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Karhunen–Loève decomposition of random fields based on a hierarchical matrix approach
Author(s) -
Allaix Diego Lorenzo,
Carbone Vincenzo Ilario
Publication year - 2013
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4485
Subject(s) - probabilistic logic , random field , discretization , finite element method , karhunen–loève theorem , solver , mathematics , random variable , matrix (chemical analysis) , computer science , mathematical optimization , set (abstract data type) , series (stratigraphy) , algorithm , artificial intelligence , engineering , structural engineering , mathematical analysis , statistics , paleontology , materials science , composite material , biology , programming language
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. Copyright © 2013 John Wiley & Sons, Ltd.