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Numerical Methods For Stochastic Computations

Author: Dongbin Xiu
Publisher: Princeton University Press
ISBN: 9781400835348
Size: 16.78 MB
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[email protected] 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

Numerical Methods For Stochastic Partial Differential Equations With White Noise

Author: Zhongqiang Zhang
Publisher: Springer
ISBN: 3319575112
Size: 66.37 MB
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This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. The book begins with some motivational and background material in the introductory chapters and is divided into three parts. Part I covers numerical stochastic ordinary differential equations. Here the authors start with numerical methods for SDEs with delay using the Wong-Zakai approximation and finite difference in time. Part II covers temporal white noise. Here the authors consider SPDEs as PDEs driven by white noise, where discretization of white noise (Brownian motion) leads to PDEs with smooth noise, which can then be treated by numerical methods for PDEs. In this part, recursive algorithms based on Wiener chaos expansion and stochastic collocation methods are presented for linear stochastic advection-diffusion-reaction equations. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made. Part III covers spatial white noise. Here the authors discuss numerical methods for nonlinear elliptic equations as well as other equations with additive noise. Numerical methods for SPDEs with multiplicative noise are also discussed using the Wiener chaos expansion method. In addition, some SPDEs driven by non-Gaussian white noise are discussed and some model reduction methods (based on Wick-Malliavin calculus) are presented for generalized polynomial chaos expansion methods. Powerful techniques are provided for solving stochastic partial differential equations. This book can be considered as self-contained. Necessary background knowledge is presented in the appendices. Basic knowledge of probability theory and stochastic calculus is presented in Appendix A. In Appendix B some semi-analytical methods for SPDEs are presented. In Appendix C an introduction to Gauss quadrature is provided. In Appendix D, all the conclusions which are needed for proofs are presented, and in Appendix E a method to compute the convergence rate empirically is included. In addition, the authors provide a thorough review of the topics, both theoretical and computational exercises in the book with practical discussion of the effectiveness of the methods. Supporting Matlab files are made available to help illustrate some of the concepts further. Bibliographic notes are included at the end of each chapter. This book serves as a reference for graduate students and researchers in the mathematical sciences who would like to understand state-of-the-art numerical methods for stochastic partial differential equations with white noise.

Data Assimilation For Atmospheric Oceanic And Hydrologic Applications

Author: Seon Ki Park
Publisher: Springer
ISBN: 3319434152
Size: 64.44 MB
Format: PDF, Kindle
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This book contains the most recent progress in data assimilation in meteorology, oceanography and hydrology including land surface. It spans both theoretical and applicative aspects with various methodologies such as variational, Kalman filter, ensemble, Monte Carlo and artificial intelligence methods. Besides data assimilation, other important topics are also covered including targeting observation, sensitivity analysis, and parameter estimation. The book will be useful to individual researchers as well as graduate students for a reference in the field of data assimilation.

Uncertainty Quantification In Computational Fluid Dynamics And Aircraft Engines

Author: Francesco Montomoli
Publisher: Springer
ISBN: 3319929437
Size: 17.84 MB
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This book introduces design techniques developed to increase the safety of aircraft engines, and demonstrates how the application of stochastic methods can overcome problems in the accurate prediction of engine lift caused by manufacturing error. This in turn addresses the issue of achieving required safety margins when hampered by limits in current design and manufacturing methods. The authors show that avoiding the potential catastrophe generated by the failure of an aircraft engine relies on the prediction of the correct behaviour of microscopic imperfections. This book shows how to quantify the possibility of such failure, and that it is possible to design components that are inherently less risky and more reliable. This new, updated and significantly expanded edition gives an introduction to engine reliability and safety to contextualise this important issue, evaluates newly-proposed methods for uncertainty quantification as applied to jet engines. Uncertainty Quantification in Computational Fluid Dynamics and Aircraft Engines will be of use to gas turbine manufacturers and designers as well as CFD practitioners, specialists and researchers. Graduate and final year undergraduate students in aerospace or mathematical engineering may also find it of interest.

Uncertainty Management For Robust Industrial Design In Aeronautics

Author: Charles Hirsch
Publisher: Springer
ISBN: 331977767X
Size: 72.96 MB
Format: PDF, ePub
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This book covers cutting-edge findings related to uncertainty quantification and optimization under uncertainties (i.e. robust and reliable optimization), with a special emphasis on aeronautics and turbomachinery, although not limited to these fields. It describes new methods for uncertainty quantification, such as non-intrusive polynomial chaos, collocation methods, perturbation methods, as well as adjoint based and multi-level Monte Carlo methods. It includes methods for characterization of most influential uncertainties, as well as formulations for robust and reliable design optimization. A distinctive element of the book is the unique collection of test cases with prescribed uncertainties, which are representative of the current engineering practice of the industrial consortium partners involved in UMRIDA, a level 1 collaborative project within the European Commission's Seventh Framework Programme (FP7). All developed methods are benchmarked against these industrial challenges. Moreover, the book includes a section dedicated to Best Practice Guidelines for uncertainty quantification and robust design optimization, summarizing the findings obtained by the consortium members within the UMRIDA project. All in all, the book offers a authoritative guide to cutting-edge methodologies for uncertainty management in engineering design, covers a wide range of applications and discusses new ideas for future research and interdisciplinary collaborations.

Handbuch Der Astrophysik

Author: W. Grotrian
Publisher: Springer-Verlag
ISBN: 3642907067
Size: 15.86 MB
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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Stadtverkehrsplanung

Author: Gerd Steierwald
Publisher: Springer-Verlag
ISBN: 3540270108
Size: 40.11 MB
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Das in der Fachwelt als Standardwerk eingeschätzte Buch behandelt die Probleme und Lösungsansätze der modernen Stadtverkehrsplanung. Ausgehend von der Einbindung der Verkehrsplanung in die Stadtplanung wird dem Leser eine grundlegende Darstellung zu den Methoden und Verfahren dieses weiten Fachgebietes vermittelt. Die als Hochschullehrer und Praktiker anerkannten Autoren behandeln die Grundlagen und Ziele der Planung, die Analyse und Prognose der Verkehrsentwicklung – insbesondere der Modellierung – und liefern nach den heutigen Erkenntnissen eine umfassende Übersicht über den Einfluss des Verkehrs auf alle Bereiche der humanen und natürlichen Umwelt einschließlich der Bewertung. Weitere Schwerpunkte bilden die Gestaltung und der Entwurf städtischer Verkehrsanlagen, bei denen der öffentliche Raum in der Stadt, die Straßen- und die Knotenpunkte, der ruhende Verkehr und die Anlagen des öffentlichen Verkehrs behandelt werden. Die neue Auflage wurde nicht nur gründlich bearbeitet und erneuert, sondern bringt zusätzliche Kapitel über Verkehrsleitbilder im Städtebau, Wirtschafts- und Güterverkehr, zur Leistungsfähigkeit von Verkehrsanlagen, zum Fußgänger- und Radverkehr, zu Verkehrsmanagement, Lichtsignalsteuerung, Technikfolgenabschätzung, Road Pricing und Planungsrecht. Die Darstellungen bieten dem Stadt- und Verkehrsplaner sowie Studierenden des Verkehrs- und Stadtbauwesens ein umfassendes Instrumentarium zur Lösung der gegenwärtigen Aufgaben, unter Berücksichtigung der wesentlichen Empfehlungen und Richtlinien.

Spectral Methods For Uncertainty Quantification

Author: Olivier Le Maitre
Publisher: Springer Science & Business Media
ISBN: 9789048135202
Size: 37.39 MB
Format: PDF
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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.