TY  - BOOK
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics 
T2  - Scientific Computation,
SN  - 9789048135202
AV  - QA71-90 
U1  - 004 23
PY  - 2010///
CY  - Dordrecht
PB  - Springer Netherlands
KW  - Mathematics
KW  - Computational complexity
KW  - Differential equations, partial
KW  - Computer science
KW  - Computational Science and Engineering
KW  - Fluid- and Aerodynamics
KW  - Numerical and Computational Physics
KW  - Partial Differential Equations
KW  - Discrete Mathematics in Computer Science
N1  - Introduction: Uncertainty Quantification andPropagation -- 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
N2  - 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 representations using mixed and discontinuous bases, multi-resolution approximations, and adaptive techniques. Readers are assumed to be familiar with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral approximation is helpful but not essential
UR  - http://dx.doi.org/10.1007/978-90-481-3520-2
ER  -