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Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems

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Abstract

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.

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Authors and Affiliations

  1. BRGM, 3 Avenue Claude Guillemin, 45060, Orléans, France

    Pierre Sochala

  2. CMAP, CNRS, INRIA, École Polytechnique, Institut Polytechnique de Paris, 91128, Palaiseau, France

    Olivier Le Maître

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  1. Pierre Sochala
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  2. Olivier Le Maître
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Correspondence to Pierre Sochala.

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The work of Pierre Sochala was supported by internal fundings of BRGM (French Geological Survey).

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Sochala, P., Le Maître, O. Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems. J Sci Comput 81, 1987–2009 (2019). https://doi.org/10.1007/s10915-019-01069-z

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  • DOI: https://doi.org/10.1007/s10915-019-01069-z

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