Extraction Of Quantifiable Information From Complex Systems
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Extraction Of Quantifiable Information From Complex Systems
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Author : Stephan Dahlke
language : en
Publisher: Springer
Release Date : 2014-11-13
Extraction Of Quantifiable Information From Complex Systems written by Stephan Dahlke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-13 with Mathematics categories.
In April 2007, the Deutsche Forschungsgemeinschaft (DFG) approved the Priority Program 1324 “Mathematical Methods for Extracting Quantifiable Information from Complex Systems.” This volume presents a comprehensive overview of the most important results obtained over the course of the program. Mathematical models of complex systems provide the foundation for further technological developments in science, engineering and computational finance. Motivated by the trend toward steadily increasing computer power, ever more realistic models have been developed in recent years. These models have also become increasingly complex, and their numerical treatment poses serious challenges. Recent developments in mathematics suggest that, in the long run, much more powerful numerical solution strategies could be derived if the interconnections between the different fields of research were systematically exploited at a conceptual level. Accordingly, a deeper understanding of the mathematical foundations as well as the development of new and efficient numerical algorithms were among the main goals of this Priority Program. The treatment of high-dimensional systems is clearly one of the most challenging tasks in applied mathematics today. Since the problem of high-dimensionality appears in many fields of application, the above-mentioned synergy and cross-fertilization effects were expected to make a great impact. To be truly successful, the following issues had to be kept in mind: theoretical research and practical applications had to be developed hand in hand; moreover, it has proven necessary to combine different fields of mathematics, such as numerical analysis and computational stochastics. To keep the whole program sufficiently focused, we concentrated on specific but related fields of application that share common characteristics and as such, they allowed us to use closely related approaches.
Quantification Of Uncertainty Improving Efficiency And Technology
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Author : Marta D'Elia
language : en
Publisher: Springer Nature
Release Date : 2020-07-30
Quantification Of Uncertainty Improving Efficiency And Technology written by Marta D'Elia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-07-30 with Mathematics categories.
This book explores four guiding themes – reduced order modelling, high dimensional problems, efficient algorithms, and applications – by reviewing recent algorithmic and mathematical advances and the development of new research directions for uncertainty quantification in the context of partial differential equations with random inputs. Highlighting the most promising approaches for (near-) future improvements in the way uncertainty quantification problems in the partial differential equation setting are solved, and gathering contributions by leading international experts, the book’s content will impact the scientific, engineering, financial, economic, environmental, social, and commercial sectors.
International Assessment Of Research And Development In Simulation Based Engineering And Science
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Author : Sharon C. Glotzer
language : en
Publisher: World Scientific
Release Date : 2011
International Assessment Of Research And Development In Simulation Based Engineering And Science written by Sharon C. Glotzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computers categories.
Simulation-Based Engineering and Science (SBE&S) cuts across disciplines, showing tremendous promise in areas from storm prediction and climate modeling to understanding the brain and the behavior of numerous other complex systems. In this groundbreaking volume, nine distinguished leaders assess the latest research trends, as a result of 52 site visits in Europe and Asia and hundreds of hours of expert interviews, and discuss the implications of their findings for the US government. The authors conclude that while the US remains the quantitative leader in SBE&S research and development, it is very much in danger of losing that edge to Europe and Asia. Commissioned by the National Science Foundation, this multifaceted study will capture the attention of Fortune 500 companies and policymakers.
Exercises In Numerical Linear Algebra And Matrix Factorizations
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Author : Tom Lyche
language : en
Publisher: Springer Nature
Release Date : 2020-11-02
Exercises In Numerical Linear Algebra And Matrix Factorizations written by Tom Lyche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Mathematics categories.
To put the world of linear algebra to advanced use, it is not enough to merely understand the theory; there is a significant gap between the theory of linear algebra and its myriad expressions in nearly every computational domain. To bridge this gap, it is essential to process the theory by solving many exercises, thus obtaining a firmer grasp of its diverse applications. Similarly, from a theoretical perspective, diving into the literature on advanced linear algebra often reveals more and more topics that are deferred to exercises instead of being treated in the main text. As exercises grow more complex and numerous, it becomes increasingly important to provide supporting material and guidelines on how to solve them, supporting students’ learning process. This book provides precisely this type of supporting material for the textbook “Numerical Linear Algebra and Matrix Factorizations,” published as Vol. 22 of Springer’s Texts in Computational Science and Engineering series. Instead of omitting details or merely providing rough outlines, this book offers detailed proofs, and connects the solutions to the corresponding results in the textbook. For the algorithmic exercises the utmost level of detail is provided in the form of MATLAB implementations. Both the textbook and solutions are self-contained. This book and the textbook are of similar length, demonstrating that solutions should not be considered a minor aspect when learning at advanced levels.
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014
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Author : Robert M. Kirby
language : en
Publisher: Springer
Release Date : 2015-11-26
Spectral And High Order Methods For Partial Differential Equations Icosahom 2014 written by Robert M. Kirby and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Computers categories.
The book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Introduction To Numerical Methods For Variational Problems
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Author : Hans Petter Langtangen
language : en
Publisher: Springer Nature
Release Date : 2019-09-26
Introduction To Numerical Methods For Variational Problems written by Hans Petter Langtangen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-26 with Mathematics categories.
This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.
Numerical Fourier Analysis
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Author : Gerlind Plonka
language : en
Publisher: Springer
Release Date : 2019-02-05
Numerical Fourier Analysis written by Gerlind Plonka and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-05 with Mathematics categories.
This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods. It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as nonequispaced and sparse FFTs in higher dimensions. Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums. The code of most of the presented algorithms is available in the authors’ public domain software packages. Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms.
Numerical Linear Algebra And Matrix Factorizations
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Author : Tom Lyche
language : en
Publisher: Springer Nature
Release Date : 2020-03-02
Numerical Linear Algebra And Matrix Factorizations written by Tom Lyche and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-02 with Mathematics categories.
After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.
Geometrically Unfitted Finite Element Methods And Applications
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Author : Stéphane P. A. Bordas
language : en
Publisher: Springer
Release Date : 2018-03-13
Geometrically Unfitted Finite Element Methods And Applications written by Stéphane P. A. Bordas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Mathematics categories.
This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.
Turbulent Cascades Ii
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Author : Mikhael Gorokhovski
language : en
Publisher: Springer
Release Date : 2019-05-21
Turbulent Cascades Ii written by Mikhael Gorokhovski and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-21 with Technology & Engineering categories.
Gathering contributions by the most prominent researchers in a highly specialised field, this proceedings volume clarifies selected aspects of the physics of turbulent cascades and their statistical universalities under complex stationary and non-homogeneous conditions. Here, these conditions are induced by the presence of a gas/liquid interface, inertial particles, strong shear, rotation, MHD and stratification. By proposing different ways to model turbulence effects under these complex conditions, the book will be of considerable interest not only to academic researchers, but also to specialists and junior researchers in the domain of propulsion and power, as well as those whose work involves various applications related to atmospheric, oceanic and planetary physics.