Wavelet and Multiresolution Analysis Schemes

  • O. P. Le MaîtreEmail author
  • O. M. Knio
Part of the Scientific Computation book series (SCIENTCOMP)


An essential aspect of spectral representations analyzed so far is the projection of the process or solution on a polynomial basis, namely on a vector space spanned by infinitely differentiable functions. It is known following the works of Wiener [Am. J. Math. 60:897–936, 1938] and Cameron and Martin [Ann. Math. 48:385–392, 1947] that such spectral representation converges in a mean square sense as N,No→∞. In the case of numerical simulation, however, on must necessarily rely on truncation, and in this case the convergence may be seriously compromised due to truncation errors and aliasing, and in extreme cases these phenomena may lead to breakdown of the computations. This chapter explores the possibility of overcoming these difficulties by using a PC expansion based on Haar wavelets or multiwavelets.


Rayleigh Number Heat Transfer Rate Random Data Resolution Level Lorenz System 
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  1. 25.
    Cameron, R., Martin, W.: The orthogonal development of nonlinear functionals in series of Fourier-Hermite functionals. Ann. Math. 48, 385–392 (1947) CrossRefMathSciNetGoogle Scholar
  2. 241.
    Wiener, S.: The homogeneous chaos. Am. J. Math. 60, 897–936 (1938) CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.LIMSI-CNRSUniversité Paris-Sud XIOrsay cedexFrance
  2. 2.Department of Mechanical EngineeringThe Johns Hopkins UniversityBaltimoreUSA

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