Numerical Methods For Stochastic Computations
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Numerical Methods For Stochastic Computations
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Author : Dongbin Xiu
language : en
Publisher: Princeton University Press
Release Date : 2010-07-01
Numerical Methods For Stochastic Computations written by Dongbin Xiu and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-01 with Mathematics categories.
The@ first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC methods through numerical examples and rigorous development; details the procedure for converting stochastic equations into deterministic ones; using both the Galerkin and collocation approaches; and discusses the distinct differences and challenges arising from high-dimensional problems. The last section is devoted to the application of gPC methods to critical areas such as inverse problems and data assimilation. Ideal for use by graduate students and researchers both in the classroom and for self-study, Numerical Methods for Stochastic Computations provides the required tools for in-depth research related to stochastic computations. The first graduate-level textbook to focus on the fundamentals of numerical methods for stochastic computations Ideal introduction for graduate courses or self-study Fast, efficient, and accurate numerical methods Polynomial approximation theory and probability theory included Basic gPC methods illustrated through examples
Stochastic Numerics For The Boltzmann Equation
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Author : Sergej Rjasanow
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-04
Stochastic Numerics For The Boltzmann Equation written by Sergej Rjasanow and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-11-04 with Mathematics categories.
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as detailed numerical studies are presented.
An Introduction To Computational Stochastic Pdes
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Author : Gabriel J. Lord
language : en
Publisher: Cambridge University Press
Release Date : 2014-08-11
An Introduction To Computational Stochastic Pdes written by Gabriel J. Lord and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-11 with Business & Economics categories.
This book offers a practical presentation of stochastic partial differential equations arising in physical applications and their numerical approximation.
Spectral Methods For Uncertainty Quantification
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Author : Olivier Le Maitre
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-03-11
Spectral Methods For Uncertainty Quantification written by Olivier Le Maitre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-11 with Science categories.
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.
Parallel And Distributed Computation Numerical Methods
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Author : Dimitri Bertsekas
language : en
Publisher: Athena Scientific
Release Date : 2015-03-01
Parallel And Distributed Computation Numerical Methods written by Dimitri Bertsekas and has been published by Athena Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-01 with Mathematics categories.
This highly acclaimed work, first published by Prentice Hall in 1989, is a comprehensive and theoretically sound treatment of parallel and distributed numerical methods. It focuses on algorithms that are naturally suited for massive parallelization, and it explores the fundamental convergence, rate of convergence, communication, and synchronization issues associated with such algorithms. This is an extensive book, which aside from its focus on parallel and distributed algorithms, contains a wealth of material on a broad variety of computation and optimization topics. It is an excellent supplement to several of our other books, including Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 1999), Dynamic Programming and Optimal Control (Athena Scientific, 2012), Neuro-Dynamic Programming (Athena Scientific, 1996), and Network Optimization (Athena Scientific, 1998). The on-line edition of the book contains a 95-page solutions manual.
Theory Numerics And Applications Of Hyperbolic Problems Ii
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Author : Christian Klingenberg
language : en
Publisher: Springer
Release Date : 2018-06-27
Theory Numerics And Applications Of Hyperbolic Problems Ii written by Christian Klingenberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-27 with Mathematics categories.
The second of two volumes, this edited proceedings book features research presented at the XVI International Conference on Hyperbolic Problems held in Aachen, Germany in summer 2016. It focuses on the theoretical, applied, and computational aspects of hyperbolic partial differential equations (systems of hyperbolic conservation laws, wave equations, etc.) and of related mathematical models (PDEs of mixed type, kinetic equations, nonlocal or/and discrete models) found in the field of applied sciences.
Multifaceted Uncertainty Quantification
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Author : Isaac Elishakoff
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-09-23
Multifaceted Uncertainty Quantification written by Isaac Elishakoff and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-23 with Technology & Engineering categories.
The book exposes three alternative and competing approaches to uncertainty analysis in engineering. It is composed of some essays on various sub-topics like random vibrations, probabilistic reliability, fuzzy-sets-based analysis, unknown-but-bounded variables, stochastic linearization, possible difficulties with stochastic analysis of structures.
Renewable Energy Microgeneration Systems
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Author : Qiang Yang
language : en
Publisher: Academic Press
Release Date : 2020-10-30
Renewable Energy Microgeneration Systems written by Qiang Yang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-30 with Science categories.
Renewable Energy Microgeneration Systems presents the latest technology advances in small-scale energy generation (electricity and heat) in the context of low/medium voltage level electric power distribution networks. With a focus on scientific innovations of the methodologies, approaches and algorithms in enabling efficient and secure operation of microgeneration systems, this book also analyzes the current understanding of motivations and barriers affecting microgeneration adoption with the aim of identifying opportunities for improving the field deployment. Considering the recent advances of theories and implementations in modeling, design, planning and management of different forms of microgeneration systems, this reference provides applied researchers in the field of electrical engineering and renewable micro generation incredible insights into microgeneration systems technologies and the potential for new technologies and markets. - Provides modeling and optimization methods and techniques for micro-generation systems - Covers multidisciplinary content, providing an opportunity for different stakeholders in various engineering fields - Includes recent research advances in the field, with a focus on real case studies and policy
Proceedings Of 8th Gacm Colloquium On Computational Mechanics
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Author : Tobias Gleim
language : en
Publisher: kassel university press GmbH
Release Date : 2019-09-04
Proceedings Of 8th Gacm Colloquium On Computational Mechanics written by Tobias Gleim and has been published by kassel university press GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-04 with Technology & Engineering categories.
This conference book contains papers presented at the 8th GACM Colloquium on Computational Mechanics for Young Scientists from Academia and Industry. The conference was held from August 28th – 30th, 2019 in Kassel, hosted by the Institute of Mechanics and Dynamics of the department for civil and environmental engineering and by the chair of Engineering Mechanics / Continuum Mechanics of the department for mechanical engineering of the University of Kassel. The aim of the conference is, to bring together young scientits who are engaged in academic and industrial research on Computational Mechanics and Computer Methods in Applied Sciences. It provides a plattform to present and discuss recent results from research efforts and industrial applications. In more than 150 presentations, given by young scientists, current scientific developments and advances in engineering practice in this field are presented and discussed. The contributions of the young researchers are supplemented by a poster session and plenary talks from four senior scientists from academia and industry as well as from the GACM Best PhD Award winners 2017 and 2018.
Risk And Reliability In Geotechnical Engineering
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Author : Kok-Kwang Phoon
language : en
Publisher: CRC Press
Release Date : 2018-10-09
Risk And Reliability In Geotechnical Engineering written by Kok-Kwang Phoon and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-09 with Technology & Engineering categories.
Establishes Geotechnical Reliability as Fundamentally Distinct from Structural Reliability Reliability-based design is relatively well established in structural design. Its use is less mature in geotechnical design, but there is a steady progression towards reliability-based design as seen in the inclusion of a new Annex D on "Reliability of Geotechnical Structures" in the third edition of ISO 2394. Reliability-based design can be viewed as a simplified form of risk-based design where different consequences of failure are implicitly covered by the adoption of different target reliability indices. Explicit risk management methodologies are required for large geotechnical systems where soil and loading conditions are too varied to be conveniently slotted into a few reliability classes (typically three) and an associated simple discrete tier of target reliability indices. Provides Realistic Practical Guidance Risk and Reliability in Geotechnical Engineering makes these reliability and risk methodologies more accessible to practitioners and researchers by presenting soil statistics which are necessary inputs, by explaining how calculations can be carried out using simple tools, and by presenting illustrative or actual examples showcasing the benefits and limitations of these methodologies. With contributions from a broad international group of authors, this text: Presents probabilistic models suited for soil parameters Provides easy-to-use Excel-based methods for reliability analysis Connects reliability analysis to design codes (including LRFD and Eurocode 7) Maximizes value of information using Bayesian updating Contains efficient reliability analysis methods Accessible To a Wide Audience Risk and Reliability in Geotechnical Engineering presents all the "need-to-know" information for a non-specialist to calculate and interpret the reliability index and risk of geotechnical structures in a realistic and robust way. It suits engineers, researchers, and students who are interested in the practical outcomes of reliability and risk analyses without going into the intricacies of the underlying mathematical theories.