Transient probabilistic systems
type: Item
instance of: scholarly article
title: Transient probabilistic systems
zbMATH Open document ID: 0619.73085
DOI: 10.1016/0045-7825(88)90067-9
author: Wing K. Liu
author: Glen H. Besterfield
author: Ted Belytschko
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: The probabilistic finite element method (PFEM) for the transient analysis of random field problems by the finite element method is presented with improved computational procedures. The theoretical development of PFEM is reviewed with the inclusion of a transformed uncorrelated random variable, the formulation of the decoupled PFEM equations, and the computations of the probabilistic distributions. A method is presented to reduce the PFEM equations to a smaller system of tridiagonal equations. The reduction scheme is based on highly efficient Lanczos algorithm which forms a reduced basis from the system eigenproblem. The application of PFEM via a sensitivity method for transient problems can result in the emergence of undesirable secular terms. A method based on Fourier analysis is presented for removing secularities from the PFEM. The effectiveness of the Lanczos reduction technique and the secularity elimination scheme is demonstrated with application to the linear continuum problem and potential applications to nonlinear problems are discussed.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 4005763
zbMATH Keywords: elimination of secularities
zbMATH Keywords: higher-order forcing functions
zbMATH Keywords: reduced eigenproblem
zbMATH Keywords: nonlinear continua
zbMATH Keywords: probabilistic finite element method
zbMATH Keywords: transient analysis
zbMATH Keywords: random field problems
zbMATH Keywords: smaller system of tridiagonal equations
zbMATH Keywords: reduction scheme
zbMATH Keywords: Lanczos algorithm
zbMATH Keywords: sensitivity method
zbMATH Keywords: Fourier analysis
zbMATH Keywords: secularity elimination scheme
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90067-9
OpenAlex ID: W2027034655
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description: scientific article; zbMATH DE number 4005763