Title of article :
Multi-resolution analysis of Wiener-type uncertainty propagation schemes
Author/Authors :
Le Ma??tre، نويسنده , , O.P. and Najm، نويسنده , , H.N. and Ghanem، نويسنده , , R.G. and Knio، نويسنده , , O.M.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
Pages :
30
From page :
502
To page :
531
Abstract :
A multi-resolution analysis (MRA) is applied to an uncertainty propagation scheme based on a generalized polynomial chaos (PC) representation. The MRA relies on an orthogonal projection of uncertain data and solution variables onto a multi-wavelet basis, consisting of compact piecewise-smooth polynomial functions. The coefficients of the expansion are computed through a Galerkin procedure. The MRA scheme is applied to the simulation of the Lorenz system having a single random parameter. The convergence of the solution with respect to the resolution level and expansion order is investigated. In particular, results are compared to two Monte-Carlo sampling strategies, demonstrating the superiority of the MRA. For more complex problems, however, the MRA approach may require excessive CPU times. Adaptive methods are consequently developed in order to overcome this drawback. Two approaches are explored: the first is based on adaptive refinement of the multi-wavelet basis, while the second is based on adaptive block-partitioning of the space of random variables. Computational tests indicate that the latter approach is better suited for large problems, leading to a more efficient, flexible and parallelizable scheme.
Keywords :
Polynomial chaos , Multi-resolution analysis , Multi-wavelets , Adaptive scheme , uncertainty quantification
Journal title :
Journal of Computational Physics
Serial Year :
2004
Journal title :
Journal of Computational Physics
Record number :
1477988
Link To Document :
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