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Multiresolution analysis for stochastic finite element problems with wavelet-based Karhunen-Loève expansion. (English) Zbl 1264.65221

Summary: Multiresolution analysis for problems involving random parameter fields is considered. The random field is discretized by a Karhunen-Loève expansion. The eigenfunctions involved in this representation are computed by a wavelet expansion. The wavelet expansion allows to control the spatial resolution of the problem. Fine and coarse scales are defined, and the fine scales are taken into account by projection operators. The influence of the truncation level for the wavelet expansion on the computed reliability is documented.

MSC:

65T50 Numerical methods for discrete and fast Fourier transforms
65C99 Probabilistic methods, stochastic differential equations

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