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A stochastic-deterministic coupling method for continuum mechanics
8 references·5 citing·35 second hop
A stochastic-deterministic coupling method for continuum mechanics (2011)A stochastic-deterministic coupling metho…The stochastic finite element method: Past, present and future (2008)The stochastic finite element…Domain decomposition of stochastic PDEs: Theoretical formulations (2008)Domain decomposition of stoch…A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations (2008)A stochastic coupling method …Stochastic model reduction for chaos representations (2007)Stochastic model reduction fo…Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure (2004)Physical Systems with Random …Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations (2004)Galerkin Finite Element Appro…Numerical solution of spectral stochastic finite element systems (1996)Numerical solution of spectra…Stochastic Finite Elements: A Spectral Approach (1991)Stochastic Finite Elements: A…A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities (2018)A multiscale method for semi-…A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities (2018)A multiscale method for semi-…Asynchronous space–time domain decomposition method with localized uncertainty quantification (2017)Asynchronous space–time domai…Error estimation and model adaptation for a stochastic‐deterministic coupling method based on the Arlequin framework (2013)Error estimation and model ad…A coupling method for stochastic continuum models at different scales (2013)A coupling method for stochas…A multiscale stochastic finite element method on elliptic problems involving uncertainties (2007)Random matrix theory for modeling uncertainties in computational mechanics (2004)Comput. Methods Appl. Mech. Engrg. (2010)A reduced spectral function approach for the stochastic finite element analysis (2011)A multiscale method with patch for the solution of stochastic partial differential equations with localized uncertainties (2012)The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (2002)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)Structural Reliability under Incomplete Probability Information (1986)Optimal Discretization of Random Fields (1993)Comparison of finite element reliability methods (2002)Uncertainty propagation in CFD using polynomial chaos decomposition (2006)Stochastic finite element methods for partial differential equations with random input data (2014)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)Solution of stochastic partial differential equations using Galerkin finite element techniques (2001)A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007)Multiscale Uncertainty Quantification Based on a Generalized Hidden Markov Model (2011)A New Sampling Approach for Response Surface Method Based Reliability Analysis and Its Application (2014)Estimation of small failure probabilities in high dimensions by subset simulation (2001)Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion (2014)Direct probability integral method for stochastic response analysis of static and dynamic structural systems (2019)Recent Trends in the Modeling and Quantification of Non-probabilistic Uncertainty (2019)Global sensitivity analysis using polynomial chaos expansions (2007)Adaptive sparse polynomial chaos expansion based on least angle regression (2010)Spectral Methods for Uncertainty Quantification (2010)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)Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion (2012)
this work references cited by second hop

References

  • 1991Stochastic Finite Elements: A Spectral Approach5,753 cited
  • 2008The stochastic finite element method: Past, present and future999 cited
  • 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations869 cited
  • 2004Physical Systems with Random Uncertainties: Chaos Representations with Arbitrary Probability Measure609 cited
  • 1996Numerical solution of spectral stochastic finite element systems294 cited
  • 2007Stochastic model reduction for chaos representations191 cited
  • 2008Domain decomposition of stochastic PDEs: Theoretical formulations65 cited
  • 2008A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations35 cited

Cited by

  • 2018A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities18 cited
  • 2013Error estimation and model adaptation for a stochastic‐deterministic coupling method based on the Arlequin framework11 cited
  • 2018A multiscale method for semi-linear elliptic equations with localized uncertainties and non-linearities11 cited
  • 2017Asynchronous space–time domain decomposition method with localized uncertainty quantification9 cited
  • 2013A coupling method for stochastic continuum models at different scales8 cited

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