Monte Carlo Treatment of Random Fields: A Broad Perspective

[+] Author and Article Information
P. D. Spanos

George R Brown School of Engineering, Rice University, Houston TX 77251

B. A. Zeldin

Parametric Technology Corporation, Waltham MA 02154

Appl. Mech. Rev 51(3), 219-237 (Mar 01, 1998) (19 pages) doi:10.1115/1.3098999 History: Online April 20, 2009


A review of a number of methods for random fields simulation in conjunction with Monte Carlo studies of probabilistic mechanics problems is presented from a broad perspective. This article complements some of the previous review articles in that it compares various simulation algorithms, assesses their relative computational efficiency and versatility, discusses the properties of generated field samples, and incorporates some of the recent developments. Collectively, a comprehensive discussion of the covariance decomposition method, the spectral method, the ARMA method, the noise shower method, the scale refinement methods, and the turning band method is attempted. For tutorial effectiveness univariate, uni-dimensional, Gaussian, and homogeneous fields are discussed, primarily in connection with various simulation methods. Nevertheless, appropriate references are included addressing the simulation of more general fields. This review article contains 110 references.

Copyright © 1998 by American Society of Mechanical Engineers
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