Stochastic finite element: a non intrusive approach by regression

By Marc Berveiller, Bruno Sudret, Maurice Lemaire. 2006

456 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Environmental Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/6b296c15de06abeef97cdd06b0cc4bea6a28ca55

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

In Environmental Engineering

In Statistics and Probability

Citations in the corpus

Global sensitivity analysis using polynomial chaos expansions (2008, methodology): “Alternatively, non intrusive methods have been recently proposed (Field, 2002; Ghiocel and Ghanem, 2002; Choi et al., 2004; Berveiller et al., 2006).”
Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations (2015, methodology): “…methods (Ghiocel and Ghanem, 2002; Le Maitre et al., 2002), stochastic or probabilistic collocation methods (Xiu and Hesthaven, 2005), gradient-based methods also known as collocation methods coupled with sensitivity derivatives (Perez, 2008), and regression methods (Berveiller et al., 2006).”
Recent Developments in Spectral Stochastic Methods for the Numerical Solution of Stochastic Partial Differential Equations (2009, methodology): “Regression Regression methods [15, 27, 28, 123] rely on the same principles as classical response surface methods [62].”
The stochastic finite element method: Past, present and future (2009, methodology): “Thus, this method can be considered as a polynomial response surface approach in which the coefficients are calculated using the Galerkin method [15].”
Polynomial-Chaos-based Kriging (2015, unknown): “This pio-neering approach called spectral stochastic ﬁnite element method (SSFEM), was later developed by Xiu and Karniadakis (2002); Sudret et al. (2004); Wan and Karniadakis (2005, 2006); Berveiller et al. (2006a), among others.”
Stochastic analysis of the fracture toughness of polymeric nanoparticle composites using polynomial chaos expansions (2017, methodology): “From various non-intrusive methods, the regression method in Berveiller et al. (2006), Choi et al. (2004), Sudret (2008) is exploited in this study.”
A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations (2007, unknown): “Non-intrusive techniques, such as Monte-Carlo simulation [1,2], response surface method, projection [3] or regression [4] methods, have the great advantage that they only require the use of a simple deterministic calculation code.”
Reliability-based design optimization using kriging surrogates and subset simulation (2011, methodology): “Various surrogates have been used in the structural reliability literature out of which: polynomial response surfaces (Faravelli, 1989; Bucher and Bourgund, 1990; Kim and Na, 1997; Das and Zheng, 2000), polynomial chaos expansions (Sudret and Der Kiureghian, 2002; Berveiller et al., 2006; Blatman an”
Adaptive sparse polynomial chaos expansion based on least angle regression (2011, methodology): “Two approaches based on a PC representation of the response are usually distinguished: – the projection approach: each PC coefficient is recast as a multidimensional integral [7, 8] which can be computed either by simulation or quadrature; – the regression approach [9, 10, 11, 12]: the PC coefficien”