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Stochastic Basis Adaptation and Spatial Domain Decomposition for Partial Differential Equations with Random Coefficients
11 references·1 citing·33 second hop
Stochastic Basis Adaptation and Spatial Domain Decomposition for Partial Differential Equations with Random Coefficients (2018)Stochastic Basis Adaptation and Spatial D…Addressing the curse of dimensionality in SSFEM using the dependence of eigenvalues in KL expansion on domain size (2016)Addressing the curse of dimen…Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs (2015)Local Polynomial Chaos Expans…A non-adapted sparse approximation of PDEs with stochastic inputs (2011)A non-adapted sparse approxim…Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids (2010)Uncertainty quantification vi…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2010)A Stochastic Collocation Meth…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 Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites (2004)A Two-Scale Nonperturbative A…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …On solving elliptic stochastic partial differential equations (2002)On solving elliptic stochasti…The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables (1999)The Nonlinear Gaussian Spectr…Conditional Karhunen–Loève regression model with Basis Adaptation for high-dimensional problems: Uncertainty quantification and inverse modeling (2023)Conditional Karhunen–Loève re…Stochastic Differential Equations: An Introduction with Applications. (1987)Stochastic Finite Elements: A Spectral Approach (1991)To be or not to be intrusive? The solution of parametric and stochastic equations - the "plain vanilla" Galerkin case. (2013)Collocation methods for fuzzy uncertainty propagation in heat conduction problem (2016)Global Sensitivity Analysis for Uncertain Parameters, Models, and Scenarios (2016)Probability, statistics, and decision for civil engineers (1970)Simulation of Stochastic Processes by Spectral Representation (1991)Spectral stochastic uncertainty quantification in chemical systems (2004)Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields (2007)Stochastic Finite Elements (2009)Modeling uncertainty in flow simulations via generalized polynomial chaos (2003)A least-squares approximation of partial differential equations with high-dimensional random inputs (2009)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)Stochastic modeling of uncertainties in computational structural dynamics—Recent theoretical advances (2011)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)A new surrogate modeling technique combining Kriging and polynomial chaos expansions – Application to uncertainty analysis in computational dosimetry (2015)POLYNOMIAL-CHAOS-BASED KRIGING (2015)Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark (2021)Verification and Validation in Computational Science and Engineering (1998)Non-Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators (2005)On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data (2006)Global sensitivity analysis using polynomial chaos expansions (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)An adaptive high-dimensional stochastic model representation technique for the solution of stochastic partial differential equations (2010)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)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)Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization (2018)A Critical Appraisal of Design of Experiments for Uncertainty Quantification (2017)Adaptive experimental design for multi‐fidelity surrogate modeling of multi‐disciplinary systems (2022)Enforcing positivity in intrusive PC-UQ methods for reactive ODE systems (2014)Algorithms for Propagating Uncertainty Across Heterogeneous Domains (2015)Stochastic Resin Transfer Molding Process (2017)
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References

  • 2002The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations4,821 cited
  • 2008A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data942 cited
  • 2011A non-adapted sparse approximation of PDEs with stochastic inputs436 cited
  • 2010A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data400 cited
  • 2002On solving elliptic stochastic partial differential equations198 cited
  • 2007Stochastic model reduction for chaos representations191 cited
  • 1999The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables130 cited
  • 2010Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids59 cited
  • 2015Local Polynomial Chaos Expansion for Linear Differential Equations with High Dimensional Random Inputs39 cited
  • 2004A Two-Scale Nonperturbative Approach to Uncertainty Analysis of Diffusion in Random Composites26 cited
  • 2016Addressing the curse of dimensionality in SSFEM using the dependence of eigenvalues in KL expansion on domain size15 cited

Cited by

  • 2023Conditional Karhunen–Loève regression model with Basis Adaptation for high-dimensional problems: Uncertainty quantification and inverse modeling6 cited

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