Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10346044 | Computers & Mathematics with Applications | 2015 | 21 Pages |
Abstract
The approximate computation of quantities of interest, such as mean value and variance for outgoing fluxes, is based on a stochastic collocation approach that uses suitable sparse grids in the range of the stochastic variables (whose number defines the stochastic dimension of the problem). This produces a non-intrusive computational method, in which the DFN flow solver is applied as a black-box. A very fast error decay, related to the analytical dependence of the observed quantities upon the stochastic variables, is obtained in the low dimensional cases using isotropic sparse grids; comparisons with Monte Carlo results show a clear gain in efficiency for the proposed method. For increasing dimensions attained via successive truncations of Karhunen-Loève expansions, results are still good although the rates of convergence are progressively reduced. Resorting to suitably tuned anisotropic grids is an effective way to contrast such curse of dimensionality: in the explored range of dimensions, the resulting convergence histories are nearly independent of the dimension.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
S. Berrone, C. Canuto, S. Pieraccini, S. Scialò,