Hp Finite Elements For Pde Constrained Optimization
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Author | : Jan-Eric Wurst |
Publisher | : Wurzburg University Press |
Total Pages | : 190 |
Release | : 2015-12-10 |
Genre | : |
ISBN | : 9783958260245 |
Optimal control theory is a versatile mathematical discipline with applications in many fields. It has gained interest over the last decades mainly because increasing computational power allowed to tackle large and complex real life problems numerically. For offering reliable results, a thorough theoretical analysis of solution algorithms, their convergence properties, and approximation quality is inevitable. We follow this need and investigate linear quadratic optimal control problems with elliptic partial differential equations. The discretization with hp-finite elements is embedded in both Newton-type and interior point methods. Different efficient strategies are presented and accompanied by new results on regularity, approximation, and convergence theory.
Author | : Katharina Hofer |
Publisher | : |
Total Pages | : |
Release | : 2016 |
Genre | : |
ISBN | : |
Author | : Michael Hintermüller |
Publisher | : |
Total Pages | : |
Release | : 2010 |
Genre | : |
ISBN | : |
Author | : Harbir Antil |
Publisher | : Springer |
Total Pages | : 434 |
Release | : 2018-10-12 |
Genre | : Mathematics |
ISBN | : 1493986368 |
This volume provides a broad and uniform introduction of PDE-constrained optimization as well as to document a number of interesting and challenging applications. Many science and engineering applications necessitate the solution of optimization problems constrained by physical laws that are described by systems of partial differential equations (PDEs). As a result, PDE-constrained optimization problems arise in a variety of disciplines including geophysics, earth and climate science, material science, chemical and mechanical engineering, medical imaging and physics. This volume is divided into two parts. The first part provides a comprehensive treatment of PDE-constrained optimization including discussions of problems constrained by PDEs with uncertain inputs and problems constrained by variational inequalities. Special emphasis is placed on algorithm development and numerical computation. In addition, a comprehensive treatment of inverse problems arising in the oil and gas industry is provided. The second part of this volume focuses on the application of PDE-constrained optimization, including problems in optimal control, optimal design, and inverse problems, among other topics.
Author | : Jens M. Melenk |
Publisher | : Springer |
Total Pages | : 331 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 354045781X |
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Author | : Howard C. Elman |
Publisher | : |
Total Pages | : 479 |
Release | : 2014 |
Genre | : Finite element method |
ISBN | : 9780191780745 |
The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part covers the Poisson and the Stokes equations. For each PDE, there is a chapter concerned with finite element discretization and a companion chapter concerned with efficient iterative solution of the algebraic equations obtained from discretization. Chapter 5 describes the basics of PDE-constrained optimization. The second part of the book is a more advanced introduction to the numerical analysis of incompressible flows.
Author | : Zhangxin Chen |
Publisher | : Springer Science & Business Media |
Total Pages | : 415 |
Release | : 2005-10-14 |
Genre | : Science |
ISBN | : 3540280782 |
Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
Author | : Lorenz T. Biegler |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 364255508X |
Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.
Author | : Günter Leugering |
Publisher | : Springer |
Total Pages | : 539 |
Release | : 2014-12-22 |
Genre | : Mathematics |
ISBN | : 3319050834 |
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 | : C. Schwab |
Publisher | : Clarendon Press |
Total Pages | : 386 |
Release | : 1998-10-15 |
Genre | : Computers |
ISBN | : 9780198503903 |
The finite element method (FEM) is a numerical procedure for solving differential equations. Ever-increasing computing power means that engineers and applied mathematicians are seeking more complicated and sophisticated numerical methods to obtain progressively more accurate answers to problems in solid and fluid mechanics. The p- and hp- finite element methods are just such methods, and are therefore of great current interest. This book is the first to cover comprehensively the mathematical underpinnings of hp-FEM in one and two dimensions and pays particular attention to its applications in engineering.