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Author :
Publisher :
ISBN 13 :
Total Pages : 29 pages
Book Rating : 4.:/5 (924 download)
Download or read book Reliable a posteriori error estimation for state-constrained optimal control written by and published by . This book was released on 2015 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints written by and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the development, analysis, and implementation of an adaptive finite element method for distributed elliptic optimal control problems with pointwise unilateral constraints on the state. In particular, two residual-type a posteriori error estimators will be derived. The first one takes advantage of the modified adjoint state, which is defined as some kind of regularization of the adjoint state. Furthermore, this error estimator will, after minor modification, be transfered to the Lavrentiev regularization of the pure state constrained case. Up to a consistency error and data oscillation, reliability and efficiency results concerning the approximation of the state, the control, and the modified adjoint state can be provided for these error estimators. With two numerical examples, the performance of the adaptive algorithm will be investigated. A benefit compared to an uniform refinement strategy will be noticeable. The second developed a posteriori error estimator results from a measure extension of the discrete measure appearing in the right-hand side of the adjoint state equation to an element in the space of square integrable functions. This error estimator provides, again up to a consistency error and data oscillation, reliability and efficiency for the approximation error in the control, in the state, and in a semi-continuous auxiliary adjoint state. Another numerical example will show that this error estimator might be advantageous.
Author : Martin Gubisch
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (989 download)
Download or read book A-posteriori Error Estimation of Discrete POD Models for PDE-constrained Optimal Control written by Martin Gubisch and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Peter Benner
Publisher : Springer
ISBN 13 : 3319587862
Total Pages : 503 pages
Book Rating : 4.3/5 (195 download)
Download or read book Model Reduction of Parametrized Systems written by Peter Benner and published by Springer. This book was released on 2017-09-05 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: The special volume offers a global guide to new concepts and approaches concerning the following topics: reduced basis methods, proper orthogonal decomposition, proper generalized decomposition, approximation theory related to model reduction, learning theory and compressed sensing, stochastic and high-dimensional problems, system-theoretic methods, nonlinear model reduction, reduction of coupled problems/multiphysics, optimization and optimal control, state estimation and control, reduced order models and domain decomposition methods, Krylov-subspace and interpolatory methods, and applications to real industrial and complex problems. The book represents the state of the art in the development of reduced order methods. It contains contributions from internationally respected experts, guaranteeing a wide range of expertise and topics. Further, it reflects an important effor t, carried out over the last 12 years, to build a growing research community in this field. Though not a textbook, some of the chapters can be used as reference materials or lecture notes for classes and tutorials (doctoral schools, master classes).
Author : Michael Kieweg
Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.:/5 (314 download)
Download or read book An a Posteriori Error Analysis for Distributed Elliptic Optimal Control Problems with Pointwise State Constraints written by Michael Kieweg and published by . This book was released on 2007 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Günter Leugering
Publisher : Springer Science & Business Media
ISBN 13 : 3034801335
Total Pages : 622 pages
Book Rating : 4.0/5 (348 download)
Download or read book Constrained Optimization and Optimal Control for Partial Differential Equations written by Günter Leugering and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This special volume focuses on optimization and control of processes governed by partial differential equations. The contributors are mostly participants of the DFG-priority program 1253: Optimization with PDE-constraints which is active since 2006. The book is organized in sections which cover almost the entire spectrum of modern research in this emerging field. Indeed, even though the field of optimal control and optimization for PDE-constrained problems has undergone a dramatic increase of interest during the last four decades, a full theory for nonlinear problems is still lacking. The contributions of this volume, some of which have the character of survey articles, therefore, aim at creating and developing further new ideas for optimization, control and corresponding numerical simulations of systems of possibly coupled nonlinear partial differential equations. The research conducted within this unique network of groups in more than fifteen German universities focuses on novel methods of optimization, control and identification for problems in infinite-dimensional spaces, shape and topology problems, model reduction and adaptivity, discretization concepts and important applications. Besides the theoretical interest, the most prominent question is about the effectiveness of model-based numerical optimization methods for PDEs versus a black-box approach that uses existing codes, often heuristic-based, for optimization.
Author : Kristina Kohls
Publisher :
ISBN 13 :
Total Pages : 13 pages
Book Rating : 4.:/5 (65 download)
Download or read book A Posteriori Error Estimators for Control Constrained Optimal Control Problems written by Kristina Kohls and published by . This book was released on 2010 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Elsevier
ISBN 13 : 0323853390
Total Pages : 596 pages
Book Rating : 4.3/5 (238 download)
Download or read book Numerical Control: Part A written by and published by Elsevier. This book was released on 2022-02-15 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Control: Part A, Volume 23 in the Handbook of Numerical Analysis series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this volume include Numerics for finite-dimensional control systems, Moments and convex optimization for analysis and control of nonlinear PDEs, The turnpike property in optimal control, Structure-Preserving Numerical Schemes for Hamiltonian Dynamics, Optimal Control of PDEs and FE-Approximation, Filtration techniques for the uniform controllability of semi-discrete hyperbolic equations, Numerical controllability properties of fractional partial differential equations, Optimal Control, Numerics, and Applications of Fractional PDEs, and much more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Numerical Analysis series Updated release includes the latest information on Numerical Control
Author : W. Fitzgibbon
Publisher : Springer Science & Business Media
ISBN 13 : 9048132398
Total Pages : 252 pages
Book Rating : 4.0/5 (481 download)
Download or read book Applied and Numerical Partial Differential Equations written by W. Fitzgibbon and published by Springer Science & Business Media. This book was released on 2010-01-08 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.
Author : Kristian Bredies
Publisher : Springer Science & Business Media
ISBN 13 : 3034806310
Total Pages : 221 pages
Book Rating : 4.0/5 (348 download)
Download or read book Control and Optimization with PDE Constraints written by Kristian Bredies and published by Springer Science & Business Media. This book was released on 2013-06-12 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical models of physical, biological and social systems involve partial differential equations (PDEs). The desire to understand and influence these systems naturally leads to considering problems of control and optimization. This book presents important topics in the areas of control of PDEs and of PDE-constrained optimization, covering the full spectrum from analysis to numerical realization and applications. Leading scientists address current topics such as non-smooth optimization, Hamilton–Jacobi–Bellmann equations, issues in optimization and control of stochastic partial differential equations, reduced-order models and domain decomposition, discretization error estimates for optimal control problems, and control of quantum-dynamical systems. These contributions originate from the “International Workshop on Control and Optimization of PDEs” in Mariatrost in October 2011. This book is an excellent resource for students and researchers in control or optimization of differential equations. Readers interested in theory or in numerical algorithms will find this book equally useful.
Author : Günter Leugering
Publisher : Springer
ISBN 13 : 3319050834
Total Pages : 539 pages
Book Rating : 4.3/5 (19 download)
Download or read book Trends in PDE Constrained Optimization written by Günter Leugering and published by Springer. This book was released on 2014-12-22 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of research was studied and further explored as part of the Deutsche Forschungsgemeinschaft (DFG) priority program 1253 on “Optimization with Partial Differential Equations” from 2006 to 2013. The investigations were motivated by the fascinating potential applications and challenging mathematical problems that arise in the field of PDE constrained optimization. New analytic and algorithmic paradigms have been developed, implemented and validated in the context of real-world applications. In this special volume, contributions from more than fifteen German universities combine the results of this interdisciplinary program with a focus on applied mathematics. The book is divided into five sections on “Constrained Optimization, Identification and Control”, “Shape and Topology Optimization”, “Adaptivity and Model Reduction”, “Discretization: Concepts and Analysis” and “Applications”. Peer-reviewed research articles present the most recent results in the field of PDE constrained optimization and control problems. Informative survey articles give an overview of topics that set sustainable trends for future research. This makes this special volume interesting not only for mathematicians, but also for engineers and for natural and medical scientists working on processes that can be modeled by PDEs.
Author : Samarjit Kar
Publisher : Springer
ISBN 13 : 9811078149
Total Pages : 399 pages
Book Rating : 4.8/5 (11 download)
Download or read book Operations Research and Optimization written by Samarjit Kar and published by Springer. This book was released on 2018-04-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses recent developments in the vast domain of optimization. Featuring papers presented at the 1st International Conference on Frontiers in Optimization: Theory and Applications (FOTA 2016), held at the Heritage Institute of Technology, Kolkata, on 24–26 December 2016, it opens new avenues of research in all topics related to optimization, such as linear and nonlinear optimization; combinatorial-, stochastic-, dynamic-, fuzzy-, and uncertain optimization; optimal control theory; as well as multi-objective, evolutionary and convex optimization and their applications in intelligent information and technology, systems science, knowledge management, information and communication, supply chain and inventory control, scheduling, networks, transportation and logistics and finance. The book is a valuable resource for researchers, scientists and engineers from both academia and industry.
Author : Alina Studinger
Publisher :
ISBN 13 :
Total Pages : 21 pages
Book Rating : 4.:/5 (985 download)
Download or read book Numerical Analysis of POD A-Posteriori Error Estimation for Optimal Control written by Alina Studinger and published by . This book was released on 2012 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Miloš Tepavčević
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (122 download)
Download or read book Discretization Error Estimates for State Constrained Optimal Control Problems written by Miloš Tepavčević and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Dieter Bothe
Publisher : Birkhäuser
ISBN 13 : 3319566024
Total Pages : 677 pages
Book Rating : 4.3/5 (195 download)
Download or read book Transport Processes at Fluidic Interfaces written by Dieter Bothe and published by Birkhäuser. This book was released on 2017-07-13 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several physico-chemical processes that determine the behavior of multiphase fluid systems – e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface – and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models, which especially account for the local processes at the interface. This book presents recent findings on the rigorous derivation and mathematical analysis of such models and on the development of numerical methods for direct numerical simulations. Validation results are based on specifically designed experiments using high-resolution experimental techniques. A special feature of this book is its focus on an interdisciplinary research approach combining Applied Analysis, Numerical Mathematics, Interface Physics and Chemistry, as well as relevant research areas in the Engineering Sciences. The contributions originated from the joint interdisciplinary research projects in the DFG Priority Programme SPP 1506 “Transport Processes at Fluidic Interfaces.”
Author : René Schneider
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (13 download)
Download or read book A-posteriori Error Estimation for Control-contrained, Linear-quadratic Optimal Control Problems written by René Schneider and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jan S Hesthaven
Publisher : Springer
ISBN 13 : 3319224700
Total Pages : 139 pages
Book Rating : 4.3/5 (192 download)
Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
