Results 151 to 160 of about 641 (195)
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Stochastic Collocation Methods for Nonlinear Parabolic Equations with Random Coefficients
SIAM/ASA Journal on Uncertainty Quantification, 2016Summary: We evaluate the performance of global stochastic collocation methods for solving nonlinear parabolic and elliptic problems (e.g., transient and steady nonlinear diffusion) with random coefficients. The robustness of these and other strategies based on a spectral decomposition of stochastic state variables depends on the regularity of the ...
Barajas-Solano, David A. +1 more
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Comparison between Wiener chaos methods and stochastic collocation methods
2017In the last two chapters, we incorporated the recursive strategy into both Wiener chaos expansion (WCE) methods and stochastic collocation methods (SCM). In this chapter, we will compare both methods for linear stochastic advection-reaction-diffusion equations with commutative and noncommutative noises. To make a fair comparison, we develop a recursive
Zhongqiang Zhang, George Em Karniadakis
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Stochastic Collocation Methods via Minimisation of the Transformed L1-Penalty
East Asian Journal on Applied Mathematics, 2018The sparse reconstruction of functions via a transformed $ℓ_1$ (TL1) minimisation is studied and theoretical results concerning recoverability and accuracy of such reconstruction from undersampled measurements are obtained. To identify the coefficients of sparse orthogonal polynomial expansions in uncertainty quantification, the method is combined with
Guo, Ling, Li, Jing, Liu, Yongle
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Numerical solution of stochastic models using spectral collocation method
2023Summary: In this article, the spectral collocation method based on radial basis functions is used to solve the mentioned models. The advantage of this method is that it converts the equations into a system of algebraic equations. Therefore, we can solve this problem with Newton's method.
Abdous, Mehrnosh +2 more
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Stochastic boundary collocation and spectral methods for solving PDEs
Monte Carlo Methods and Applications, 2012We 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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Application of collocation method to stochastic conservation laws
2017In this chapter we demonstrate how to apply the methods we presented in the previous chapters to stochastic nonlinear conservations laws. Specifically, since the problem is nonlinear we apply the stochastic collocation method (SCM) using Smolyak’s sparse grid for a one-dimensional piston problem and test its computational performance.
Zhongqiang Zhang, George Em Karniadakis
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Stochastic analysis of unsaturated flow with probabilistic collocation method
Water Resources Research, 2009In this study, we present an efficient approach, called the probabilistic collocation method (PCM), for uncertainty analysis of flow in unsaturated zones, in which the constitutive relationship between the pressure head and the unsaturated conductivity is assumed to follow the van Genuchten‐Mualem model.
Weixuan Li, Zhiming Lu, Dongxiao Zhang
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New collocation method for stochastic response surface reliability analyses
Engineering with Computers, 2019The stochastic response surface method (SRSM) is widely used in engineering reliability analyses due to its efficiency and accuracy. The selection of collocation points in the SRSM has great significance, as it may strongly affect the computed results. This paper investigates the performance of different selection strategies in SRSM, and proposes a new
Peng Zeng +5 more
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Stochastic Reachability Analysis using Sparse-Collocation Method
AIAA SCITECH 2023 Forum, 2023Amit Jain, Puneet Singla
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Applications of Stochastic Collocation Method in Electromagnetic Compatibility
2017The paper reviews the use of deterministic-stochastic models in some electromagnetic compatibility (EMC) applications where the uncertainty in input data set exists. In other words, of interest are cases where some properties of a system are partly or entirely unknown.
Poljak, Dragan +4 more
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