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Zbl 1227.65013
Proppe, C.
A stochastic finite-element method for transformed normal random parameter fields. (English)
[J] Int. J. Uncertain. Quantif. 1, No. 3, 189-201 (2011). ISSN 2152-5080; ISSN 2152-5099/e

Summary: Transformed normal random fields are convenient models, e.g., for random material property fields obtained from microstructure analysis. In the context of the stochastic finite-element (FE) method, discretization of non-normal random fields by polynomial chaos expansions has been frequently employed. This introduces a non-linear relationship between the system matrix and normal random variables. For transformed normal random fields, the truncated Karhunen-Loève expansion of the transformed field is introduced into the stochastic FE formulation. This leads to a linear dependence of the system matrix on non-normal random variables. These non-normal random variables are then utilized to represent the discretized solution of the stochastic boundary value problem. Introduction of the approximations into the variational formulation of the stochastic boundary value problem and application of a collocation scheme yields a nonintrusive algorithm that allows coupling of reliability estimation procedures and existing FE solvers.
MSC 2000:
*65C30 Stochastic differential and integral equations
60H15 Stochastic partial differential equations
35R60 PDE with randomness
60G60 Random fields
65N30 Finite numerical methods (BVP of PDE)

Keywords: polynomial chaos; stochastic finite-element method; stochastic sparse grid collocation; Smolyak algorithm; stochastic response surface method; adaptivity; random fields; Karhunen-Loève expansion; stochastic boundary value problem; algorithm

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