Karhunen–Loève decomposition of random fields based on a hierarchical matrix approach

SUMMARY The simulation of the behavior of structures with uncertain properties is a challenging issue, because it requires suitable probabilistic models and adequate numerical tools. Nowadays, it is possible to perform probabilistic investigations of the structural performance, which take into account a space-variant uncertainty characterization of the structures. Given a structural solver and the probabilistic models, the reliability analysis of the structural response depends on the continuous random fields approximation, which is carried out by means of a finite set of random variables. The paper analyzes the main aspects of discretization in the case of 2D problems. The combination of the well-known Karhunen–Loeve series expansion, the finite element method and the hierarchical matrices approach is proposed in the paper. Copyright © 2013 John Wiley & Sons, Ltd.

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