Efficient numerical strategies for spectral stochastic finite element models

International Journal for Numerical Methods in Engineering

Volumn 64, Issue 10, 2005, Pages 1334-1349

  Chung, Doo Bo ^a   Gutiérrez, Miguel A ^a   Graham Brady, Lori L ^b   Lingen, Frederik Jan ^c  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Johns Hopkins University   (United States)

^c Habanera Software Company   (Netherlands)

Author keywords

Element by element algorithms; Numerical solution strategies; Spectral stochastic finite element method

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; GRADIENT METHODS; MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION; RANDOM PROCESSES; STIFFNESS MATRIX;

ELEMENT-BY-ELEMENT ALGORITHMS; NUMERICAL SOLUTION STRATEGIES; SPECTRAL STOCHASTIC FINITE ELEMENT METHOD;

NUMERICAL METHODS;

FINITE ELEMENT METHOD;

EID: 27644597167     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1404     Document Type: Article

References (14)

1. Lawrence MA. Basic random variables in finite element analysis. International Journal for Numerical Methods in Engineering 1997; 24:1849-1863.
2. Ghanem RG, Kruger RM. Numerical solution of spectral stochastic finite element systems. Computer Methods in Applied Mechanics and Engineering 1996; 129:289-303.
3. Le Maître OP, Knio OM, Debusschere BJ, Najm HN, Ghanem RG. A multigrid solver for two-dimensional stochastic diffusion equations. Computer Methods in Applied Mechanics and Engineering 2003; 192: 4723-4744.
4. Elman HC, Ernst OG, O'Leary DP, Stewart M. Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering. Computer Methods in Applied Mechanics and Engineering 2004; 194:1037-1055.
5. Matthies HG, Keese A. Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations. Computer Methods in Applied Mechanics and Engineering 2004; 194:1295-1331.
6. Pellissetti MF, Ghanem RG. Iterative solution of systems of linear equations arising in the context of stochastic finite elements. Advances in Engineering Software 2000; 31:607-616.
7. Ghanem RG, Spanos PD. Stochastic Finite Elements: A Spectral Approach. Springer: Berlin, 1991.
8. Gutiérrez MA, Krenk S. In Stochastic Finite Element Methods, Encyclopedia of Computational Mechanics, Stein E, de Borst R, Hughes TJR (eds). Wiley: New York, 2004; 2:657-681.
9. Zienkiewicz O, Taylor R. The Finite Element Method, vol. 2, Solid Mechanics. Butterworth-Heinemann: Stoneham, MA, 2000.
10. Golub GH, Van Loan CF. Matrix Computations. The Johns Hopkins University Press: Baltimore, MD, 1996.
11. Saad Y. Iterative Methods for Sparse Linear Systems. PWS Publishing Company: MA, 1996.
12. Barrett R, Berry M, Chan TF, Demmel J, Donato J, Dongarra J, Eijkhout V, Pozo R, Romine C, Van der Vorst H. Templates for Solution of Linear Systems: Building Blocks for Iterative Methods (2nd edn). SIAM: Philadelphia, PA, 1994.
13. Lingen FJ. Design of an object oriented finite element package for parallel computers. ISBN 90-9013710-6, 2000.
14. Chung DB, Gutiérrez MA, De Borst R. Object-oriented stochastic finite element analysis of fibre-metal laminates. Computer Methods in Applied Mechanics and Engineering 2004; 194:1427-1446.