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Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation
16 references·0 citing·21 second hop
Intrusive Polynomial Chaos Methods for Forward Uncertainty Propagation (2015)Intrusive Polynomial Chaos Methods for Fo…On the convergence of generalized polynomial chaos expansions (2011)On the convergence of general…Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)Uncertainty Quantification an…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…An adaptive multi-element generalized polynomial chaos method for stochastic differential equations (2005)An adaptive multi-element gen…Uncertainty propagation using Wiener–Haar expansions (2004)Uncertainty propagation using…Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Solving elliptic boundary val…Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes (2004)Numerical Challenges in the U…Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Multi-resolution analysis of …Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Galerkin methods for linear a…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…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…Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…A Stochastic Projection Method for Fluid Flow (2001)A Stochastic Projection Metho…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)The Malliavin Calculus and Related Topics (2006)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)An Introduction to Computational Stochastic PDEs (2014)Response Surfaces: Designs and Analyses (1997)An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Point-Collocation Nonintrusive Polynomial Chaos Method for Stochastic Computational Fluid Dynamics (2010)A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011)A 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)Review of uncertainty-based multidisciplinary design optimization methods for aerospace vehicles (2011)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)An adaptive hierarchical sparse grid collocation algorithm for the solution of stochastic differential equations (2009)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Fast Numerical Methods for Stochastic Computations: A Review (2009)
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References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2003Modeling uncertainty in flow simulations via generalized polynomial chaos1,428 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2008Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics769 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2002A Stochastic Projection Method for Fluid Flow503 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 cited
  • 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes451 cited
  • 2004Uncertainty propagation using Wiener–Haar expansions438 cited
  • 2001Solution of stochastic partial differential equations using Galerkin finite element techniques414 cited
  • 2011On the convergence of generalized polynomial chaos expansions414 cited
  • 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation

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345 cited
  • 2001A Stochastic Projection Method for Fluid Flow338 cited
  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
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