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Titlebook: Spectral Methods for Uncertainty Quantification; With Applications to O. P. Le Maître,Omar M. Knio Book 2010 Springer Science+Business Medi

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书目名称Spectral Methods for Uncertainty Quantification
副标题With Applications to
编辑O. P. Le Maître,Omar M. Knio
视频video
概述Application-oriented introduction into spectral methods for uncertainty propagation and quantification in model-based computations..With carefully selected examples on incompressible vortex-dominated
丛书名称Scientific Computation
图书封面Titlebook: Spectral Methods for Uncertainty Quantification; With Applications to O. P. Le Maître,Omar M. Knio Book 2010 Springer Science+Business Medi
描述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-depend
出版日期Book 2010
关键词CFD book; Navier-Stokes equation; algorithms fluid dynamics; application spectral methods; computational
版次1
doihttps://doi.org/10.1007/978-90-481-3520-2
isbn_softcover978-94-007-3192-9
isbn_ebook978-90-481-3520-2Series ISSN 1434-8322 Series E-ISSN 2198-2589
issn_series 1434-8322
copyrightSpringer Science+Business Media B.V. 2010
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1434-8322 efully selected examples on incompressible vortex-dominated 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
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Wavelet and Multiresolution Analysis Schemesreme cases these phenomena may lead to breakdown of the computations. This chapter explores the possibility of overcoming these difficulties by using a PC expansion based on Haar wavelets or multiwavelets.
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Epilogueonclusion, we provide a brief discussion of selected topics, which we attempt to group into the following (somewhat connected) categories: (a) potential extensions of methodologies outlined in previous chapters, (b) open problems, and (c) new desirable capabilities.
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,Introduction: Uncertainty Quantification and Propagation, development has been made possible thanks to the constant evolution of numerical techniques and increasing availability of computational resources. Nowadays, simulations are essential tools for engineers throughout the design process. The simulations minimize the need for costly physical experiment
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Non-intrusive Methodsa finite set of independent random parameters defined on a suitable probability space. As discussed Chap. 2, we are concerned with models having a unique solution for almost all realizations of the random parameters, so the model can be seen as a surjective mapping from the parameters domain to the
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Galerkin Methodse based on a weighted residual formalism to form systems of governing equations for the solution’s PC coefficients. This chapter is devoted to the formulation of Galerkin methods of UQ using PC expansions.
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