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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 215109, 15 pages
http://dx.doi.org/10.1155/2012/215109
Research Article

Multiresolution Analysis for Stochastic Finite Element Problems with Wavelet-Based Karhunen-Loève Expansion

Karlsruhe Institute of Technology (KIT), Institute of Engineering Mechanics, Kaiserstraße 12, Building 10.23, 76131 Karlsruhe, Germany

Received 28 October 2011; Revised 12 March 2012; Accepted 25 March 2012

Academic Editor: M. D. S. Aliyu

Copyright © 2012 Carsten Proppe. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.