Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems
| Autor: | Pierre Sochala, Olivier Le Maitre |
|---|---|
| Přispěvatelé: | Bureau de Recherches Géologiques et Minières (BRGM) (BRGM), Uncertainty Quantification in Scientific Computing and Engineering (PLATON), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria) |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Offset (computer science)
Direct model uncertain scalar field approximation 01 natural sciences Theoretical Computer Science preconditioning [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] Gibbs phenomenon Applied mathematics 0101 mathematics [SDU.STU.HY]Sciences of the Universe [physics]/Earth Sciences/Hydrology Spurious oscillations non intrusive spectral method [STAT.CO]Statistics [stat]/Computation [stat.CO] Mathematics Numerical Analysis Polynomial chaos Applied Mathematics Direct method General Engineering Sparse grid 010101 applied mathematics Computational Mathematics Test case Computational Theory and Mathematics Polynomial series front propagation Software |
| Zdroj: | Journal of Scientific Computing Journal of Scientific Computing, 2019, 81 (3), pp.1987-2009. ⟨10.1007/s10915-019-01069-z⟩ Journal of Scientific Computing, Springer Verlag, 2019, 81 (3), pp.1987-2009. ⟨10.1007/s10915-019-01069-z⟩ |
| ISSN: | 0885-7474 1573-7691 |
| Popis: | International audience; We propose an alternative approach to the direct polynomial chaos expansion in order to approximate one-dimensional uncertain field exhibiting steep fronts. The principle of our non-intrusive approach is to decompose the level points of the quantity of interest in order to avoid the spurious oscillations encountered in the direct approach. This method is more accurate and less expensive than the direct approach since the regularity of the level points with respect to the input parameters allows achieving the convergence with low-order polynomial series. The additional computational cost induced in the post-processing phase is largely offset by the use of low-level sparse grids that require a weak number of direct model evaluations in comparison with high-level sparse grids. We apply the method to subsurface flows problem with uncertain hydraulic conductivity. Infiltration test cases having different levels of complexity are presented. |
| Databáze: | OpenAIRE |
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