear thermo-mechanical problems, and shows that the moving frame allows an optimal design of the RBs.
Journal ArticleDOI
A reduced-order Crank-Nicolson finite volume element formulation based on POD method for parabolic equations
Zhendong Luo,Hong Li,Ping Sun +2 more
TL;DR: It is shown that the reduced-order CNFVE formulation based on POD method is feasible and efficient for solving two-dimensional parabolic equations.
Journal ArticleDOI
Comparison of Model Order Reduction Methods for Optimal Sensor Placement for Thermo-Elastic Models
TL;DR: In this article, an optimal sensor placement problem for a thermo-elastic solid body model is considered, where temperature sensors are placed in a near-optimal way so that their measurements allow an accomodation in the body.
Journal ArticleDOI
Proper orthogonal decomposition and Monte Carlo based isogeometric stochastic method for material, geometric and force multi-dimensional uncertainties
TL;DR: A proper orthogonal decomposition (POD) and Monte Carlo simulation (MCS) based isogeometric stochastic method for multi-dimensional uncertainties and reduces the full order system whose DOFs is N to a much smaller DOF s.
Posted Content
Multivariate predictions of local reduced-order-model errors and dimensions
TL;DR: In this article, the authors employ Gaussian Processes and Artificial Neural Networks to construct approximations of these multivariate mappings, which are referred to as the MP-LROM models.
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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