Spectral Methods for Uncertainty Quantification : With Applications to Computational Fluid Dynamics. 1st ed. 2010

種類:

電子ブック

責任表示:

by Olivier Le Maitre, Omar M Knio

出版情報:

Dordrecht : Springer Netherlands : Imprint: Springer, 2010

著者名:

• Le Maitre, Olivier.
• Knio, Omar M.
• SpringerLink (Online service)

シリーズ名:

Scientific Computation ;

ISBN:

9789048135202 [9048135206]    

注記:

Introduction: Uncertainty Quantification and Propagation -- Basic Formulations -- Spectral Expansions -- Non-intrusive Methods -- Galerkin Methods -- Detailed Elementary Applications -- Application to Navier-Stokes Equations -- Advanced topics -- Solvers for Stochastic Galerkin Problems -- Wavelet and Multiresolution Analysis Schemes -- Adaptive Methods -- Epilogue.
This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundations associated with probability and measure spaces. A brief discussion is provided of only those theoretical aspects needed to set the stage for subsequent applications. These are demonstrated through detailed treatments of elementary problems, as well as in more elaborate examples involving vortex-dominated flows and compressible flows at low Mach numbers. Some recent developments are also outlined in the book, including iterative techniques (such as stochastic multigrids and Newton schemes), intrusive and non-intrusive formalisms, spectral representat

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