Sparse high order FEM for elliptic sPDEs

By Marcel Bieri, Christoph Schwab. 2009

159 citations recorded by the source corpus.

Subfields: Environmental Engineering, Mechanics of Materials, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b97a93de9a3e96b69c507189159246678b00a059

How researchers see this paper

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

In Environmental Engineering

1. Houman Owhadi
2. Alireza Doostan
3. M. Christie
4. Mohammad Hossein Ahmadi
5. Hamid Bazargan
6. Ahmed H. Elsheikh
7. Roman Andreev
8. Ivan V. Oseledets

In Mechanics of Materials

1. Alireza Doostan
2. Roman Andreev
3. Houman Owhadi
4. Ivan V. Oseledets
5. M. Christie
6. Ahmed H. Elsheikh
7. Mohammad Hossein Ahmadi
8. Hamid Bazargan

In Statistics and Probability

1. Alireza Doostan
2. Ahmed H. Elsheikh
3. Houman Owhadi
4. M. Christie
5. Mohammad Hossein Ahmadi
6. Hamid Bazargan
7. Roman Andreev
8. Gianluca Iaccarino

Citations in the corpus

• A non-adapted sparse approximation of PDEs with stochastic inputs (2010, methodology): “Among them are the multi-scale model reduction of [33] and the sparse decomposition of [60,8,6,7] for the stochastic Galerkin technique, adaptive sparse regression approaches of [10,11] for PC expansions, anisotropic and adaptive sparse grids of [50,44] for the stochastic collocation scheme, and the”
• Non-intrusive low-rank separated approximation of high-dimensional stochastic models (2012, background): “The relevance of the sparse PC approximation of PDEs with random inputs has been discussed in several work including [11, 20, 27].”
• Metamodel-based sensitivity analysis: polynomial chaos expansions and Gaussian processes (2016, unknown): “In order to find directly the significant polynomials and associated coefficients, sparse PCE have been introduced recently by Blatman and Sudret [10, 11]; Bieri and Schwab [8].”
• Constructive Representation of Functions in Low-Rank Tensor Formats (2012, background): “Low-parametric approximation of multivariate functions is very important in high-dimensional applications (financial mathematics [33, 36], quantum chemistry [18, 19, 22], multiparametric and stochastic problems [3], and numerical analysis and sci-entific computing [10, 20, 23]).”
• Surrogate accelerated sampling of reservoir models with complex structures using sparse polynomial chaos expansion (2015, methodology): “Among them are the multi-scale model reduction of [57] and the sparse decomposition of [60, 59, 58] for the stochastic Galerkin technique, anisotropic and adaptive sparse grids of [51, 62, 61] for the stochastic collocation scheme, and low-rank solution approximations of [63, 64, 65, 78].”
• Sparse tensor approximation of parametric eigenvalue problems (2012, methodology): “The multiindex sets Λ(μ, ε) were introduced in [9] and investigated in the context of the stochastic Galerkin method for elliptic stochastic PDEs in [8].”