Generalized spectral decomposition for stochastic nonlinear problems
- Research Institute in Civil Engineering and Mechanics (GeM), Nantes Atlantic University, Ecole Centrale Nantes, UMR CNRS 6183, 2 rue de la Houssiniere, B.P. 92208, 44322 Nantes Cedex 3 (France)
- LIMSI-CNRS, BP133, F-91403 Orsay (France)
We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.
- OSTI ID:
- 21167745
- Journal Information:
- Journal of Computational Physics, Vol. 228, Issue 1; Other Information: DOI: 10.1016/j.jcp.2008.09.010; PII: S0021-9991(08)00473-7; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
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