Scientific Computation

Spectral Methods for Uncertainty Quantification

With Applications to Computational Fluid Dynamics

Authors: Le Maitre, Olivier, Knio, Omar M

  • Offers an application oriented introduction into spectral methods for uncertainty propagation and quantification in model-based computations.
  • Includes carefully selected examples on incompressible vortex-dominated flows and compressible flows at low mach numbers.
  • Alludes only to those theoretical aspects needed to set the stage for subsequent applications.
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eBook $99.00
price for USA (gross)
  • ISBN 978-90-481-3520-2
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Hardcover $129.00
price for USA
  • ISBN 978-90-481-3519-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
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  • ISBN 978-94-007-3192-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (10 chapters)

  • Introduction: Uncertainty Quantification and Propagation

    Le Maître, O. P. (et al.)

    Pages 1-13

  • Spectral Expansions

    Le Maître, O. P. (et al.)

    Pages 17-44

  • Non-intrusive Methods

    Le Maître, O. P. (et al.)

    Pages 45-72

  • Galerkin Methods

    Le Maître, O. P. (et al.)

    Pages 73-105

  • Detailed Elementary Applications

    Le Maître, O. P. (et al.)

    Pages 107-156

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-90-481-3520-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for USA
  • ISBN 978-90-481-3519-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-94-007-3192-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Spectral Methods for Uncertainty Quantification
Book Subtitle
With Applications to Computational Fluid Dynamics
Authors
Series Title
Scientific Computation
Copyright
2010
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media B.V.
eBook ISBN
978-90-481-3520-2
DOI
10.1007/978-90-481-3520-2
Hardcover ISBN
978-90-481-3519-6
Softcover ISBN
978-94-007-3192-9
Series ISSN
1434-8322
Edition Number
1
Number of Pages
XVI, 536
Topics