Frontiers in PDE-Constrained Optimization
Frontiers in PDE-Constrained Optimization

Author: Harbir Antil

Publisher: Springer

Published: 2018-10-12

Total Pages: 435

ISBN-13: 1493986368

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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.

Real-time PDE-constrained Optimization
Real-time PDE-constrained Optimization

Author: Lorenz T. Biegler

Publisher: SIAM

Published: 2007-01-01

Total Pages: 335

ISBN-13: 9780898718935

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Many engineering and scientific problems in design, control, and parameter estimation can be formulated as optimization problems that are governed by partial differential equations (PDEs). The complexities of the PDEs--and the requirement for rapid solution--pose significant difficulties. A particularly challenging class of PDE-constrained optimization problems is characterized by the need for real-time solution, i.e., in time scales that are sufficiently rapid to support simulation-based decision making. Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. In addition to presenting state-of-the-art algorithms and formulations, the text illustrates these algorithms with a diverse set of applications that includes problems in the areas of aerodynamics, biology, fluid dynamics, medicine, chemical processes, homeland security, and structural dynamics. Audience: readers who have expertise in simulation and are interested in incorporating optimization into their simulations, who have expertise in numerical optimization and are interested in adapting optimization methods to the class of infinite-dimensional simulation problems, or who have worked in "offline" optimization contexts and are interested in moving to "online" optimization.

Model Validation and Uncertainty Quantification, Volume 3
Model Validation and Uncertainty Quantification, Volume 3

Author: Roland Platz

Publisher: Springer Nature

Published: 2023-10-06

Total Pages: 208

ISBN-13: 3031370031

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Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 41st IMAC, A Conference and Exposition on Structural Dynamics, 2023, the third volume of ten from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Introduction of Uncertainty Quantification Uncertainty Quantification in Dynamics Model Form Uncertainty and Selection incl. Round Robin Challenge Sensor and Information Fusion Virtual Sensing, Certification, and Real-Time Monitoring Surrogate Modeling

Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces
Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces

Author: Michael Ulbrich

Publisher: SIAM

Published: 2011-07-28

Total Pages: 315

ISBN-13: 1611970687

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A comprehensive treatment of semismooth Newton methods in function spaces: from their foundations to recent progress in the field. This book is appropriate for researchers and practitioners in PDE-constrained optimization, nonlinear optimization and numerical analysis, as well as engineers interested in the current theory and methods for solving variational inequalities.

Trends in PDE Constrained Optimization
Trends in PDE Constrained Optimization

Author: Günter Leugering

Publisher: Springer

Published: 2014-12-22

Total Pages: 539

ISBN-13: 3319050834

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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.

Large-Scale PDE-Constrained Optimization
Large-Scale PDE-Constrained Optimization

Author: Lorenz T. Biegler

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 347

ISBN-13: 364255508X

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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.

Non-Smooth and Complementarity-Based Distributed Parameter Systems
Non-Smooth and Complementarity-Based Distributed Parameter Systems

Author: Michael Hintermüller

Publisher: Springer Nature

Published: 2022-02-18

Total Pages: 518

ISBN-13: 3030793931

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Many of the most challenging problems in the applied sciences involve non-differentiable structures as well as partial differential operators, thus leading to non-smooth distributed parameter systems. This edited volume aims to establish a theoretical and numerical foundation and develop new algorithmic paradigms for the treatment of non-smooth phenomena and associated parameter influences. Other goals include the realization and further advancement of these concepts in the context of robust and hierarchical optimization, partial differential games, and nonlinear partial differential complementarity problems, as well as their validation in the context of complex applications. Areas for which applications are considered include optimal control of multiphase fluids and of superconductors, image processing, thermoforming, and the formation of rivers and networks. Chapters are written by leading researchers and present results obtained in the first funding phase of the DFG Special Priority Program on Nonsmooth and Complementarity Based Distributed Parameter Systems: Simulation and Hierarchical Optimization that ran from 2016 to 2019.

Frontiers in Numerical Analysis - Durham 2010
Frontiers in Numerical Analysis - Durham 2010

Author: James Blowey

Publisher: Springer Science & Business Media

Published: 2012-01-10

Total Pages: 298

ISBN-13: 3642239145

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This book contains detailed lecture notes on four topics at the forefront of current research in computational mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to gain quickly an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research are given. This book is also suitable for professional mathematicians who require a succint and accurate account of recent research in areas parallel to their own, and graduates in mathematical sciences.

Frontiers and Challenges in Warm Dense Matter
Frontiers and Challenges in Warm Dense Matter

Author: Frank Graziani

Publisher: Springer Science & Business

Published: 2014-04-28

Total Pages: 294

ISBN-13: 3319049127

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Warm Dense Matter (WDM) occupies a loosely defined region of phase space intermediate between solid, liquid, gas, and plasma, and typically shares characteristics of two or more of these phases. WDM is generally associated with the combination of strongly coupled ions and moderately degenerate electrons, and careful attention to quantum physics and electronic structure is essential. The lack of a small perturbation parameter greatly limits approximate attempts at its accurate description. Since WDM resides at the intersection of solid state and high energy density physics, many high energy density physics (HEDP) experiments pass through this difficult region of phase space. Thus, understanding and modeling WDM is key to the success of experiments on diverse facilities. These include the National Ignition Campaign centered on the National Ignition Facility (NIF), pulsed-power driven experiments on the Z machine, ion-beam-driven WDM experiments on the NDCX-II, and fundamental WDM research at the Linear Coherent Light Source (LCLS). Warm Dense Matter is also ubiquitous in planetary science and astrophysics, particularly with respect to unresolved questions concerning the structure and age of the gas giants, the nature of exosolar planets, and the cosmochronology of white dwarf stars. In this book we explore established and promising approaches to the modeling of WDM, foundational issues concerning the correct theoretical description of WDM, and the challenging practical issues of numerically modeling strongly coupled systems with many degrees of freedom.