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Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
ISBN: 3642149413
Category : Mathematics
Languages : en
Pages : 356
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Book Description
This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
ISBN: 3642149413
Category : Mathematics
Languages : en
Pages : 356
Get Book Here
Book Description
This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Author: Jochen Garcke
Publisher: Springer Science & Business Media
ISBN: 3642317022
Category : Mathematics
Languages : en
Pages : 290
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Book Description
In the recent decade, there has been a growing interest in the numerical treatment of high-dimensional problems. It is well known that classical numerical discretization schemes fail in more than three or four dimensions due to the curse of dimensionality. The technique of sparse grids helps overcome this problem to some extent under suitable regularity assumptions. This discretization approach is obtained from a multi-scale basis by a tensor product construction and subsequent truncation of the resulting multiresolution series expansion. This volume of LNCSE is a collection of the papers from the proceedings of the workshop on sparse grids and its applications held in Bonn in May 2011. The selected articles present recent advances in the mathematical understanding and analysis of sparse grid discretization. Aspects arising from applications are given particular attention.
Author: Walter Gander
Publisher: Springer Science & Business
ISBN: 3319043250
Category : Mathematics
Languages : en
Pages : 926
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Book Description
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”.
Author: Amit Agrawal
Publisher: Springer
ISBN: 3030106624
Category : Science
Languages : en
Pages : 375
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Book Description
This book covers concepts and the latest developments on microscale flow and heat transfer phenomena involving a gas. The book is organised in two parts: the first part focuses on the fluid flow and heat transfer characteristics of gaseous slip flows. The second part presents modelling of such flows using higher-order continuum transport equations. The Navier-Stokes equations based solution is provided to various problems in the slip regime. Several interesting characteristics of slip flows along with useful empirical correlations are documented in the first part of the book. The examples bring out the failure of the conventional equations to adequately describe various phenomena at the microscale. Thereby the readers are introduced to higher order continuum transport (Burnett and Grad) equations, which can potentially overcome these limitations. A clear and easy to follow step by step derivation of the Burnett and Grad equations (superset of the Navier-Stokes equations) is provided in the second part of the book. Analytical solution of these equations, the latest developments in the field, along with scope for future work in this area are also brought out. Presents characteristics of flow in the slip and transition regimes for a clear understanding of microscale flow problems; Provides a derivation of Navier-Stokes equations from microscopic viewpoint; Features a clear and easy to follow step-by-step approach to derive Burnett and Grad equations; Describes a complete compilation of few known exact solutions of the Burnett and Grad equations, along with a discussion of the solution aided with plots; Introduces the variants of the Navier-Stokes, Burnett and Grad equations, including the recently proposed Onsager-Burnett and O13 moment equations.
Author: Fernando F. Grinstein
Publisher: Cambridge University Press
ISBN: 1316571742
Category : Technology & Engineering
Languages : en
Pages : 481
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Book Description
Small-scale turbulent flow dynamics is traditionally viewed as universal and as enslaved to that of larger scales. In coarse grained simulation (CGS), large energy-containing structures are resolved, smaller structures are spatially filtered out, and unresolved subgrid scale (SGS) effects are modeled. Coarse Grained Simulation and Turbulent Mixing reviews our understanding of CGS. Beginning with an introduction to the fundamental theory the discussion then moves to the crucial challenges of predictability. Next, it addresses verification and validation, the primary means of assessing accuracy and reliability of numerical simulation. The final part reports on the progress made in addressing difficult non-equilibrium applications of timely current interest involving variable density turbulent mixing. The book will be of fundamental interest to graduate students, research scientists, and professionals involved in the design and analysis of complex turbulent flows.
Author: Aslak Tveito
Publisher: Springer Science & Business Media
ISBN: 3642112986
Category : Mathematics
Languages : en
Pages : 470
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Book Description
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. This book is a gentle introduction to such computational methods where the techniques are explained through examples. It is our goal to teach principles and ideas that carry over from field to field. You will learn basic methods and how to implement them. In order to gain the most from this text, you will need prior knowledge of calculus, basic linear algebra and elementary programming.
Author: Ronald Hoppe
Publisher: Springer
ISBN: 3319080253
Category : Computers
Languages : en
Pages : 422
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Book Description
This book on PDE Constrained Optimization contains contributions on the mathematical analysis and numerical solution of constrained optimal control and optimization problems where a partial differential equation (PDE) or a system of PDEs appears as an essential part of the constraints. The appropriate treatment of such problems requires a fundamental understanding of the subtle interplay between optimization in function spaces and numerical discretization techniques and relies on advanced methodologies from the theory of PDEs and numerical analysis as well as scientific computing. The contributions reflect the work of the European Science Foundation Networking Programme ’Optimization with PDEs’ (OPTPDE).
Author: Juan Carlos Moreno Piraján
Publisher: BoD – Books on Demand
ISBN: 9533076275
Category : Technology & Engineering
Languages : en
Pages : 418
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Book Description
Thermodynamics is one of the most exciting branches of physical chemistry which has greatly contributed to the modern science. Being concentrated on a wide range of applications of thermodynamics, this book gathers a series of contributions by the finest scientists in the world, gathered in an orderly manner. It can be used in post-graduate courses for students and as a reference book, as it is written in a language pleasing to the reader. It can also serve as a reference material for researchers to whom the thermodynamics is one of the area of interest.
Author: Markus Holtz
Publisher: Springer Science & Business Media
ISBN: 3642160042
Category : Mathematics
Languages : en
Pages : 194
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Book Description
This book deals with the numerical analysis and efficient numerical treatment of high-dimensional integrals using sparse grids and other dimension-wise integration techniques with applications to finance and insurance. The book focuses on providing insights into the interplay between coordinate transformations, effective dimensions and the convergence behaviour of sparse grid methods. The techniques, derivations and algorithms are illustrated by many examples, figures and code segments. Numerical experiments with applications from finance and insurance show that the approaches presented in this book can be faster and more accurate than (quasi-) Monte Carlo methods, even for integrands with hundreds of dimensions.
Author: Jochen Garcke
Publisher: Springer Science & Business Media
ISBN: 3319045377
Category : Mathematics
Languages : en
Pages : 345
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Book Description
Sparse grids have gained increasing interest in recent years for the numerical treatment of high-dimensional problems. Whereas classical numerical discretization schemes fail in more than three or four dimensions, sparse grids make it possible to overcome the “curse” of dimensionality to some degree, extending the number of dimensions that can be dealt with. This volume of LNCSE collects the papers from the proceedings of the second workshop on sparse grids and applications, demonstrating once again the importance of this numerical discretization scheme. The selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures, and the range of applications extends to uncertainty quantification settings and clustering, to name but a few examples.
