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Probabilistic models for stochastic elliptic partial differential equations
11 references·12 citing·37 second hop
Probabilistic models for stochastic elliptic partial differential equations (2010)Probabilistic models for stochastic ellip…The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications (2008)The multi-element probabilist…A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)A Stochastic Collocation Meth…Karhunen–Loève approximation of random fields by generalized fast multipole methods (2006)Karhunen–Loève approximation …Evaluation of Karhunen–Loève, Spectral, and Sampling Representations for Stochastic Processes (2006)Evaluation of Karhunen–Loève,…On the accuracy of the polynomial chaos approximation (2004)On the accuracy of the polyno…Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Finite elements for elliptic problems with stochastic coefficients (2004)Finite elements for elliptic …Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering (2004)Efficient iterative algorithm…Stochastic Calculus: Applications in Science and Engineering (2002)Stochastic Calculus: Applicat…Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions (1995)Applied non-Gaussian processe…Extremes and related properties of random sequences and processes (1984)Extremes and related properti…A spectral surrogate model for stochastic simulators computed from trajectory samples (2023)A spectral surrogate model fo…Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion (2022)Stochastic analysis of struct…Independent component analysis-based arbitrary polynomial chaos method for stochastic analysis of structures under limited observations (2022)Independent component analysi…Distribution-free P-box processes based on translation theory: Definition and simulation (2022)Distribution-free P-box proce…3rd-order Spectral Representation Method: Simulation of multi-dimensional random fields and ergodic multi-variate random processes with fast Fourier transform implementation (2021)3rd-order Spectral Representa…Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials (2020)Modeling non-Gaussian random …Bayesian identification and model comparison for random property fields derived from material microstructure (2020)Bayesian identification and m…The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling (2019)The dynamic analysis of stoch…Microstructure Models and Material Response by Extreme Value Theory (2016)Microstructure Models and Mat…Response Statistics for Random Heterogeneous Microstructures (2014)Response Statistics for Rando…Stochastic collocation with kernel density estimation (2012)Stochastic collocation with k…A method for solving stochastic equations by reduced order models and local approximations (2012)A method for solving stochast…The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)High-Order Collocation Methods for Differential Equations with Random Inputs (2005)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)Stochastic Finite Elements: A Spectral Approach (1991)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)Random vibration and statistical linearization (1990)Verification and Validation in Computational Science and Engineering (1998)Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations (2004)Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics (2008)An Introduction to Computational Stochastic PDEs (2014)Simulation of Stochastic Processes by Spectral Representation (1991)Random vibration of mechanical and structural systems (1993)Reliability assessment in structural dynamics (2013)Simulation of multi-dimensional random fields by Karhunen–Loève expansion (2017)An explicit method for simulating non-Gaussian and non-stationary stochastic processes by Karhunen-Loève and polynomial chaos expansion (2018)Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements (1997)Implementation of Karhunen–Loeve expansion for simulation using a wavelet-Galerkin scheme (2002)Assessment of spectral representation and Karhunen–Loève expansion methods for the simulation of Gaussian stochastic fields (2007)Karhunen–Loéve Expansion of Stochastic Processes with a Modified Exponential Covariance Kernel (2007)Stochastic Differential Equations (2003)Multi-element probabilistic collocation method in high dimensions (2009)Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems (2010)Time-dependent generalized polynomial chaos (2010)Probabilistic engineering mechanics (1993)Stochastic Finite Elements (2009)A simple and efficient methodology to approximate a general non-Gaussian stationary stochastic process by a translation process (2011)Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes (1989)The tail index of exchange rate returns (1990)Extreme events: dynamics, statistics and prediction (2011)Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010)Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients (2011)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Computational stochastic mechanics – recent advances (2001)Simulation of second-order processes using Karhunen–Loeve expansion (2002)
this work references cited by second hop

References

  • 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data1,396 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 1984Extremes and related properties of random sequences and processes485 cited
  • 2004Finite elements for elliptic problems with stochastic coefficients364 cited
  • 2006Karhunen–Loève approximation of random fields by generalized fast multipole methods355 cited
  • 2002Stochastic Calculus: Applications in Science and Engineering345 cited
  • 1995Applied non-Gaussian processes : examples, theory, simulation, linear random vibration, and MATLAB solutions288 cited
  • 2008The multi-element probabilistic collocation method (ME-PCM): Error analysis and applications214 cited
  • 2004On the accuracy of the polynomial chaos approximation140 cited
  • 2006Evaluation of Karhunen–Loève, Spectral, and Sampling Representations for Stochastic Processes103 cited
  • 2004Efficient iterative algorithms for the stochastic finite element method with application to acoustic scattering69 cited

Cited by

  • 2020Bayesian identification and model comparison for random property fields derived from material microstructure36 cited
  • 2023A spectral surrogate model for stochastic simulators computed from trajectory samples33 cited

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2012
A method for solving stochastic equations by reduced order models and local approximations
29 cited
  • 2022Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion24 cited
  • 2016Microstructure Models and Material Response by Extreme Value Theory20 cited
  • 20213rd-order Spectral Representation Method: Simulation of multi-dimensional random fields and ergodic multi-variate random processes with fast Fourier transform implementation20 cited
  • 2022Independent component analysis-based arbitrary polynomial chaos method for stochastic analysis of structures under limited observations20 cited
  • 2020Modeling non-Gaussian random fields of material properties in multiscale mechanics of materials19 cited
  • 2022Distribution-free P-box processes based on translation theory: Definition and simulation16 cited
  • 2014Response Statistics for Random Heterogeneous Microstructures14 cited
  • 2012Stochastic collocation with kernel density estimation14 cited
  • 2019The dynamic analysis of stochastic thin-walled structures under thermal–structural–acoustic coupling10 cited