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STOCHASTIC COLLOCATION ALGORITHMS USING l1-MINIMIZATION
International Journal for Uncertainty Quantification, 2012Summary: 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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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, 2010Non-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 +2 more
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Stochastic Collocation Method for Stochastic Optimal Boundary Control of the Navier–Stokes Equations
Applied Mathematics & Optimization, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenju Zhao, Max Gunzburger
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Unscented transform and stochastic collocation methods for stochastic electromagnetic compatibility
CEM'11 Computational Electromagnetics International Workshop, 2011This 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 +3 more
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A Stochastic Collocation Algorithm with Multifidelity Models
SIAM Journal on Scientific Computing, 2014We present a numerical method for utilizing stochastic models with differing fideli- ties to approximate parameterized functions. A representative case is where a high-fidelity and a low-fidelity model are available. The low-fidelity model represents a coarse and rather crude ap- proximation to the underlying physical system.
Akil Narayan +2 more
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Stochastic Projection and Collocation
2018This 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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Efficient Stochastic Optimization using Chaos Collocation Method with modeFRONTIER
SAE International Journal of Materials and Manufacturing, 2008<div class="htmlview paragraph">Robust Design Optimization (RDO) using traditional approaches such as Monte Carlo (MC) sampling requires tremendous computational expense. Performing a RDO for problems involving time consuming CAE analysis may not even be possible within time constraints.
PEDIRODA, VALENTINO +5 more
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AIP Conference Proceedings, 2012
In this paper, we investigate the model of three-dimensional (3D) stochastic multi-symplectic Hamiltonian Maxwell's equations, and consider the stochastic multi-symplectic numerical methods of solving such equations. In particular, multi-symplectic wavelet collocation method (MSWCM) is applied to such equations.
Jialin Hong, Lihai Ji
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In this paper, we investigate the model of three-dimensional (3D) stochastic multi-symplectic Hamiltonian Maxwell's equations, and consider the stochastic multi-symplectic numerical methods of solving such equations. In particular, multi-symplectic wavelet collocation method (MSWCM) is applied to such equations.
Jialin Hong, Lihai Ji
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An h-adaptive stochastic collocation method for stochastic EMC/EMI analysis
2010 IEEE Antennas and Propagation Society International Symposium, 2010The analysis of electromagnetic compatibility and interference (EMC/EMI) phenomena is often fraught by randomness in a system's excitation (e.g., the amplitude, phase, and location of internal noise sources) or configuration (e.g., the routing of cables, the placement of electronic systems, component specifications, etc.).
Abdulkadir C Yucel +2 more
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