Trends in PDE Constrained Optimization

Trends in PDE Constrained Optimization
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.

New Trends in Shape Optimization

New Trends in Shape Optimization
Author: Aldo Pratelli
Publisher: Birkhäuser
Total Pages: 312
Release: 2015-12-01
Genre: Mathematics
ISBN: 3319175637

This volume reflects “New Trends in Shape Optimization” and is based on a workshop of the same name organized at the Friedrich-Alexander University Erlangen-Nürnberg in September 2013. During the workshop senior mathematicians and young scientists alike presented their latest findings. The format of the meeting allowed fruitful discussions on challenging open problems, and triggered a number of new and spontaneous collaborations. As such, the idea was born to produce this book, each chapter of which was written by a workshop participant, often with a collaborator. The content of the individual chapters ranges from survey papers to original articles; some focus on the topics discussed at the Workshop, while others involve arguments outside its scope but which are no less relevant for the field today. As such, the book offers readers a balanced introduction to the emerging field of shape optimization.

Optimization and Control for Partial Differential Equations

Optimization and Control for Partial Differential Equations
Author: Roland Herzog
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 386
Release: 2022-03-07
Genre: Mathematics
ISBN: 3110696002

This book highlights new developments in the wide and growing field of partial differential equations (PDE)-constrained optimization. Optimization problems where the dynamics evolve according to a system of PDEs arise in science, engineering, and economic applications and they can take the form of inverse problems, optimal control problems or optimal design problems. This book covers new theoretical, computational as well as implementation aspects for PDE-constrained optimization problems under uncertainty, in shape optimization, and in feedback control, and it illustrates the new developments on representative problems from a variety of applications.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018
Author: Spencer J. Sherwin
Publisher: Springer Nature
Total Pages: 658
Release: 2020-08-11
Genre: Mathematics
ISBN: 3030396479

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.

New Trends of Mathematical Inverse Problems and Applications

New Trends of Mathematical Inverse Problems and Applications
Author: Amine Laghrib
Publisher: Springer Nature
Total Pages: 178
Release: 2023-07-15
Genre: Mathematics
ISBN: 3031330692

This volume comprises the thoroughly reviewed and revised papers of the First International Conference on New Trends in Applied Mathematics, ICNTAM 2022, which took place in Béni Mellal, Morocco, 19-21 May 2022. The papers deal with the following topics: Inverse Problems, Partial Differential Equations, Mathematical Control, Numerical Analysis and Computer Science. The main interest is in recent trends on Inverse Problems analysis and real applications in Computer Science. The latter is viewed as a dynamic branch on the interface of mathematics and related fields, that has been growing rapidly over the past several decades. However, its mathematical analysis and interpretation still not well-detailed and needs much more clarifications. The main contribution of this book is to give some sufficient mathematical content with expressive results and accurate applications. As a growing field, it is gaining a lot of attention both in media as well as in the industry world, which will attract the interest of readers from different scientist discipline.

Realization and Model Reduction of Dynamical Systems

Realization and Model Reduction of Dynamical Systems
Author: Christopher Beattie
Publisher: Springer Nature
Total Pages: 462
Release: 2022-06-09
Genre: Science
ISBN: 303095157X

This book celebrates Professor Thanos Antoulas's 70th birthday, marking his fundamental contributions to systems and control theory, especially model reduction and, more recently, data-driven modeling and system identification. Model reduction is a prominent research topic with wide ranging scientific and engineering applications.

Domain Decomposition Methods in Science and Engineering XXIV

Domain Decomposition Methods in Science and Engineering XXIV
Author: Petter E. Bjørstad
Publisher: Springer
Total Pages: 556
Release: 2019-01-05
Genre: Mathematics
ISBN: 3319938738

These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2017.

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1
Author: Jens M. Melenk
Publisher: Springer Nature
Total Pages: 571
Release: 2023-06-30
Genre: Mathematics
ISBN: 3031204328

The volume features high-quality papers based on the presentations at the ICOSAHOM 2020+1 on spectral and high order methods. The carefully reviewed articles cover state of the art topics in high order discretizations of partial differential equations. The volume presents a wide range of topics including the design and analysis of high order methods, the development of fast solvers on modern computer architecture, and the application of these methods in fluid and structural mechanics computations.

Numerical Control: Part A

Numerical Control: Part A
Author:
Publisher: Elsevier
Total Pages: 596
Release: 2022-02-15
Genre: Mathematics
ISBN: 0323853390

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