Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid DynamicsSpringer Science & Business Media, 11 thg 3, 2010 - 536 trang 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. |
Nội dung
1 | |
14 | |
Advanced Topics | 284 |
Appendix A Essential Elements of Probability Theory and Random Processes | 483 |
Appendix B Orthogonal Polynomials | 499 |
Appendix C Implementation of Product and Moment Formulas | 514 |
References | 519 |
Index | 531 |
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Spectral Methods for Uncertainty Quantification: With Applications to ... Olivier Le Maitre,Omar M Knio Không có bản xem trước - 2010 |
Spectral Methods for Uncertainty Quantification: With Applications to ... Olivier Le Maitre,Omar M Knio Không có bản xem trước - 2012 |
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Thuật ngữ và cụm từ thông dụng
Adapted algorithms analysis application approach approximation assumed basis boundary conditions coefficients computational consider consists construction convergence corresponding decomposition defined denote density dependence determine deterministic diffusion dimension direction discretization discussed distribution domain efficiency element equations error estimate example expansion expected expressed extended fact field finite flow formulation function Galerkin given grid illustrated increases independent indicated initial integration involving iterations linear mean measure methods modes needed nonlinear Note observed obtained operator orthogonal parameters particle PC expansion performed plot points polynomials predictions present probability problem projection quadrature random variables reduced refinement representation requires residual resolution respectively sampling scale scheme second-order Sect shown shows simulation solution solved space spatial Specifically spectral standard deviation steady step stochastic strategy structure temperature tion uncertainty values vector velocity viscosity wall