Proper Generalized Decompositions
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Proper Generalized Decompositions
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Author : Elías Cueto
language : en
Publisher: Springer
Release Date : 2016-03-01
Proper Generalized Decompositions written by Elías Cueto and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-01 with Science categories.
This book is intended to help researchers overcome the entrance barrier to Proper Generalized Decomposition (PGD), by providing a valuable tool to begin the programming task. Detailed Matlab Codes are included for every chapter in the book, in which the theory previously described is translated into practice. Examples include parametric problems, non-linear model order reduction and real-time simulation, among others. Proper Generalized Decomposition (PGD) is a method for numerical simulation in many fields of applied science and engineering. As a generalization of Proper Orthogonal Decomposition or Principal Component Analysis to an arbitrary number of dimensions, PGD is able to provide the analyst with very accurate solutions for problems defined in high dimensional spaces, parametric problems and even real-time simulation.
The Proper Generalized Decomposition For Advanced Numerical Simulations
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Author : Francisco Chinesta
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-08
The Proper Generalized Decomposition For Advanced Numerical Simulations written by Francisco Chinesta 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 2013-10-08 with Technology & Engineering categories.
Many problems in scientific computing are intractable with classical numerical techniques. These fail, for example, in the solution of high-dimensional models due to the exponential increase of the number of degrees of freedom. Recently, the authors of this book and their collaborators have developed a novel technique, called Proper Generalized Decomposition (PGD) that has proven to be a significant step forward. The PGD builds by means of a successive enrichment strategy a numerical approximation of the unknown fields in a separated form. Although first introduced and successfully demonstrated in the context of high-dimensional problems, the PGD allows for a completely new approach for addressing more standard problems in science and engineering. Indeed, many challenging problems can be efficiently cast into a multi-dimensional framework, thus opening entirely new solution strategies in the PGD framework. For instance, the material parameters and boundary conditions appearing in a particular mathematical model can be regarded as extra-coordinates of the problem in addition to the usual coordinates such as space and time. In the PGD framework, this enriched model is solved only once to yield a parametric solution that includes all particular solutions for specific values of the parameters. The PGD has now attracted the attention of a large number of research groups worldwide. The present text is the first available book describing the PGD. It provides a very readable and practical introduction that allows the reader to quickly grasp the main features of the method. Throughout the book, the PGD is applied to problems of increasing complexity, and the methodology is illustrated by means of carefully selected numerical examples. Moreover, the reader has free access to the Matlab© software used to generate these examples.
The Proper Generalized Decomposition For Advanced Numerical Simulations
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Author : Francisco Chinesta
language : en
Publisher:
Release Date : 2013-11-30
The Proper Generalized Decomposition For Advanced Numerical Simulations written by Francisco Chinesta and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-30 with categories.
Snapshot Based Methods And Algorithms
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Author : Peter Benner
language : en
Publisher: de Gruyter
Release Date : 2021
Snapshot Based Methods And Algorithms written by Peter Benner and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematics categories.
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This second volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.
Pgd Based Modeling Of Materials Structures And Processes
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Author : Francisco Chinesta
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-23
Pgd Based Modeling Of Materials Structures And Processes written by Francisco Chinesta and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-23 with Science categories.
This book focuses on the development of a new simulation paradigm allowing for the solution of models that up to now have never been resolved and which result in spectacular CPU time savings (in the order of millions) that, combined with supercomputing, could revolutionize future ICT (information and communication technologies) at the heart of science and technology. The authors have recently proposed a new paradigm for simulation-based engineering sciences called Proper Generalized Decomposition, PGD, which has proved a tremendous potential in many aspects of forming process simulation. In this book a review of the basics of the technique is made, together with different examples of application.
Separated Representations And Pgd Based Model Reduction
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Author : Francisco Chinesta
language : en
Publisher: Springer
Release Date : 2014-09-02
Separated Representations And Pgd Based Model Reduction written by Francisco Chinesta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Technology & Engineering categories.
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.
Model Order Reduction Proper Generalized Decomposition In The Context Of Non Linearity And Motion In Electrical Machines
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Author : Fabian Müller
language : en
Publisher:
Release Date : 2024
Model Order Reduction Proper Generalized Decomposition In The Context Of Non Linearity And Motion In Electrical Machines written by Fabian Müller and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with categories.
Decomposition Techniques In Mathematical Programming
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Author : Antonio J. Conejo
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-28
Decomposition Techniques In Mathematical Programming written by Antonio J. Conejo 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 2006-04-28 with Technology & Engineering categories.
Optimization plainly dominates the design, planning, operation, and c- trol of engineering systems. This is a book on optimization that considers particular cases of optimization problems, those with a decomposable str- ture that can be advantageously exploited. Those decomposable optimization problems are ubiquitous in engineering and science applications. The book considers problems with both complicating constraints and complicating va- ables, and analyzes linear and nonlinear problems, with and without in- ger variables. The decomposition techniques analyzed include Dantzig-Wolfe, Benders, Lagrangian relaxation, Augmented Lagrangian decomposition, and others. Heuristic techniques are also considered. Additionally, a comprehensive sensitivity analysis for characterizing the solution of optimization problems is carried out. This material is particularly novel and of high practical interest. This book is built based on many clarifying, illustrative, and compu- tional examples, which facilitate the learning procedure. For the sake of cl- ity, theoretical concepts and computational algorithms are assembled based on these examples. The results are simplicity, clarity, and easy-learning. We feel that this book is needed by the engineering community that has to tackle complex optimization problems, particularly by practitioners and researchersinEngineering,OperationsResearch,andAppliedEconomics.The descriptions of most decomposition techniques are available only in complex and specialized mathematical journals, di?cult to understand by engineers. A book describing a wide range of decomposition techniques, emphasizing problem-solving, and appropriately blending theory and application, was not previously available.
Advances In Green Energies And Materials Technology
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Author : Younes Chiba
language : en
Publisher: Springer Nature
Release Date : 2021-06-09
Advances In Green Energies And Materials Technology written by Younes Chiba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-09 with Technology & Engineering categories.
This book presents selected articles from the Algerian Symposium on Renewable Energy and Materials (ASREM-2020) held at Médéa, Algeria. It highlights the latest advances in the field of green energies and material technology with specific accentuation on numerical plans and recent methodologies designed to solve engineering problems. It includes mathematical models and experimental measurements to study different problems in renewable energy and materials characterization, with contributions from experts in both academia and industry, and presents a platform to further collaborations in this important area.
Projection Matrices Generalized Inverse Matrices And Singular Value Decomposition
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Author : Haruo Yanai
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-04-06
Projection Matrices Generalized Inverse Matrices And Singular Value Decomposition written by Haruo Yanai 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 2011-04-06 with Mathematics categories.
Aside from distribution theory, projections and the singular value decomposition (SVD) are the two most important concepts for understanding the basic mechanism of multivariate analysis. The former underlies the least squares estimation in regression analysis, which is essentially a projection of one subspace onto another, and the latter underlies principal component analysis, which seeks to find a subspace that captures the largest variability in the original space. This book is about projections and SVD. A thorough discussion of generalized inverse (g-inverse) matrices is also given because it is closely related to the former. The book provides systematic and in-depth accounts of these concepts from a unified viewpoint of linear transformations finite dimensional vector spaces. More specially, it shows that projection matrices (projectors) and g-inverse matrices can be defined in various ways so that a vector space is decomposed into a direct-sum of (disjoint) subspaces. Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition will be useful for researchers, practitioners, and students in applied mathematics, statistics, engineering, behaviormetrics, and other fields.