000 03527nam a22005295i 4500
001 978-90-481-3520-2
003 DE-He213
005 20140220084558.0
007 cr nn 008mamaa
008 100316s2010 ne | s |||| 0|eng d
020 _a9789048135202
_9978-90-481-3520-2
024 7 _a10.1007/978-90-481-3520-2
_2doi
050 4 _aQA71-90
072 7 _aPDE
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aMAT003000
_2bisacsh
082 0 4 _a004
_223
100 1 _aLe Maître, O. P.
_eauthor.
245 1 0 _aSpectral Methods for Uncertainty Quantification
_h[electronic resource] :
_bWith Applications to Computational Fluid Dynamics /
_cby O. P. Le Maître, Omar M. Knio.
264 1 _aDordrecht :
_bSpringer Netherlands,
_c2010.
300 _aXVI, 552p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aScientific Computation,
_x1434-8322
505 0 _aIntroduction: 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.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aComputational complexity.
650 0 _aDifferential equations, partial.
650 0 _aComputer science.
650 1 4 _aMathematics.
650 2 4 _aComputational Science and Engineering.
650 2 4 _aFluid- and Aerodynamics.
650 2 4 _aNumerical and Computational Physics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aDiscrete Mathematics in Computer Science.
700 1 _aKnio, Omar M.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789048135196
830 0 _aScientific Computation,
_x1434-8322
856 4 0 _uhttp://dx.doi.org/10.1007/978-90-481-3520-2
912 _aZDB-2-PHA
999 _c113370
_d113370