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Karhunen-Loève decomposition of random fields based on a hierarchical matrix approach. (English) Zbl 1352.65464

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-Loève series expansion, the finite element method and the hierarchical matrices approach is proposed in the paper.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
60G60 Random fields
65N75 Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
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