Proper Orthogonal Decomposition Methods For Partial Differential Equations
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Proper Orthogonal Decomposition Methods For Partial Differential Equations
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Author : Zhendong Luo
language : en
Publisher: Academic Press
Release Date : 2018-11-26
Proper Orthogonal Decomposition Methods For Partial Differential Equations written by Zhendong Luo and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-26 with Mathematics categories.
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
Reduced Basis Methods For Partial Differential Equations
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Author : Alfio Quarteroni
language : en
Publisher: Springer
Release Date : 2015-08-19
Reduced Basis Methods For Partial Differential Equations written by Alfio Quarteroni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-19 with Mathematics categories.
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
Finite Element And Reduced Dimension Methods For Partial Differential Equations
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Author : Zhendong Luo
language : en
Publisher: Springer Nature
Release Date : 2024-08-30
Finite Element And Reduced Dimension Methods For Partial Differential Equations written by Zhendong Luo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-30 with Mathematics categories.
This book aims to provide with some approaches for lessening the unknowns of the FE methods of unsteady PDEs. It provides a very detailed theoretical foundation of finite element (FE) and mixed finite element (MFE) methods in the first 2 chapters, and then Chapter 3 provides the FE and MFE methods to solve unsteady partial differential equations (PDEs). In the following 2 chapters, the principle and application of two proper orthogonal decomposition (POD) methods are introduced in detail. This book can be used as both the introduction of FE method and the gateway to the FE frontier. For readers who want to learn the FE and MFE methods for solving various steady and unsteady PDEs, they will find the first 3 chapters very helpful. While those who care about engineering applications may jump to the last 2 chapters that introduce the construction of dimension reduction models and their applications to practical process calculations. This part could help them to improve the calculation efficiency and save CPU runtime so as to do wonders for their engineering calculations.
Data Driven Modeling Scientific Computation
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Author : Jose Nathan Kutz
language : en
Publisher:
Release Date : 2013-08-08
Data Driven Modeling Scientific Computation written by Jose Nathan Kutz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-08 with Computers categories.
Combining scientific computing methods and algorithms with modern data analysis techniques, including basic applications of compressive sensing and machine learning, this book develops techniques that allow for the integration of the dynamics of complex systems and big data. MATLAB is used throughout for mathematical solution strategies.
Model Order Reduction Theory Research Aspects And Applications
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Author : Wilhelmus H. Schilders
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-27
Model Order Reduction Theory Research Aspects And Applications written by Wilhelmus H. Schilders and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-27 with Mathematics categories.
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.
Certified Reduced Basis Methods For Parametrized Partial Differential Equations
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Author : Jan S Hesthaven
language : en
Publisher: Springer
Release Date : 2015-08-20
Certified Reduced Basis Methods For Parametrized Partial Differential Equations written by Jan S Hesthaven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-08-20 with Mathematics categories.
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
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Author : Günter Leugering
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-01-03
Constrained Optimization And Optimal Control For Partial Differential Equations written by Günter Leugering and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-03 with Mathematics categories.
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
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Author : S. S. Ravindran
language : en
Publisher:
Release Date : 1999
Proper Orthogonal Decomposition In Optimal Control Of Fluids written by S. S. Ravindran and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Fluid dynamics categories.
Dimension Reduction Of Large Scale Systems
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Author : Peter Benner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30
Dimension Reduction Of Large Scale Systems written by Peter Benner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-30 with Technology & Engineering categories.
In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines.
Recent Advances In Mechanics And Fluid Structure Interaction With Applications
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Author : Fernando Carapau
language : en
Publisher: Springer Nature
Release Date : 2022-11-28
Recent Advances In Mechanics And Fluid Structure Interaction With Applications written by Fernando Carapau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-28 with Mathematics categories.
This volume examines current research in mechanics and its applications to various disciplines, with a particular focus on fluid-structure interaction (FSI). The topics have been chosen in commemoration of Dr. Bong Jae Chung and with respect to his wide range of research interests. This volume stands apart because of this diversity of interests, featuring an interdisciplinary and in-depth analysis of FSI that is difficult to find conveniently collected elsewhere in the literature. Contributors include mathematicians, physicists, mechanical and biomechanical engineers, and psychologists. This volume is structured into four thematic areas in order to increase its accessibility: theory, computations, experiments, and applications. Recent Advances in Mechanics and Fluid-Structure Interaction with Applications will appeal to established researchers as well as postdocs and graduate students interested in this active area of research.