Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods

By Heng Li, Dongxiao Zhang. 2007

263 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6d48583ede9d4e049020b03feebf3ef85943e903

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In Civil and Structural Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Efficient and Accurate Quantification of Uncertainty for Multiphase Flow With the Probabilistic Collocation Method (2009, background): “However, its main disadvantage is the requirement of large computational efforts because of the large number of model simulations needed to obtain statistically accurate results.”
Global sensitivity analysis: a flexible and efficient framework with an example from stochastic hydrogeology (2012, methodology): “In this paper, we use the non-intrusive probabilistic collocation method (PCM) [25].”
Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations (2013, background): “, [41]) to truncate the representation of spatial heterogeneity can be very useful.”
An efficient, high-order probabilistic collocation method on sparse grids for three-dimensional flow and solute transport in randomly heterogeneous porous media (2009, methodology): “The procedure to obtain the statistical properties in our approach is different from the one in [15], which first expands the random field with polynomial chaos expansion and then solves a set of linear equations on the collocation points to obtain the expansion coefficients.”
A Comparative Study of the Probabilistic-Collocation and Experimental-Design Methods for Petroleum-Reservoir Uncertainty Quantification (2011, methodology): “The collocation points at a given order of polynomial chaos expansion can be selected from the roots of the next-higher-order orthogonal polynomial for each uncertain parameter if the probability distribution is continuous (Li and Zhang 2007).”
Efficient posterior exploration of a high‐dimensional groundwater model from two‐stage Markov chain Monte Carlo simulation and polynomial chaos expansion (2013, methodology): “…chaos based surrogates have mainly been used in the hydrologic literature for stochastic analysis with known parameter distributions [e.g., Li and Zhang, 2007; Li et al., 2009] or global sensitivity analysis [e.g., Fajraoui et al., 2011; Ciriello et al., 2013], but rarely within the…”
Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012, methodology): “([16], [26]) have been receiving increasing attention.”
Stochastic collocation and mixed finite elements for flow in porous media (2008, background): “Choices of collocation points include tensor product of zeros of orthogonal polynomials [2,39], sparse grid approximations [39,27,28], and probabilistic collocation [23].”
Use of global sensitivity analysis and polynomial chaos expansion for interpretation of nonreactive transport experiments in laboratory‐scale porous media (2011, methodology): “The PC coefficients can then be computed by least squares regression as S ¼ WTW 1 WT F : ð9Þ [22] Regression-based methods often select the collocation points closest to the origin of the sampling space [Huang et al., 2007; Li and Zhang, 2007; Sudret 2008].”
Slope reliability analysis considering spatially variable shear strength parameters using a non-intrusive stochastic finite element method (2014, methodology): “The unknown coefficients in the 2nd order Hermite PCE can be determined using the collocation point method based on the linearly independent principle (e.g., Li and Zhang, 2007; Li et al., 2013a).”
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, methodology): “…inputs Uncertain output(s) Type of polynomial Order of PCE(s) Method for selection of data points Method for the estimation of PCE coefficients Li and Zhang (2007) UP Flow in saturated media (1D, 2D/HE) 6, 7/hydraulic conductivity field (KLE) Hydraulic heads Hermite 2, 3, 4 Deterministic…”
Polynomial chaos expansions for dependent random variables (2019, methodology): “In the following we will assume that the rate parameters a = 2(Z1+3)/3 ∈ [0, 4] and b = 30(Z2+2)/7+5 ∈ [5, 35] in (28) are random variables where the posterior distribution (29) of Z is ω(z) = C exp(−( 1 10 z(4) 1 + 1 2 (2z2 − z(2) 1)(2))), z ∈ Ω = [−3, 3]× [−2, 6], (30)”