SZodixStudyAcademic Library
ShelvesOpen access
Study · an open academic library·Metadata from OpenAlex (CC0)·Shelves·OpenAlex metadata, de-duplicated
Karhunen–Loève approximation of random fields by generalized fast multipole methods
4 references·16 citing·36 second hop
Karhunen–Loève approximation of random fields by generalized fast multipole methods (2006)Karhunen–Loève approximation of random fi…Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation (2004)Solving elliptic boundary val…Finite elements for elliptic problems with stochastic coefficients (2004)Finite elements for elliptic …The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)The Wiener--Askey Polynomial …Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen-Loève expansion (2019)Simulation of non-stationary …Analysis of the domain mapping method for elliptic diffusion problems on random domains (2016)Analysis of the domain mappin…Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format (2015)Polynomial Chaos Expansion of…Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs (2015)Error Analysis of the Dynamic…Practical Application of the Stochastic Finite Element Method (2014)Practical Application of the …Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Numerical methods for the dis…Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs (2013)Analytic Regularity and GPC A…Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem (2011)Uncertainty Quantification an…Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Multi-level Monte Carlo Finit…Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010)Convergence Rates of Best N-t…Sparse Tensor Discretization of Elliptic sPDEs (2009)Sparse Tensor Discretization …Polynomial chaos representation of spatio-temporal random fields from experimental measurements (2009)Polynomial chaos representati…Stochastic collocation and mixed finite elements for flow in porous media (2008)Stochastic collocation and mi…Sparse high order FEM for elliptic sPDEs (2008)Sparse high order FEM for ell…Efficient stochastic Galerkin methods for random diffusion equations (2008)Efficient stochastic Galerkin…Simulation of simply cross correlated random fields by series expansion methods (2007)Simulation of simply cross co…High-Order Collocation Methods for Differential Equations with Random Inputs (2005)Adaptive ANOVA decomposition of stochastic incompressible and compressible flows (2011)Optimal Uncertainty Quantification (2013)Metamodel-Based Sensitivity Analysis: Polynomial Chaos Expansions and Gaussian Processes (2015)Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Comparison of Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Quantification (2009)Recent Advances in Non-Intrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design (2009)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)Multilevel Monte Carlo Path Simulation (2008)Finite Element Error Analysis of Elliptic PDEs with Random Coefficients and Its Application to Multilevel Monte Carlo Methods (2013)Further analysis of multilevel Monte Carlo methods for elliptic PDEs with random coefficients (2013)Stochastic finite element methods for partial differential equations with random input data (2014)Fuzzy sets (1965)Fuzzy sets (1996)Stochastic model reduction for chaos representations (2007)Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009)The Logic of Scientific Discovery (2013)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)FReET: Software for the statistical and reliability analysis of engineering problems and FReET-D: Degradation module (2013)Towards efficient uncertainty quantification in complex and large-scale biomechanical problems based on a Bayesian multi-fidelity scheme (2014)Simulation of multi-dimensional random fields by Karhunen–Loève expansion (2017)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)A Critical Assessment of Kriging Model Variants for High-Fidelity Uncertainty Quantification in Dynamics of composite Shells (2016)Metamodel based high-fidelity stochastic analysis of composite laminates: A concise review with critical comparative assessment (2017)Structural Reliability Analysis and Prediction (2017)Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties (2019)Structural Reliability under Incomplete Probability Information (1986)The stochastic finite element method: Past, present and future (2008)An explicit method for simulating non-Gaussian and non-stationary stochastic processes by Karhunen-Loève and polynomial chaos expansion (2018)Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty (2019)Global sensitivity analysis using polynomial chaos expansions (2007)AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation (2011)Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs (2011)Enhancing ℓ1 -minimization estimates of polynomial chaos expansions using basis selection (2015)
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
  • 2004Finite elements for elliptic problems with stochastic coefficients364 cited
  • 2004Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation345 cited

Cited by

  • 2014Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion315 cited
  • 2010Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs306 cited
  • 2011Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients296 cited
  • 2014Practical Application of the Stochastic Finite Element Method144 cited
  • 2007Simulation of simply cross correlated random fields by series expansion methods143 cited
  • 2008Sparse high order FEM for elliptic sPDEs137 cited
  • 2019Simulation of non-stationary non-Gaussian random fields from sparse measurements using Bayesian compressive sampling and Karhunen-Loève expansion120 cited
  • 2009Sparse Tensor Discretization of Elliptic sPDEs107 cited
  • 2011Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem93 cited
  • 2008Efficient stochastic Galerkin methods for random diffusion equations

Only edges whose both ends are imported exist here. Widen the year window, or show the whole map. Back to the work

90 cited
  • 2009Polynomial chaos representation of spatio-temporal random fields from experimental measurements80 cited
  • 2015Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs72 cited
  • 2015Polynomial Chaos Expansion of Random Coefficients and the Solution of Stochastic Partial Differential Equations in the Tensor Train Format63 cited
  • 2016Analysis of the domain mapping method for elliptic diffusion problems on random domains62 cited
  • 2008Stochastic collocation and mixed finite elements for flow in porous media59 cited
  • 2013Analytic Regularity and GPC Approximation for Control Problems Constrained by Linear Parametric Elliptic and Parabolic PDEs56 cited