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 Article
Mortar Finite Elements for Coupling Compressible and Nearly Incompressible Materials in Elasticity
TL;DR: This work considers the coupling of compressible and nearly incompressible materials within the framework of mortar methods, and a priori error analysis is carried out for the coupled problem, and several numerical examples are presented.
Journal ArticleDOI
Reduced-Order Modelling for the Allen-Cahn Equation Based on Scalar Auxiliary Variable Approaches
TL;DR: Numerical experiments show that the computational efficiency is significantly enhanced as compared to directly solving the full order system and the discretized Allen-Cahn system resulting from the POD-DEIM method inherits this favorable property by using the scalar auxiliary variable approach.
Proceedings ArticleDOI
POD-based optimal control of current profile in tokamak plasmas via nonlinear programming
Chao Xu,J. Dalessio,Yongsheng Ou,Eugenio Schuster,T.C. Luce,J.R. Ferron,M.L. Walker,D.A. Humphreys +7 more
TL;DR: To solve this constrained finite-time open-loop optimal control problem, model reduction based on proper orthogonal decomposition (POD) is combined with sequential quadratic programming (SQP) in an iterative fashion to reduce the computational effort and therefore the time required to solve the optimization problem.
Journal ArticleDOI
Error analysis of proper orthogonal decomposition data assimilation schemes with grad-div stabilization for the Navier-Stokes equations
TL;DR: In this paper , the error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out.
Proceedings ArticleDOI
Combined rotation profile and plasma stored energy control for the DIII-D tokamak via MPC
TL;DR: A feedback controller is designed in a model predictive control framework to regulate the rotation profile while satisfying constraints associated with the desired plasma stored energy and β (kinetic to magnetic pressure ratio) limits.
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