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Hierarchical parallelisation for the solution of stochastic finite element equations
12 references·16 citing·31 second hop
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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
  • 1997Stochastic Analysis1,035 cited
  • 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations556 cited
  • 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos552 cited
  • 1997A state-of-the-art report on computational stochastic mechanics424 cited
  • 1997Uncertainties in probabilistic numerical analysis of structures and solids-Stochastic finite elements354 cited
  • 1996Numerical solution of spectral stochastic finite element systems294 cited
  • 2020Stochastic partial differential equations216 cited
  • 1991Computational Stochastic Mechanics215 cited
  • 2002On solving elliptic stochastic partial differential equations198 cited
  • 1998Probabilistic characterization of transport in heterogeneous media166 cited

Cited by

  • 2004Uncertainty Quantification with Stochastic Finite Elements70 cited
  • 2015On the dual iterative stochastic perturbation-based finite element method in solid mechanics with Gaussian uncertainties56 cited
  • 2010

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eXtended Stochastic Finite Element Method for the numerical simulation of heterogeneous materials with random material interfaces
55 cited
  • 2010Comput. Methods Appl. Mech. Engrg.51 cited
  • 2009Generalized stochastic perturbation technique in engineering computations50 cited
  • 2014A new perspective on the solution of uncertainty quantification and reliability analysis of large-scale problems47 cited
  • 2017A Copula-based perturbation stochastic method for fiber-reinforced composite structures with correlations40 cited
  • 2013A hybrid spectral and metamodeling approach for the stochastic finite element analysis of structural dynamic systems35 cited
  • 2009A reduced-order stochastic finite element approach for design optimization under uncertainty34 cited
  • 2016The performance prediction and optimization of the fiber-reinforced composite structure with uncertain parameters32 cited
  • 2011On the Capabilities of the Polynomial Chaos Expansion Method within SFE Analysis—An Overview32 cited
  • 2021Structural stochastic responses determination via a sample-based stochastic finite element method30 cited
  • 2009Parallel processing in structural reliability29 cited
  • 2013Generalized Neumann Expansion and Its Application in Stochastic Finite Element Methods24 cited
  • 2017A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner–Mindlin plates23 cited
  • 2007On stochastic finite element method for linear elastostatics by the Taylor expansion23 cited