A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data

By Fabio Nobile, Raúl Tempone, Clayton G. Webster. SIAM Journal on Numerical Analysis, 2008

614 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2f0be89e6ce2a14ab0a57783d4295915c57c01cf

Citations in the corpus

• Non-intrusive reduced order modelling of the Navier-Stokes equations (2015, neutral): “This sparse grid method has been widely applied in various applications [26–28], including numerical integration [29], partial differential equations [30], economics [31,32], stochastic natural convection problems [33], sensitivity analysis [34], portfolio problems [35] and high dimensional interpol”
• Convergence Rates of Best N-term Galerkin Approximations for a Class of Elliptic sPDEs (2010, neutral): “Let us mention that other strategies for selecting the sparse polynomial spaces in the variable y ∈U have been proposed and investigated recently in [13–15] based on the concept of sparse grid introduced in [18].”
• Stochastic Spectral Galerkin and Collocation Methods for PDEs with Random Coefficients: A Numerical Comparison (2011, neutral): “[26, 16, 9] and the references therein.”
• A non-adapted sparse approximation of PDEs with stochastic inputs (2010, neutral): “Stochastic collocation schemes [58,45,66,1,51] belong to a different class of methods that rely upon (isotropic) sparse grid integration/ interpolation in the stochastic space of the problem to reduce the curse-of-dimensionality associated with the conventional”
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs (2015, neutral): “Collocation methods [10, 12, 7, 21, 22, 4] produce a polynomial approximation in XΛ based on the data of particular solution instances u := u(y) for some chosen values y ∈ Γ of the parameter vector with i = 1, .”
• Stochastic Galerkin Methods for the Boltzmann-Poisson system (2019, neutral): “An overview of several UQ approaches for hyperbolic and kinetic equations in particular can be found in [6], [7], [8], [9], [10], [11].”
• Sparse adaptive Taylor approximation algorithms for parametric and stochastic elliptic PDEs (2011, neutral): “This is the point of view adopted for example in [16, 21, 2, 15, 1, 24, 25].”
• Polynomial chaos expansions for dependent random variables (2019, neutral): “, Gaussian) quadrature rules that are optimal for tensor product approximation [46, 41].”
• Efficient Analysis of High Dimensional Data in Tensor Formats (2012, neutral): “3 Quadrature rules and sparse integration grids Sparse grids are usually used together with collocation method [39] or for computing PCE coefficents of random fields κ(x, ω), f(x, ω) and u(x, ω) (the last are used, for instance, for building the response surface of the solution [29, 30]).”
• Analytic regularity and polynomial approximation of parametric and stochastic elliptic PDEs (2010, neutral): “This is the point of view adopted for example in [14, 16, 4, 13, 3, 18, 19].”