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A MULTI-FIDELITY STOCHASTIC COLLOCATION METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA
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A MULTI-FIDELITY STOCHASTIC COLLOCATION METHOD FOR PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS WITH RANDOM INPUT DATA (2014)A MULTI-FIDELITY STOCHASTIC COLLOCATION M…An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)An adaptive hierarchical spar…An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)An Anisotropic Sparse Grid St…A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)A Sparse Grid Stochastic Coll…Stochastic model reduction for chaos representations (2007)Stochastic model reduction fo…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics (2006)Wiener Chaos expansions and n…Uncertainty propagation in CFD using polynomial chaos decomposition (2006)Uncertainty propagation in CF…On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data (2006)On the construction and analy…Numerical Methods for Differential Equations in Random Domains (2006)Numerical Methods for Differe…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Modeling uncertainty in flow …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …A Stochastic Projection Method for Fluid Flow (2002)A Stochastic Projection Metho…Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos (2001)Stochastic Modeling of Flow-S…An efficient method for parametric uncertainty analysis of numerical geophysical models (1997)An efficient method for param…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Stochastic Differential Equations: An Introduction with Applications. (1987)Stochastic finite element methods for partial differential equations with random input data (2014)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (1979)Uncertainty Analysis of Transport-Transformation Models (1999)A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code (2000)Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)Probabilistic collocation method for flow in porous media: Comparisons with other stochastic methods (2007)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)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)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's manual. (2010)An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)Fast Numerical Methods for Stochastic Computations: A Review (2009)Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2008An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data494 cited
  • 2009An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations447 cited
  • 1997An efficient method for parametric uncertainty analysis of numerical geophysical models334 cited
  • 2001Stochastic Modeling of Flow-Structure Interactions Using Generalized Polynomial Chaos273 cited
  • 2006Uncertainty propagation in CFD using polynomial chaos decomposition254 cited
  • 2006Wiener Chaos expansions and numerical solutions of randomly forced equations of fluid mechanics194 cited
  • 2007Stochastic model reduction for chaos representations

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191 cited
  • 2006On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data191 cited
  • 2006Numerical Methods for Differential Equations in Random Domains163 cited
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