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Adaptive Discontinuous Galerkin Methods For State Constrained Optimal Control Problems Governed By Convection Diffusion Equations
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Book Synopsis Adaptive Discontinuous Galerkin Methods for State Constrained Optimal Control Problems Governed by Convection Diffusion Equations by : Hamdullah Yücel
Download or read book Adaptive Discontinuous Galerkin Methods for State Constrained Optimal Control Problems Governed by Convection Diffusion Equations written by Hamdullah Yücel and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicators for each regularization technique due to the regularity issues. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented to illustrate the effectiveness of the adaptivity for both regularization techniques.
Book Synopsis Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-diffusion Equations by : Hamdullah Yücel
Download or read book Adaptive Discontinuous Galerkin Approximation of Optimal Control Problems Governed by Transient Convection-diffusion Equations written by Hamdullah Yücel and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: In this paper, we investigate an a posteriori error estimate of a control constrained optimal control problem governed by a time-dependent convection diffusion equation. Control constraints are handled by using the primal-dual active set algorithm as a semi-smooth Newton method or by adding a Moreau-Yosida-type penalty function to the cost functional. An adaptive mesh refinement indicated by a posteriori error estimates is applied for both approaches. A symmetric interior penalty Galerkin method in space and a backward Euler in time are applied in order to discretize the optimization problem. Numerical results are presented, which illustrate the performance of the proposed error estimator.
Book Synopsis Numerical Mathematics and Advanced Applications - ENUMATH 2013 by : Assyr Abdulle
Download or read book Numerical Mathematics and Advanced Applications - ENUMATH 2013 written by Assyr Abdulle and published by Springer. This book was released on 2014-11-25 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale methods, numerical linear algebra and discretization techniques for fluid mechanics and optics are presented. As such, the book offers a valuable resource for a wide range of readers looking for a state-of-the-art overview of advanced techniques, algorithms and results in numerical mathematics and scientific computing.
Book Synopsis Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows by : Murat Uzunca
Download or read book Adaptive Discontinuous Galerkin Methods for Non-linear Reactive Flows written by Murat Uzunca and published by Birkhäuser. This book was released on 2016-05-17 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this monograph is the development of space-time adaptive methods to solve the convection/reaction dominated non-stationary semi-linear advection diffusion reaction (ADR) equations with internal/boundary layers in an accurate and efficient way. After introducing the ADR equations and discontinuous Galerkin discretization, robust residual-based a posteriori error estimators in space and time are derived. The elliptic reconstruction technique is then utilized to derive the a posteriori error bounds for the fully discrete system and to obtain optimal orders of convergence.As coupled surface and subsurface flow over large space and time scales is described by (ADR) equation the methods described in this book are of high importance in many areas of Geosciences including oil and gas recovery, groundwater contamination and sustainable use of groundwater resources, storing greenhouse gases or radioactive waste in the subsurface.
Book Synopsis Discontinuous Galerkin Method by : Vít Dolejší
Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2015-07-17 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Book Synopsis Optimal Control of Nonsmooth Distributed Parameter Systems by : Dan Tiba
Download or read book Optimal Control of Nonsmooth Distributed Parameter Systems written by Dan Tiba and published by Springer. This book was released on 2006-11-14 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to the study of distributed control problems governed by various nonsmooth state systems. The main questions investigated include: existence of optimal pairs, first order optimality conditions, state-constrained systems, approximation and discretization, bang-bang and regularity properties for optimal control. In order to give the reader a better overview of the domain, several sections deal with topics that do not enter directly into the announced subject: boundary control, delay differential equations. In a subject still actively developing, the methods can be more important than the results and these include: adapted penalization techniques, the singular control systems approach, the variational inequality method, the Ekeland variational principle. Some prerequisites relating to convex analysis, nonlinear operators and partial differential equations are collected in the first chapter or are supplied appropriately in the text. The monograph is intended for graduate students and for researchers interested in this area of mathematics.
Book Synopsis Optimal Control of Systems Governed by Partial Differential Equations by : Jacques Louis Lions
Download or read book Optimal Control of Systems Governed by Partial Differential Equations written by Jacques Louis Lions and published by Springer. This book was released on 2011-11-12 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. The development of a theory of optimal control (deterministic) requires the following initial data: (i) a control u belonging to some set ilIi ad (the set of 'admissible controls') which is at our disposition, (ii) for a given control u, the state y(u) of the system which is to be controlled is given by the solution of an equation (*) Ay(u)=given function ofu where A is an operator (assumed known) which specifies the system to be controlled (A is the 'model' of the system), (iii) the observation z(u) which is a function of y(u) (assumed to be known exactly; we consider only deterministic problems in this book), (iv) the "cost function" J(u) ("economic function") which is defined in terms of a numerical function z-+
Book Synopsis Adaptive Numerical Solution of State Constrained Optimal Control Problems by : Olaf Benedix
Download or read book Adaptive Numerical Solution of State Constrained Optimal Control Problems written by Olaf Benedix and published by . This book was released on 2011 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Discontinuous Galerkin Methods by : Bernardo Cockburn
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Author :University of Minnesota. Institute for Mathematics and Its Applications Publisher : ISBN 13 : Total Pages : pages Book Rating :4.:/5 (123 download)
Book Synopsis Maximum Principle for State-constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations by : University of Minnesota. Institute for Mathematics and Its Applications
Download or read book Maximum Principle for State-constrained Optimal Control Problems Governed by Quasilinear Elliptic Equations written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1992 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni
Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
Book Synopsis Optimality Conditions for Convex State by : Anton Schiela
Download or read book Optimality Conditions for Convex State written by Anton Schiela and published by . This book was released on 2007 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Optimization with PDE Constraints by : Michael Hinze
Download or read book Optimization with PDE Constraints written by Michael Hinze and published by Springer Science & Business Media. This book was released on 2008-10-16 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving optimization problems subject to constraints given in terms of partial d- ferential equations (PDEs) with additional constraints on the controls and/or states is one of the most challenging problems in the context of industrial, medical and economical applications, where the transition from model-based numerical si- lations to model-based design and optimal control is crucial. For the treatment of such optimization problems the interaction of optimization techniques and num- ical simulation plays a central role. After proper discretization, the number of op- 3 10 timization variables varies between 10 and 10 . It is only very recently that the enormous advances in computing power have made it possible to attack problems of this size. However, in order to accomplish this task it is crucial to utilize and f- ther explore the speci?c mathematical structure of optimization problems with PDE constraints, and to develop new mathematical approaches concerning mathematical analysis, structure exploiting algorithms, and discretization, with a special focus on prototype applications. The present book provides a modern introduction to the rapidly developing ma- ematical ?eld of optimization with PDE constraints. The ?rst chapter introduces to the analytical background and optimality theory for optimization problems with PDEs. Optimization problems with PDE-constraints are posed in in?nite dim- sional spaces. Therefore, functional analytic techniques, function space theory, as well as existence- and uniqueness results for the underlying PDE are essential to study the existence of optimal solutions and to derive optimality conditions.
Book Synopsis Optimal Control of Partial Differential Equations by : Fredi Tröltzsch
Download or read book Optimal Control of Partial Differential Equations written by Fredi Tröltzsch and published by American Mathematical Society. This book was released on 2024-03-21 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tröltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization.
Book Synopsis On the Solution of Optimal Control Problems with State Variable Inequality Constraints by : William Eugene Hamilton
Download or read book On the Solution of Optimal Control Problems with State Variable Inequality Constraints written by William Eugene Hamilton and published by . This book was released on 1970 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report deals with theoretical and computational aspects or optimal control problems with state variable inequality constraints. The computational methods developed here solve bounded state variable problems by searching the constraint surface (or boundary) for the optimal junction point between the subarc on the boundary and the unconstrained subarc. The results obtained for the bounded state variables problem are extended to problems with discontinuous state variable and/or discontinuous differential equations. (Author).
Book Synopsis Multiple Shooting and Time Domain Decomposition Methods by : Thomas Carraro
Download or read book Multiple Shooting and Time Domain Decomposition Methods written by Thomas Carraro and published by Springer. This book was released on 2015-10-26 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive collection of the most advanced numerical techniques for the efficient and effective solution of simulation and optimization problems governed by systems of time-dependent differential equations. The contributions present various approaches to time domain decomposition, focusing on multiple shooting and parareal algorithms. The range of topics covers theoretical analysis of the methods, as well as their algorithmic formulation and guidelines for practical implementation. Selected examples show that the discussed approaches are mandatory for the solution of challenging practical problems. The practicability and efficiency of the presented methods is illustrated by several case studies from fluid dynamics, data compression, image processing and computational biology, giving rise to possible new research topics. This volume, resulting from the workshop Multiple Shooting and Time Domain Decomposition Methods, held in Heidelberg in May 2013, will be of great interest to applied mathematicians, computer scientists and all scientists using mathematical methods.
Book Synopsis Error Control, Adaptive Discretizations, and Applications, Part 1 by :
Download or read book Error Control, Adaptive Discretizations, and Applications, Part 1 written by and published by Elsevier. This book was released on 2024-06-21 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: Error Control, Adaptive Discretizations, and Applications, Volume 58, Part One highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Chapters in this release cover hp adaptive Discontinuous Galerkin strategies driven by a posteriori error estimation with application to aeronautical flow problems, An anisotropic mesh adaptation method based on gradient recovery and optimal shape elements, and Model reduction techniques for parametrized nonlinear partial differential equations.
