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Polynomial Chaos: Modeling, Estimation, and Approximation
16 references·0 citing·31 second hop
Polynomial Chaos: Modeling, Estimation, and Approximation (2016)Polynomial Chaos: Modeling, Estimation, a…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures (2006)Multi-Element Generalized Pol…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)High-Order Collocation Method…Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Solving elliptic boundary val…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …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…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…A nonparametric model of random uncertainties for reduced matrix models in structural dynamics (2000)A nonparametric model of rand…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Neumann Expansion for Stochastic Finite Element Analysis (1988)Neumann Expansion for Stochas…Probabilistic finite elements for nonlinear structural dynamics (1986)Probabilistic finite elements…Random Eigenvalue Problems in Structural Analysis (1972)Random Eigenvalue Problems in…Multiple Wiener Integral (1951)Multiple Wiener IntegralModeling uncertainty in flow simulations via generalized polynomial chaos (2003)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)Digital simulation of random processes and its applications (1972)Monte Carlo solution of structural dynamics (1972)Stochastic Finite Element Expansion for Random Media (1989)A generalized dimension‐reduction method for multidimensional integration in stochastic mechanics (2004)Probability density evolution method for dynamic response analysis of structures with uncertain parameters (2004)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)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)Large Sample Properties of Simulations Using Latin Hypercube Sampling (1987)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data (2008)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)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)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Fast Numerical Methods for Stochastic Computations: A Review (2009)On the convergence of generalized polynomial chaos expansions (2011)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Convergence of integrated processes of arbitrary Hermite rank (1979)Integration with respect to fractal functions and stochastic calculus. I (1998)Stochastic Calculus for Fractional Brownian Motion I. Theory (2000)
this work references cited by second hop

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
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 1951Multiple Wiener Integral699 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 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
  • 1988Neumann Expansion for Stochastic Finite Element Analysis496 cited
  • 2000A nonparametric model of random uncertainties for reduced matrix models in structural dynamics475 cited
  • 2007Sparse grid collocation schemes for stochastic natural convection problems401 cited
  • 1986Probabilistic finite elements for nonlinear structural dynamics396 cited
  • 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation345 cited

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  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
  • 1972Random Eigenvalue Problems in Structural Analysis205 cited
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