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An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems
16 references·4 citing·33 second hop
An analysis of polynomial chaos approximations for modeling single-fluid-phase flow in porous medium systems (2007)An analysis of polynomial chaos approxima…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects (2006)Modeling Multibody Systems wi…A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes (2006)A non-intrusive stochastic Ga…Stochastic Approaches to Uncertainty Quantification in CFD Simulations (2005)Stochastic Approaches to Unce…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Finite elements for elliptic problems with stochastic coefficients (2004)Finite elements for elliptic …A Stochastic Collocation Algorithm for Uncertainty Analysis (2003)A Stochastic Collocation Algo…On solving elliptic stochastic partial differential equations (2002)On solving elliptic stochasti…Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos (2002)Modeling uncertainty in stead…Convergence study of the truncated Karhunen–Loeve expansion for simulation of stochastic processes (2001)Convergence study of the trun…Ingredients for a general purpose stochastic finite elements implementation (1999)Ingredients for a general pur…Probabilistic characterization of transport in heterogeneous media (1998)Probabilistic characterizatio…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)Large Sample Properties of Si…Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method (2018)Statistical moment analysis o…The estimation of functional uncertainty using polynomial chaos and adjoint equations (2010)The estimation of functional …Computational Aspects for Constructing Realizations of Polynomial Chaos in High Dimension (2010)Computational Aspects for Con…A polynomial chaos approach to stochastic variational inequalities (2010)A polynomial chaos approach t…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis (2009)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)The Malliavin Calculus and Related Topics (2006)On the convergence of generalized polynomial chaos expansions (2011)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)A Stochastic Projection Method for Fluid Flow (2001)Efficient Sampling for Non-Intrusive Polynomial Chaos Applications with Multiple Uncertain Input Variables (2007)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)Random Fields: Analysis and Synthesis (1983)Simulation of Stochastic Processes by Spectral Representation (1991)Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme (2002)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Random function based spectral representation of stationary and non-stationary stochastic processes (2016)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Karhunen–Loève approximation of random fields by generalized fast multipole methods (2006)Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification (2009)Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design (2009)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A review of techniques for 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References

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166 cited
  • 2003A Stochastic Collocation Algorithm for Uncertainty Analysis148 cited
  • 2006A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes86 cited
  • Cited by

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    • 2010The estimation of functional uncertainty using polynomial chaos and adjoint equations27 cited
    • 2018Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method19 cited
    • 2010A polynomial chaos approach to stochastic variational inequalities17 cited