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Author: Elías Cueto Publisher: Springer ISBN: 3319299948 Category : Science Languages : en Pages : 103
Book Description
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.
Author: Elías Cueto Publisher: Springer ISBN: 3319299948 Category : Science Languages : en Pages : 103
Book Description
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.
Author: Francisco Chinesta Publisher: Springer Science & Business ISBN: 3319061828 Category : Science Languages : en Pages : 226
Book Description
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.
Author: Francisco Chinesta Publisher: Springer Science & Business Media ISBN: 3319028650 Category : Technology & Engineering Languages : en Pages : 127
Author: Bernat Serra Zueras Publisher: ISBN: Category : Languages : en Pages :
Book Description
Computational simulations are valuable tools for engineers because they facilitate design processes. Complex systems or problems are unreachable by the standard methods (like Finite Element Method, FEM) and Model Order Reduction (MOR) techniques are required. Among those, the Proper Orthogonal Decomposition has proved to be useful in many fields of science and engineering, and especially in solid mechanics. Alternatively, an a priori strategy MOR, the Proper Generalized Decomposition (PGD), is being developed to solve parametric problems in what, in certain areas, are considered "real-time" conditions. The purpose of this study is to introduce the PGD emergent technique and its potential. This approach has been put into context by qualitatively describing MOR techniques when applied in computational solid mechanics, like the also introduced FEM. The PGD key features and advantages, as well as drawbacks, have been introduced in comparison with the POD, a widely extended technique. Regarding the potential of the PGD, its adequacy in augmented reality in computational surgery has already been documented. In this study, the PGD has first been implemented to solve two 2D academic problems successfully (Poisson equation and linear elastics) with full mathematical formulation. Next, based on the linear elastic case study, a real-time application program has been contrived. In the latter, the problem's configuration has been updated, adding more complexity. Throughout this report, the good results obtained with the PGD have been demonstrated. Results show, first, the ability to solve simple cases using a PGD code applied in Matlab and, therefore, validates this approach. Second, it has been proved that it is useful to develop real-time applications, performing as expected. However, there are still open concepts and related issues to improve the methodology. The study has achieved to develop a simple and comfortable approach to the PGD. At the same time, it provides the readers with the basic tools to encourage them to make their first steps in the PGD methodology. With the hope that all this will allow the reader understand the importance and potential of this methodology.
Author: Haruo Yanai Publisher: Springer Science & Business Media ISBN: 144199887X Category : Mathematics Languages : en Pages : 244
Book Description
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.
Author: Younes Chiba Publisher: Springer Nature ISBN: 9811603782 Category : Technology & Engineering Languages : en Pages : 435
Book Description
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.
Author: Antonio J. Conejo Publisher: Springer Science & Business Media ISBN: 3540276866 Category : Technology & Engineering Languages : en Pages : 542
Book Description
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.
Author: Pierre Ladeveze Publisher: Springer Science & Business Media ISBN: 1461214327 Category : Technology & Engineering Languages : en Pages : 230
Book Description
This book treats computational modeling of structures in which strong nonlinearities are present. It is therefore a work in mechanics and engineering, although the discussion centers on methods that are considered parts of applied mathematics. The task is to simulate numerically the behavior of a structure under various imposed excitations, forces, and displacements, and then to determine the resulting damage to the structure, and ultimately to optimize it so as to minimize the damage, subject to various constraints. The method used is iterative: at each stage an approximation to the displacements, strains, and stresses throughout the structure is computated and over all times in the interval of interest. This method leads to a general approach for understanding structural models and the necessary approximations.
Author: Peter Benner Publisher: Springer ISBN: 3319587862 Category : Mathematics Languages : en Pages : 503
Book Description
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).
Author: Elías Cueto
Author: Elías Cueto
Author: Francisco Chinesta
Author: Francisco Chinesta
Author: Francisco Chinesta
Author: Bernat Serra Zueras
Author: Haruo Yanai
Author: Younes Chiba
Author: Antonio J. Conejo
Author: Pierre Ladeveze
Author: Peter Benner