Results 171 to 180 of about 720 (188)

Computational Aspects of Stochastic Collocation with Multifidelity Models

SIAM/ASA Journal on Uncertainty Quantification, 2014
In this paper we discuss a numerical approach for the stochastic collocation method with multifidelity simulation models. The method we consider was recently proposed in [A. Narayan, C. Gittelson, and D. Xiu, SIAM J. Sci. Comput., 36 (2014), pp. A495--A521] to combine the computational efficiency of low-fidelity models with the high accuracy of high ...
Xueyu Zhu, Akil Narayan 0001, Dongbin Xiu   +2 more
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STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION

International Journal for Uncertainty Quantification, 2012
Summary: The idea of \(\ell_1\)-minimization is the basis of the widely adopted compressive sensing method for function approximation. In this paper, we extend its application to high-dimensional stochastic collocation methods. To facilitate practical implementation, we employ orthogonal polynomials, particularly Legendre polynomials, as basis ...
Yan, Liang, Guo, Ling, Xiu, Dongbin
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Stochastic Collocation Method for Stochastic Optimal Boundary Control of the Navier–Stokes Equations

Applied Mathematics & Optimization, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenju Zhao, Max Gunzburger
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The convergence problem of collocation solutions in the framework of the stochastic interpretation

Journal of Geodesy, 2010
The convergence of the collocation solution to the true gravity field is a problem defined long ago; some results were derived, in particular by T. Krarup, already in 1981. The problem is taken up again in the context of the stochastic interpretation of collocation theory and some new results are derived, showing that, when the potential T can be ...
SANSO', FERNANDO, VENUTI, GIOVANNA
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Collocation methods for nonlinear stochastic Volterra integral equations

Computational and Applied Mathematics, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoli Xu, Yu Xiao, Haiying Zhang
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Stochastic Projection and Collocation

2018
This chapter is concerned with expansions of functions of random variables in terms of common random variables. The chapter covers spectral expansions (polynomial chaos methods) and computational realizations of this using quadrature, collocation, and Galerkin projection. Sparse quadratures are also discussed to evaluate multiple dimensional integrals.
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Global Sensitivity Analysis for Stochastic Collocation

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th AIAA/ASME/AHS Adaptive Structures Conference<BR> 12th, 2010
Non-intrusive stochastic expansion methods for uncertainty quantication (UQ) has received a great deal of attention the past decade because of their rigorous mathematical foundations and their ability to e ciently accurately characterize the probablilistic metrics of complex engineering systems.
Gary Tang, Gianluca Iaccarino, Michael Eldred   +2 more
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Unscented transform and stochastic collocation methods for stochastic electromagnetic compatibility

CEM'11 Computational Electromagnetics International Workshop, 2011
This paper deals with the current growing interest concerning the use of stochastic techniques for electromagnetic compatability (EMC) issues. Various methods allow to face this problem: obviously, we may focus on the Monte Carlo (MC) formalism but other techniques have been implemented more recently (the unscented transform, UT, or stochastic ...
Sebastien Lallechere, Pierre Bonnet, Ibrahim El Baba, Francoise Paladian   +3 more
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Stochastic boundary collocation and spectral methods for solving PDEs

Monte Carlo Methods and Applications, 2012
We develop a stochastic boundary method (SBM) which can be considered as a randomized version of the method of fundamental solutions (MFS). We suggest solving the large system of linear equations for the weights in the expansion over the fundamental solutions by a randomized SVD method introduced by Sabelfeld and Mozartova (2011).
Karl Sabelfeld, Nadezhda Mozartova
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A Fast Collocation Method for Solving Stochastic Integral Equations

SIAM Journal on Numerical Analysis, 2009
Based on sparse grid multiscale piecewise polynomial bases, we develop a fast collocation method for solving Fredholm integral equations of the second kind with stochastic loading terms. It is proved that the proposed method preserves the optimal rate of convergence and has linear (up to a logarithmic factor) computational complexity.
Yanzhao Cao, Bin Wu, Yuesheng Xu
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