Incremental Proper Orthogonal Decomposition For Pde Simulation Data

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Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics

Author : Felix Fritzen
Publisher : MDPI
ISBN 13 : 3039214098
Total Pages : 254 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by : Felix Fritzen

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.

Computational Methods for the Atmosphere and the Oceans

Author : Roger Temam
Publisher : Elsevier
ISBN 13 : 0080931030
Total Pages : 797 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Computational Methods for the Atmosphere and the Oceans by : Roger Temam

Download or read book Computational Methods for the Atmosphere and the Oceans written by Roger Temam and published by Elsevier. This book was released on 2009-06-16 with total page 797 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.• Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics • Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences• Contributions uniquely address central problems and provide a survey of the frontier of research

Model Reduction and Approximation

Author : Peter Benner
Publisher : SIAM
ISBN 13 : 161197481X
Total Pages : 421 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Model Reduction and Approximation by : Peter Benner

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.

Automated Solution of Differential Equations by the Finite Element Method

Author : Anders Logg
Publisher : Springer Science & Business Media
ISBN 13 : 3642230997
Total Pages : 723 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Encyclopedia of Computational Mechanics

Author : Erwin Stein
Publisher :
ISBN 13 :
Total Pages : 870 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Encyclopedia of Computational Mechanics by : Erwin Stein

Download or read book Encyclopedia of Computational Mechanics written by Erwin Stein and published by . This book was released on 2004 with total page 870 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Computational Mechanics provides a comprehensive collection of knowledge about the theory and practice of computational mechanics.

Reduced Order Methods for Modeling and Computational Reduction

Author : Alfio Quarteroni
Publisher : Springer
ISBN 13 : 3319020900
Total Pages : 338 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Reduced Order Methods for Modeling and Computational Reduction by : Alfio Quarteroni

Download or read book Reduced Order Methods for Modeling and Computational Reduction written by Alfio Quarteroni and published by Springer. This book was released on 2014-06-05 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods for Large Eigenvalue Problems

Author : Yousef Saad
Publisher : SIAM
ISBN 13 : 9781611970739
Total Pages : 292 pages
Book Rating : 4.9/5 (77 download)

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Book Synopsis Numerical Methods for Large Eigenvalue Problems by : Yousef Saad

Download or read book Numerical Methods for Large Eigenvalue Problems written by Yousef Saad and published by SIAM. This book was released on 2011-01-01 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Numerical Algorithms

Author : Justin Solomon
Publisher : CRC Press
ISBN 13 : 1482251892
Total Pages : 400 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Numerical Algorithms by : Justin Solomon

Download or read book Numerical Algorithms written by Justin Solomon and published by CRC Press. This book was released on 2015-06-24 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics presents a new approach to numerical analysis for modern computer scientists. Using examples from a broad base of computational tasks, including data processing, computational photography, and animation, the textbook introduces numerical modeling and algorithmic desig

Interpolatory Methods for Model Reduction

Author : A. C. Antoulas
Publisher : SIAM
ISBN 13 : 1611976081
Total Pages : 245 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Interpolatory Methods for Model Reduction by : A. C. Antoulas

Download or read book Interpolatory Methods for Model Reduction written by A. C. Antoulas and published by SIAM. This book was released on 2020-01-13 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available strategy for accurate prediction or control, inevitably creating a considerable burden on computational resources. This is the main context where one considers model reduction, seeking to replace large systems of coupled differential and algebraic equations that constitute high fidelity system models with substantially fewer equations that are crafted to control the loss of fidelity that order reduction may induce in the system response. Interpolatory methods are among the most widely used model reduction techniques, and Interpolatory Methods for Model Reduction is the first comprehensive analysis of this approach available in a single, extensive resource. It introduces state-of-the-art methods reflecting significant developments over the past two decades, covering both classical projection frameworks for model reduction and data-driven, nonintrusive frameworks. This textbook is appropriate for a wide audience of engineers and other scientists working in the general areas of large-scale dynamical systems and data-driven modeling of dynamics.

Turbulence, Coherent Structures, Dynamical Systems and Symmetry

Author : Philip Holmes
Publisher : Cambridge University Press
ISBN 13 : 1107008255
Total Pages : 403 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Turbulence, Coherent Structures, Dynamical Systems and Symmetry by : Philip Holmes

Download or read book Turbulence, Coherent Structures, Dynamical Systems and Symmetry written by Philip Holmes and published by Cambridge University Press. This book was released on 2012-02-23 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes methods revealing the structures and dynamics of turbulence for engineering, physical science and mathematics researchers working in fluid dynamics.

Certified Reduced Basis Methods for Parametrized Partial Differential Equations

Author : Jan S Hesthaven
Publisher : Springer
ISBN 13 : 3319224700
Total Pages : 139 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Certified Reduced Basis Methods for Parametrized Partial Differential Equations by : Jan S Hesthaven

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.

Process Modelling and Simulation

Author : César de Prada
Publisher : MDPI
ISBN 13 : 3039214551
Total Pages : 298 pages
Book Rating : 4.0/5 (392 download)

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Book Synopsis Process Modelling and Simulation by : César de Prada

Download or read book Process Modelling and Simulation written by César de Prada and published by MDPI. This book was released on 2019-09-23 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since process models are nowadays ubiquitous in many applications, the challenges and alternatives related to their development, validation, and efficient use have become more apparent. In addition, the massive amounts of both offline and online data available today open the door for new applications and solutions. However, transforming data into useful models and information in the context of the process industry or of bio-systems requires specific approaches and considerations such as new modelling methodologies incorporating the complex, stochastic, hybrid and distributed nature of many processes in particular. The same can be said about the tools and software environments used to describe, code, and solve such models for their further exploitation. Going well beyond mere simulation tools, these advanced tools offer a software suite built around the models, facilitating tasks such as experiment design, parameter estimation, model initialization, validation, analysis, size reduction, discretization, optimization, distributed computation, co-simulation, etc. This Special Issue collects novel developments in these topics in order to address the challenges brought by the use of models in their different facets, and to reflect state of the art developments in methods, tools and industrial applications.

Scientific Computing - An Introduction using Maple and MATLAB

Author : Walter Gander
Publisher : Springer Science & Business
ISBN 13 : 3319043250
Total Pages : 926 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Scientific Computing - An Introduction using Maple and MATLAB by : Walter Gander

Download or read book Scientific Computing - An Introduction using Maple and MATLAB written by Walter Gander and published by Springer Science & Business. This book was released on 2014-04-23 with total page 926 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

The Finite Volume Method in Computational Fluid Dynamics

Author : F. Moukalled
Publisher : Springer
ISBN 13 : 3319168746
Total Pages : 799 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis The Finite Volume Method in Computational Fluid Dynamics by : F. Moukalled

Download or read book The Finite Volume Method in Computational Fluid Dynamics written by F. Moukalled and published by Springer. This book was released on 2015-08-13 with total page 799 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.

Stochastic Processes and Applications

Author : Grigorios A. Pavliotis
Publisher : Springer
ISBN 13 : 1493913239
Total Pages : 345 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Stochastic Processes and Applications by : Grigorios A. Pavliotis

Download or read book Stochastic Processes and Applications written by Grigorios A. Pavliotis and published by Springer. This book was released on 2014-11-19 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.

The Koopman Operator in Systems and Control

Author : Alexandre Mauroy
Publisher : Springer Nature
ISBN 13 : 3030357139
Total Pages : 568 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis The Koopman Operator in Systems and Control by : Alexandre Mauroy

Download or read book The Koopman Operator in Systems and Control written by Alexandre Mauroy and published by Springer Nature. This book was released on 2020-02-22 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad overview of state-of-the-art research at the intersection of the Koopman operator theory and control theory. It also reviews novel theoretical results obtained and efficient numerical methods developed within the framework of Koopman operator theory. The contributions discuss the latest findings and techniques in several areas of control theory, including model predictive control, optimal control, observer design, systems identification and structural analysis of controlled systems, addressing both theoretical and numerical aspects and presenting open research directions, as well as detailed numerical schemes and data-driven methods. Each contribution addresses a specific problem. After a brief introduction of the Koopman operator framework, including basic notions and definitions, the book explores numerical methods, such as the dynamic mode decomposition (DMD) algorithm and Arnoldi-based methods, which are used to represent the operator in a finite-dimensional basis and to compute its spectral properties from data. The main body of the book is divided into three parts: theoretical results and numerical techniques for observer design, synthesis analysis, stability analysis, parameter estimation, and identification; data-driven techniques based on DMD, which extract the spectral properties of the Koopman operator from data for the structural analysis of controlled systems; and Koopman operator techniques with specific applications in systems and control, which range from heat transfer analysis to robot control. A useful reference resource on the Koopman operator theory for control theorists and practitioners, the book is also of interest to graduate students, researchers, and engineers looking for an introduction to a novel and comprehensive approach to systems and control, from pure theory to data-driven methods.

Partial Differential Equations and the Finite Element Method

Author : Pavel Ŝolín
Publisher : John Wiley & Sons
ISBN 13 : 0471764094
Total Pages : 505 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Partial Differential Equations and the Finite Element Method by : Pavel Ŝolín

Download or read book Partial Differential Equations and the Finite Element Method written by Pavel Ŝolín and published by John Wiley & Sons. This book was released on 2005-12-16 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A systematic introduction to partial differential equations and modern finite element methods for their efficient numerical solution Partial Differential Equations and the Finite Element Method provides a much-needed, clear, and systematic introduction to modern theory of partial differential equations (PDEs) and finite element methods (FEM). Both nodal and hierachic concepts of the FEM are examined. Reflecting the growing complexity and multiscale nature of current engineering and scientific problems, the author emphasizes higher-order finite element methods such as the spectral or hp-FEM. A solid introduction to the theory of PDEs and FEM contained in Chapters 1-4 serves as the core and foundation of the publication. Chapter 5 is devoted to modern higher-order methods for the numerical solution of ordinary differential equations (ODEs) that arise in the semidiscretization of time-dependent PDEs by the Method of Lines (MOL). Chapter 6 discusses fourth-order PDEs rooted in the bending of elastic beams and plates and approximates their solution by means of higher-order Hermite and Argyris elements. Finally, Chapter 7 introduces the reader to various PDEs governing computational electromagnetics and describes their finite element approximation, including modern higher-order edge elements for Maxwell's equations. The understanding of many theoretical and practical aspects of both PDEs and FEM requires a solid knowledge of linear algebra and elementary functional analysis, such as functions and linear operators in the Lebesgue, Hilbert, and Sobolev spaces. These topics are discussed with the help of many illustrative examples in Appendix A, which is provided as a service for those readers who need to gain the necessary background or require a refresher tutorial. Appendix B presents several finite element computations rooted in practical engineering problems and demonstrates the benefits of using higher-order FEM. Numerous finite element algorithms are written out in detail alongside implementation discussions. Exercises, including many that involve programming the FEM, are designed to assist the reader in solving typical problems in engineering and science. Specifically designed as a coursebook, this student-tested publication is geared to upper-level undergraduates and graduate students in all disciplines of computational engineeringand science. It is also a practical problem-solving reference for researchers, engineers, and physicists.