Download or read book Separated Representations and PGD Based Model Reduction written by Francisco Chinesta and published by Springer. This book was released on 2014-09-02 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Snapshot Based Methods and Algorithms written by Peter Benner and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-12-16 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book PGD Based Modeling of Materials Structures and Processes written by Francisco Chinesta and published by Springer Science & Business. This book was released on 2014-04-23 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Machine Learning Low Rank Approximations and Reduced Order Modeling in Computational Mechanics written by Felix Fritzen and published by MDPI. This book was released on 2019-09-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.

Download or read book Virtual Design and Validation written by Peter Wriggers and published by Springer Nature. This book was released on 2020-03-03 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the experimental characterization of materials and their numerical modeling, as well as the development of new computational methods for virtual design. Its 17 contributions are divided into four main sections: experiments and virtual design, composites, fractures and fatigue, and uncertainty quantification. The first section explores new experimental methods that can be used to more accurately characterize material behavior. Furthermore, it presents a combined experimental and numerical approach to optimizing the properties of a structure, as well as new developments in the field of computational methods for virtual design. In turn, the second section is dedicated to experimental and numerical investigations of composites, with a special focus on the modeling of failure modes and the optimization of these materials. Since fatigue also includes wear due to frictional contact and aging of elastomers, new numerical schemes in the field of crack modeling and fatigue prediction are also discussed. The input parameters of a classical numerical simulation represent mean values of actual observations, though certain deviations arise: to illustrate the uncertainties of parameters used in calculations, the book’s final section presents new and efficient approaches to uncertainty quantification.

Download or read book Numerical Methods for PDEs written by Daniele Antonio Di Pietro and published by Springer. This book was released on 2018-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the approximate solution of PDEs is a key discipline in applied mathematics, and over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. This book is intended for researchers in the field.

Download or read book Real Time Reduced Order Computational Mechanics written by Gianluigi Rozza and published by Springer Nature. This book was released on 2024 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Zusammenfassung: The book is made up by several worked out problems concerning the application of reduced order modeling to different parametric partial differential equations problems with an increasing degree of complexity. This work is based on some experience acquired during lectures and exercises in classes taught at SISSA Mathematics Area in the Doctoral Programme "Mathematical Analysis, Modelling and Applications", especially in computational mechanics classes, as well as regular courses previously taught at EPF Lausanne and during several summer and winter schools. The book is a companion for master and doctoral degree classes by allowing to go more deeply inside some partial differential equations worked out problems, examples and even exercises, but it is also addressed for researchers who are newcomers in computational mechanics with reduced order modeling. In order to discuss computational results for the worked out problems presented in this booklet, we will rely on the RBniCS Project. The RBniCS Project contains an implementation in FEniCS of the reduced order modeling techniques (such as certified reduced basis method and Proper Orthogonal Decomposition-Galerkin methods) for parametric problems that will be introduced in this booklet

Download or read book The Proper Generalized Decomposition for Advanced Numerical Simulations written by Francisco Chinesta and published by Springer Science & Business Media. This book was released on 2013-10-08 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Certified Reduced Basis Methods for Parametrized Partial Differential Equations written by Jan S Hesthaven and published by Springer. This book was released on 2015-08-20 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book High Performance Computing of Big Data for Turbulence and Combustion written by Sergio Pirozzoli and published by Springer. This book was released on 2019-05-28 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides state-of-art information on high-accuracy scientific computing and its future prospects, as applicable to the broad areas of fluid mechanics and combustion, and across all speed regimes. Beginning with the concepts of space-time discretization and dispersion relation in numerical computing, the foundations are laid for the efficient solution of the Navier-Stokes equations, with special reference to prominent approaches such as LES, DES and DNS. The basis of high-accuracy computing is rooted in the concept of stability, dispersion and phase errors, which require the comprehensive analysis of discrete computing by rigorously applying error dynamics. In this context, high-order finite-difference and finite-volume methods are presented. Naturally, the coverage also includes fundamental notions of high-performance computing and advanced concepts on parallel computing, including their implementation in prospective hexascale computers. Moreover, the book seeks to raise the bar beyond the pedagogical use of high-accuracy computing by addressing more complex physical scenarios, including turbulent combustion. Tools like proper orthogonal decomposition (POD), proper generalized decomposition (PGD), singular value decomposition (SVD), recursive POD, and high-order SVD in multi-parameter spaces are presented. Special attention is paid to bivariate and multivariate datasets in connection with various canonical flow and heat transfer cases. The book mainly addresses the needs of researchers and doctoral students in mechanical engineering, aerospace engineering, and all applied disciplines including applied mathematics, offering these readers a unique resource.

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2021-07-14 with total page 929 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Download or read book The Structural Integrity of Carbon Fiber Composites written by Peter W. R Beaumont and published by Springer. This book was released on 2016-11-26 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a diverse compilation of inter-disciplinary chapters on fundamental aspects of carbon fiber composite materials and multi-functional composite structures: including synthesis, characterization, and evaluation from the nano-structure to structure meters in length. The content and focus of contributions under the umbrella of structural integrity of composite materials embraces topics at the forefront of composite materials science and technology, the disciplines of mechanics, and development of a new predictive design methodology of the safe operation of engineering structures from cradle to grave. Multi-authored papers on multi-scale modelling of problems in material design and predicting the safe performance of engineering structure illustrate the inter-disciplinary nature of the subject. The book examines topics such as Stochastic micro-mechanics theory and application for advanced composite systems Construction of the evaluation process for structural integrity of material and structure Nano- and meso-mechanics modelling of structure evolution during the accumulation of damage Statistical meso-mechanics of composite materials Hierarchical analysis including "age-aware," high-fidelity simulation and virtual mechanical testing of composite structures right up to the point of failure. The volume is ideal for scientists, engineers, and students interested in carbon fiber composite materials, and other composite material systems.

Download or read book Mathematical Methods And Models In Composites Second Edition written by Vladislav Mantic and published by World Scientific. This book was released on 2023-03-10 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.

Download or read book Magneto Active Polymers written by Jean-Paul Pelteret and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-16 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: From fabrication to testing and modeling this monograph covers all aspects on the materials class of magneto active polymers. The focus is on computational modeling of manufacturing processes and material parameters. As other smart materials, these elastomers have the ability to change electrical and mechanical properties upon application of magnetic fields. This allows for novel applications ranging from biomedical engineering to mechatronics.

Download or read book Issues in Computation 2011 Edition written by and published by ScholarlyEditions. This book was released on 2012-01-09 with total page 2054 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in Computation / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Computation. The editors have built Issues in Computation: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Computation in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Computation / 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Download or read book Reduced Order Models for the Biomechanics of Living Organs written by Francisco Chinesta and published by Elsevier. This book was released on 2023-05-25 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reduced Order Models for the Biomechanics of Living Organs, a new volume in the Biomechanics of Living Organisms series, provides a comprehensive overview of the state-of-the-art in biomechanical computations using reduced order models, along with a deeper understanding of the associated reduction algorithms that will face students, researchers, clinicians and industrial partners in the future. The book gathers perspectives from key opinion scientists who describe and detail their approaches, methodologies and findings. It is the first to synthesize complementary advances in Biomechanical modelling of living organs using reduced order techniques in the design of medical devices and clinical interventions, including surgical procedures. This book provides an opportunity for students, researchers, clinicians and engineers to study the main topics related to biomechanics and reduced models in a single reference, with this volume summarizing all biomechanical aspects of each living organ in one comprehensive reference. - Introduces the fundamental aspects of reduced order models - Presents the main computational studies in the field of solid and fluid biomechanical modeling of living organs - Explores the use of reduced order models in the fields of biomechanical electrophysiology, tissue growth and prosthetic designs

Download or read book Model Reduction and Approximation written by Peter Benner and published by SIAM. This book was released on 2017-07-06 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.