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Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection
16 references·5 citing·17 second hop
Multiscale Stochastic Preconditioners in Non-intrusive Spectral Projection (2011)Multiscale Stochastic Preconditioners in …Spectral methods for uncertainty quantification : with applications to computational fluid dynamics (2010)Spectral methods for uncertai…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A Stochastic Collocation Meth…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…Sparse grid collocation schemes for stochastic natural convection problems (2007)Sparse grid collocation schem…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Stochastic finite element: a non intrusive approach by regression (2006)Stochastic finite element: a …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…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…Multi-resolution analysis of Wiener-type uncertainty propagation schemes (2004)Multi-resolution analysis of …Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection (2003)Uncertainty quantification in…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)Solution of stochastic partia…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins (2017)Uncertainty Quantification of…Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems (2014)Enforcing positivity in intru…Preconditioned Bayesian Regression for Stochastic Chemical Kinetics (2013)Preconditioned Bayesian Regre…On spectral methods for variance based sensitivity analysis (2013)On spectral methods for varia…Simplified CSP analysis of a stiff stochastic ODE system (2012)Simplified CSP analysis of a …Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems (2003)A non-adapted sparse approximation of PDEs with stochastic inputs (2011)Stochastic Differential Equations: An Introduction with Applications. (1987)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)Simulation-based optimal Bayesian experimental design for nonlinear systems (2012)Compressive sampling of polynomial chaos expansions: Convergence analysis and sampling strategies (2014)Stochastic finite element methods for partial differential equations with random input data (2014)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)Efficient Collocational Approach for Parametric Uncertainty Analysis (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Stochastic spectral methods for efficient Bayesian solution of inverse problems (2006)
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References

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  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2005High-Order Collocation Methods for Differential Equations with Random Inputs1,522 cited
  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2005An adaptive multi-element generalized polynomial chaos method for stochastic differential equations578 cited
  • 2010Spectral methods for uncertainty quantification : with applications to computational fluid dynamics572 cited
  • 2006Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures498 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
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  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data

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400 cited
  • 2004Multi-resolution analysis of Wiener-type uncertainty propagation schemes335 cited
  • 2003Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection333 cited
  • Cited by

    • 2017Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins22 cited
    • 2013Preconditioned Bayesian Regression for Stochastic Chemical Kinetics18 cited
    • 2014Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems15 cited
    • 2012Simplified CSP analysis of a stiff stochastic ODE system14 cited
    • 2013On spectral methods for variance based sensitivity analysis13 cited