Proper Orthogonal Decomposition Methods For Partial Differential Equations

Proper Orthogonal Decomposition Methods For Partial Differential Equations Book PDF
✏Book Title : Proper Orthogonal Decomposition Methods for Partial Differential Equations
✏Author : Zhendong Luo
✏Publisher : Academic Press
✏Release Date : 2018-11-26
✏Pages : 278
✏ISBN : 9780128167991
✏Available Language : English, Spanish, And French

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✏Proper Orthogonal Decomposition Methods for Partial Differential Equations Book Summary : Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Incremental Proper Orthogonal Decomposition For Pde Simulation Data Book PDF
✏Book Title : Incremental Proper Orthogonal Decomposition for PDE Simulation Data
✏Author :
✏Publisher :
✏Release Date : 2018
✏Pages :
✏ISBN : OCLC:1051408139
✏Available Language : English, Spanish, And French

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✏Incremental Proper Orthogonal Decomposition for PDE Simulation Data Book Summary : Abstract: We propose an incremental algorithm to compute the proper orthogonal decomposition (POD) of simulation data for a partial differential equation. Specifically, we modify an incremental matrix SVD algorithm of Brand to accommodate data arising from Galerkin-type simulation methods for time dependent PDEs. The algorithm is applicable to data generated by many numerical methods for PDEs, including finite element and discontinuous Galerkin methods. The algorithm initializes and efficiently updates the dominant POD eigenvalues and modes during the time stepping in a PDE solver without storing the simulation data. We prove that the algorithm without truncation updates the POD exactly. We demonstrate the effectiveness of the algorithm using finite element computations for a 1D Burgers' equation and a 2D Navier–Stokes problem.

Reduced Basis Methods For Partial Differential Equations Book PDF
✏Book Title : Reduced Basis Methods for Partial Differential Equations
✏Author : Alfio Quarteroni
✏Publisher : Springer
✏Release Date : 2015-08-19
✏Pages : 296
✏ISBN : 9783319154312
✏Available Language : English, Spanish, And French

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✏Reduced Basis Methods for Partial Differential Equations Book Summary : This book provides a basic introduction to reduced basis (RB) methods for problems involving the repeated solution of partial differential equations (PDEs) arising from engineering and applied sciences, such as PDEs depending on several parameters and PDE-constrained optimization. The book presents a general mathematical formulation of RB methods, analyzes their fundamental theoretical properties, discusses the related algorithmic and implementation aspects, and highlights their built-in algebraic and geometric structures. More specifically, the authors discuss alternative strategies for constructing accurate RB spaces using greedy algorithms and proper orthogonal decomposition techniques, investigate their approximation properties and analyze offline-online decomposition strategies aimed at the reduction of computational complexity. Furthermore, they carry out both a priori and a posteriori error analysis. The whole mathematical presentation is made more stimulating by the use of representative examples of applicative interest in the context of both linear and nonlinear PDEs. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The book will be ideal for upper undergraduate students and, more generally, people interested in scientific computing. All these pseudocodes are in fact implemented in a MATLAB package that is freely available at https://github.com/redbkit

Trust Region Proper Orthogonal Decomposition For Flow Control Book PDF
✏Book Title : Trust region Proper Orthogonal Decomposition for Flow Control
✏Author : E. Arian
✏Publisher :
✏Release Date : 2000
✏Pages : 18
✏ISBN : NASA:31769000711625
✏Available Language : English, Spanish, And French

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✏Trust region Proper Orthogonal Decomposition for Flow Control Book Summary : The proper orthogonal decomposition (POD) is a model reduction technique for the simulation of physical processes governed by partial differential equations, e.g., fluid flows. It can also be used to develop reduced order control models. Fundamental is the computation of POD basis functions that represent the influence of the control action on the system in order to get a suitable control model. We present an approach where suitable reduced order models are derived successively and give global convergence results.

Certified Reduced Basis Methods For Parametrized Partial Differential Equations Book PDF
✏Book Title : Certified Reduced Basis Methods for Parametrized Partial Differential Equations
✏Author : Jan S Hesthaven
✏Publisher : Springer
✏Release Date : 2015-08-20
✏Pages : 131
✏ISBN : 9783319224701
✏Available Language : English, Spanish, And French

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✏Certified Reduced Basis Methods for Parametrized Partial Differential Equations Book Summary : 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.

Constrained Optimization And Optimal Control For Partial Differential Equations Book PDF
✏Book Title : Constrained Optimization and Optimal Control for Partial Differential Equations
✏Author : Günter Leugering
✏Publisher : Springer Science & Business Media
✏Release Date : 2012-01-03
✏Pages : 624
✏ISBN : 9783034801331
✏Available Language : English, Spanish, And French

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✏Constrained Optimization and Optimal Control for Partial Differential Equations Book Summary : 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.

Proper Orthogonal Decomposition In Optimal Control Of Fluids Book PDF
✏Book Title : Proper Orthogonal Decomposition in Optimal Control of Fluids
✏Author : S. S. Ravindran
✏Publisher :
✏Release Date : 1999
✏Pages : 30
✏ISBN : NASA:31769000632292
✏Available Language : English, Spanish, And French

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✏Proper Orthogonal Decomposition in Optimal Control of Fluids Book Summary :

Model Reduction And Approximation Book PDF
✏Book Title : Model Reduction and Approximation
✏Author : Peter Benner
✏Publisher : SIAM
✏Release Date : 2017-07-06
✏Pages : 412
✏ISBN : 9781611974812
✏Available Language : English, Spanish, And French

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✏Model Reduction and Approximation Book Summary : Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.

Control And Estimation Of Distributed Parameter Systems Book PDF
✏Book Title : Control and Estimation of Distributed Parameter Systems
✏Author : Wolfgang Desch
✏Publisher : Springer Science & Business Media
✏Release Date : 2003
✏Pages : 269
✏ISBN : 3764370041
✏Available Language : English, Spanish, And French

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✏Control and Estimation of Distributed Parameter Systems Book Summary : Consisting of 16 refereed original contributions, this volume presents a diversified collection of recent results in control of distributed parameter systems, including applications in fluid mechanics, partial differential equations, perturbation theory and shape optimization. Advanced graduate students and researchers will find the book an excellent guide to the forefront of control and estimation of distributed pa

Model Reduction Of Parametrized Systems Book PDF
✏Book Title : Model Reduction of Parametrized Systems
✏Author : Peter Benner
✏Publisher : Springer
✏Release Date : 2017-09-05
✏Pages : 504
✏ISBN : 9783319587868
✏Available Language : English, Spanish, And French

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✏Model Reduction of Parametrized Systems Book Summary : 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).

Trends In Pde Constrained Optimization Book PDF
✏Book Title : Trends in PDE Constrained Optimization
✏Author : Günter Leugering
✏Publisher : Springer
✏Release Date : 2014-12-22
✏Pages : 543
✏ISBN : 9783319050836
✏Available Language : English, Spanish, And French

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✏Trends in PDE Constrained Optimization Book Summary : 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.

Separated Representations And Pgd Based Model Reduction Book PDF
✏Book Title : Separated Representations and PGD Based Model Reduction
✏Author : Francisco Chinesta
✏Publisher : Springer
✏Release Date : 2014-09-02
✏Pages : 227
✏ISBN : 9783709117941
✏Available Language : English, Spanish, And French

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✏Separated Representations and PGD Based Model Reduction Book Summary : The papers in this volume start with a description of the construction of reduced models through a review of Proper Orthogonal Decomposition (POD) and reduced basis models, including their mathematical foundations and some challenging applications, then followed by a description of a new generation of simulation strategies based on the use of separated representations (space-parameters, space-time, space-time-parameters, space-space,...), which have led to what is known as Proper Generalized Decomposition (PGD) techniques. The models can be enriched by treating parameters as additional coordinates, leading to fast and inexpensive online calculations based on richer offline parametric solutions. Separated representations are analyzed in detail in the course, from their mathematical foundations to their most spectacular applications. It is also shown how such an approximation could evolve into a new paradigm in computational science, enabling one to circumvent various computational issues in a vast array of applications in engineering science.

Large Scale Pde Constrained Optimization Book PDF
✏Book Title : Large Scale PDE Constrained Optimization
✏Author : Lorenz T. Biegler
✏Publisher : Springer Science & Business Media
✏Release Date : 2012-12-06
✏Pages : 349
✏ISBN : 9783642555084
✏Available Language : English, Spanish, And French

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✏Large Scale PDE Constrained Optimization Book Summary : 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.

Reduced Order Methods For Modeling And Computational Reduction Book PDF
✏Book Title : Reduced Order Methods for Modeling and Computational Reduction
✏Author : Alfio Quarteroni
✏Publisher : Springer
✏Release Date : 2014-06-05
✏Pages : 334
✏ISBN : 9783319020907
✏Available Language : English, Spanish, And French

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✏Reduced Order Methods for Modeling and Computational Reduction Book Summary : This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Multidisciplinary Design Optimization In Computational Mechanics Book PDF
✏Book Title : Multidisciplinary Design Optimization in Computational Mechanics
✏Author : Piotr Breitkopf
✏Publisher : John Wiley & Sons
✏Release Date : 2013-02-04
✏Pages : 549
✏ISBN : 9781118600009
✏Available Language : English, Spanish, And French

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✏Multidisciplinary Design Optimization in Computational Mechanics Book Summary : This book provides a comprehensive introduction to the mathematical and algorithmic methods for the Multidisciplinary Design Optimization (MDO) of complex mechanical systems such as aircraft or car engines. We have focused on the presentation of strategies efficiently and economically managing the different levels of complexity in coupled disciplines (e.g. structure, fluid, thermal, acoustics, etc.), ranging from Reduced Order Models (ROM) to full-scale Finite Element (FE) or Finite Volume (FV) simulations. Particular focus is given to the uncertainty quantification and its impact on the robustness of the optimal designs. A large collection of examples from academia, software editing and industry should also help the reader to develop a practical insight on MDO methods.

Data Driven Modeling Scientific Computation Book PDF
✏Book Title : Data Driven Modeling Scientific Computation
✏Author : J. Nathan Kutz
✏Publisher : OUP Oxford
✏Release Date : 2013-08-08
✏Pages : 608
✏ISBN : 9780191635885
✏Available Language : English, Spanish, And French

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✏Data Driven Modeling Scientific Computation Book Summary : The burgeoning field of data analysis is expanding at an incredible pace due to the proliferation of data collection in almost every area of science. The enormous data sets now routinely encountered in the sciences provide an incentive to develop mathematical techniques and computational algorithms that help synthesize, interpret and give meaning to the data in the context of its scientific setting. A specific aim of this book is to integrate standard scientific computing methods with data analysis. By doing so, it brings together, in a self-consistent fashion, the key ideas from: · statistics, · time-frequency analysis, and · low-dimensional reductions The blend of these ideas provides meaningful insight into the data sets one is faced with in every scientific subject today, including those generated from complex dynamical systems. This is a particularly exciting field and much of the final part of the book is driven by intuitive examples from it, showing how the three areas can be used in combination to give critical insight into the fundamental workings of various problems. Data-Driven Modeling and Scientific Computation is a survey of practical numerical solution techniques for ordinary and partial differential equations as well as algorithms for data manipulation and analysis. Emphasis is on the implementation of numerical schemes to practical problems in the engineering, biological and physical sciences. An accessible introductory-to-advanced text, this book fully integrates MATLAB and its versatile and high-level programming functionality, while bringing together computational and data skills for both undergraduate and graduate students in scientific computing.

Simulation Of Ode Pde Models With Matlab Octave And Scilab Book PDF
✏Book Title : Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB
✏Author : Alain Vande Wouwer
✏Publisher : Springer
✏Release Date : 2014-06-07
✏Pages : 406
✏ISBN : 9783319067902
✏Available Language : English, Spanish, And French

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✏Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB Book Summary : Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Mathematical Methods In Engineering Book PDF
✏Book Title : Mathematical Methods in Engineering
✏Author : K. Tas
✏Publisher : Springer Science & Business Media
✏Release Date : 2007-11-25
✏Pages : 468
✏ISBN : 9781402056789
✏Available Language : English, Spanish, And French

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✏Mathematical Methods in Engineering Book Summary : This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.

📒Multiscale Methods ✍ Jacob Fish

Multiscale Methods Book PDF
✏Book Title : Multiscale Methods
✏Author : Jacob Fish
✏Publisher : OUP Oxford
✏Release Date : 2009-10-22
✏Pages : 624
✏ISBN : 9780191579738
✏Available Language : English, Spanish, And French

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✏Multiscale Methods Book Summary : Small scale features and processes occurring at nanometer and femtosecond scales have a profound impact on what happens at a larger scale and over an extensive period of time. The primary objective of this volume is to reflect the state-of-the-art in multiscale mathematics, modeling, and simulations and to address the following barriers: What is the information that needs to be transferred from one model or scale to another and what physical principles must be satisfied during the transfer of information? What are the optimal ways to achieve such transfer of information? How can variability of physical parameters at multiple scales be quantified and how can it be accounted for to ensure design robustness? The multiscale approaches in space and time presented in this volume are grouped into two main categories: information-passing and concurrent. In the concurrent approaches various scales are simultaneously resolved, whereas in the information-passing methods the fine scale is modeled and its gross response is infused into the continuum scale. The issue of reliability of multiscale modeling and simulation tools which focus on a hierarchy of multiscale models and an a posteriori model of error estimation including uncertainty quantification, is discussed in several chapters. Component software that can be effectively combined to address a wide range of multiscale simulations is also described. Applications range from advanced materials to nanoelectromechanical systems (NEMS), biological systems, and nanoporous catalysts where physical phenomena operates across 12 orders of magnitude in time scales and 10 orders of magnitude in spatial scales. This volume is a valuable reference book for scientists, engineers and graduate students practicing in traditional engineering and science disciplines as well as in emerging fields of nanotechnology, biotechnology, microelectronics and energy.

Real Time Pde Constrained Optimization Book PDF
✏Book Title : Real Time PDE Constrained Optimization
✏Author : Lorenz T. Biegler
✏Publisher : SIAM
✏Release Date : 2007-07-12
✏Pages : 312
✏ISBN : 9780898716214
✏Available Language : English, Spanish, And French

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✏Real Time PDE Constrained Optimization Book Summary : “…a timely contribution to a field of growing importance. This carefully edited book presents a rich collection of chapters ranging from mathematical methodology to emerging applications. I recommend it to students as a rigorous and comprehensive presentation of simulation-based optimization and to researchers as an overview of recent advances and challenges in the field.” — Jorge Nocedal, Professor, Northwestern University.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. Despite difficulties, there is a pressing need to capitalize on continuing advances in computing power to develop optimization methods that will replace simple rule-based decision making with optimized decisions based on complex PDE simulations. Audience The book is aimed at 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.Contents Preface; Part I: Concepts and Properties of Real-Time, Online Strategies. Chapter 1: Constrained Optimal Feedback Control of Systems Governed by Large Differential Algebraic Equations; Chapter 2: A Stabilizing Real-Time Implementation of Nonlinear Model Predictive Control; Chapter 3: Numerical Feedback Controller Design for PDE Systems Using Model Reduction: Techniques and Case Studies; Chapter 4: Least-Squares Finite Element Method for Optimization and Control Problems; Part II: Fast PDE-Constrained Optimization Solvers. Chapter 5: Space-Time Multigrid Methods for Solving Unsteady Optimal Control Problems; Chapter 6: A Time-Parallel Implicit Methodology for the Near-Real-Time Solution of Systems of Linear Oscillators; Chapter 7: Generalized SQP Methods with “Parareal” Time-Domain Decomposition for Time-Dependent PDE-Constrained Optimization; Chapter 8: Simultaneous Pseudo-Timestepping for State-Constrained Optimization Problems in Aerodynamics; Chapter 9: Digital Filter Stepsize Control in DASPK and Its Effect on Control Optimization Performance; Part III: Reduced Order Modeling. Chapter 10: Certified Rapid Solution of Partial Differential Equations for Real-Time Parameter Estimation and Optimization; Chapter 11: Model Reduction for Large-Scale Applications in Computational Fluid Dynamics; Chapter 12: Suboptimal Feedback Control of Flow Separation by POD Model Reduction; Part IV: Applications. Chapter 13: A Combined Shape-Newton and Topology Optimization Technique in Real-Time Image Segmentation; Chapter 14: COFIR: Coarse and Fine Image Registration; Chapter 15: Real-Time, Large Scale Optimization of Water Network Systems Using a Sub-domain Approach; Index.

Model Order Reduction Theory Research Aspects And Applications Book PDF
✏Book Title : Model Order Reduction Theory Research Aspects and Applications
✏Author : Wilhelmus H. Schilders
✏Publisher : Springer Science & Business Media
✏Release Date : 2008-08-27
✏Pages : 471
✏ISBN : 9783540788416
✏Available Language : English, Spanish, And French

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✏Model Order Reduction Theory Research Aspects and Applications Book Summary : The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

Electromagnetic Nondestructive Evaluation Vi  Book PDF
✏Book Title : Electromagnetic Nondestructive Evaluation VI
✏Author : F. Kojima
✏Publisher : IOS Press
✏Release Date : 2002
✏Pages : 302
✏ISBN : 1586032453
✏Available Language : English, Spanish, And French

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✏Electromagnetic Nondestructive Evaluation VI Book Summary : This work is a collection of papers on electromagnetic nondestructive evaluation. It discusses developments in the growing field of electromagnetic nondestructive evaluation methods. Topics include evaluation of degradation mechanism in magnetic materials.

Shape Optimization And Optimal Design Book PDF
✏Book Title : Shape Optimization And Optimal Design
✏Author : John Cagnol
✏Publisher : CRC Press
✏Release Date : 2017-08-02
✏Pages : 450
✏ISBN : 0203904168
✏Available Language : English, Spanish, And French

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✏Shape Optimization And Optimal Design Book Summary : This volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates wi

Proceedings Book PDF
✏Book Title : Proceedings
✏Author :
✏Publisher :
✏Release Date : 2002
✏Pages : 520
✏ISBN : STANFORD:36105124274395
✏Available Language : English, Spanish, And French

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✏Proceedings Book Summary :

Siam Journal On Scientific Computing Book PDF
✏Book Title : SIAM Journal on Scientific Computing
✏Author :
✏Publisher :
✏Release Date : 2009
✏Pages :
✏ISBN : UCSD:31822036925279
✏Available Language : English, Spanish, And French

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✏SIAM Journal on Scientific Computing Book Summary :

Discussiones Mathematicae Book PDF
✏Book Title : Discussiones Mathematicae
✏Author :
✏Publisher :
✏Release Date : 2006
✏Pages :
✏ISBN : UOM:39015081659628
✏Available Language : English, Spanish, And French

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✏Discussiones Mathematicae Book Summary :

Turbulence Coherent Structures Dynamical Systems And Symmetry Book PDF
✏Book Title : Turbulence Coherent Structures Dynamical Systems and Symmetry
✏Author : Philip Holmes
✏Publisher : Cambridge University Press
✏Release Date : 2012-02-23
✏Pages : 386
✏ISBN : 9781107008250
✏Available Language : English, Spanish, And French

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✏Turbulence Coherent Structures Dynamical Systems and Symmetry Book Summary : Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

Mathematical Reviews Book PDF
✏Book Title : Mathematical Reviews
✏Author :
✏Publisher :
✏Release Date : 2006
✏Pages :
✏ISBN : UOM:39015067268261
✏Available Language : English, Spanish, And French

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✏Mathematical Reviews Book Summary :

Grazer Mathematische Berichte Book PDF
✏Book Title : Grazer mathematische Berichte
✏Author :
✏Publisher :
✏Release Date : 1999
✏Pages :
✏ISBN : UOM:39015053987957
✏Available Language : English, Spanish, And French

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✏Grazer mathematische Berichte Book Summary :

A Reduced Order Gauss Newton Method For Nonlinear Problems Based On Compressed Sensing For Pde Applications Book PDF
✏Book Title : A Reduced Order Gauss Newton Method for Nonlinear Problems Based on Compressed Sensing for PDE Applications
✏Author : Horacio Florez
✏Publisher :
✏Release Date : 2018
✏Pages :
✏ISBN : OCLC:1154211528
✏Available Language : English, Spanish, And French

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✏A Reduced Order Gauss Newton Method for Nonlinear Problems Based on Compressed Sensing for PDE Applications Book Summary : A global regularized Gauss-Newton (GN) method is proposed to obtain a zero residual for square nonlinear problems on an affine subspace built by wavelets, which allows reducing systems that arise from the discretization of nonlinear elliptic partial differential equations (PDEs) without performing a priori simulations. This chapter introduces a Petrov-Galerkin (PG) GN approach together with its standard assumptions that ensure retaining the q-quadratic rate of convergence. It also proposes a regularization strategy, which maintains the fast pace of convergence, to avoid singularities and high nonlinearities. It also includes a line-search method for achieving global convergence. The numerical results manifest the capability of the algorithm for reproducing the full-order model (FOM) essential features while decreasing the runtime by a significant magnitude. This chapter refers to a wavelet-based reduced-order model (ROM) as WROM, while PROM is the proper orthogonal decomposition (POD)-based counterpart. The authors also implemented the combination of WROM and PROM as a hybrid method referred herein as (HROM). Preliminary results with Bratu?s problem show that if the WROM could correctly reproduce the FOM behavior, then HROM can also reproduce that FOM accurately.