Výsledky vyhledávání - Stochastic Galerkin methods. Stochastic Collocation methods

Stochastic collocation and stochastic Galerkin methods for linear differential algebraic equations Autor Pulch, Roland

“… Alternatively, stochastic collocation methods or the stochastic Galerkin approach yield larger coupled systems of differential algebraic equations…”
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Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients Autor Nobile, F., Tempone, Raul

“… The stochastic coefficients of the PDE are approximated by truncated Karhunen–Loève expansions driven by a finite number of uncorrelated random variables…”
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A Sparse Grid Stochastic Collocation Discontinuous Galerkin Method for Constrained Optimal Control Problem Governed by Random Convection Dominated Diffusion Equations Autor Ge, Liang, Sun, Tongjun

“…A sparse grid stochastic collocation method combined with discontinuous Galerkin method is developed for solving convection dominated diffusion optimal control problem with random coefficients…”
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On the efficacy of stochastic collocation, stochastic Galerkin, and stochastic reduced order models for solving stochastic problems Autor Field, R.V., Grigoriu, M., Emery, J.M.

“…The stochastic collocation (SC) and stochastic Galerkin (SG) methods are two well-established and successful approaches for solving general stochastic problems…”
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A stochastic kinetic scheme for multi-scale plasma transport with uncertainty quantification Autor Xiao, Tianbai, Frank, Martin

“… methods are often employed at separate scales with corresponding assumptions and approximations…”
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On the relationship between the stochastic Galerkin method and the pseudo-spectral collocation method for linear differential algebraic equations Autor Manfredi, Paolo, De Zutter, Daniël, Vande Ginste, Dries

“… Most of the implementations are based on either the intrusive stochastic Galerkin method or on non-intrusive collocation approaches, of which a very common example is the pseudo-spectral method based…”
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On collocation-Galerkin method and fractional B-spline functions for a class of stochastic fractional integro-differential equations Autor Masti, I., Sayevand, K.

“…In recent years, as detailed in several monographs, derivations of the fractional differential equations and fractional integral equations are based on random functional or stochastic equations…”
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High-Order Collocation Methods for Differential Equations with Random Inputs Autor Xiu, Dongbin, Hesthaven, Jan S.

“… To this end, stochastic Galerkin methods appear to be superior to other nonsampling methods and, in many cases, to several sampling methods…”
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A stochastic kinetic scheme for multi-scale flow transport with uncertainty quantification Autor Xiao, Tianbai, Frank, Martin

“…•An accelerative hybrid Galerkin-collocation method is proposed for the treatment of source term in the kinetic equation…”
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A Legendre–Galerkin Chebyshev collocation method for the Burgers equation with a random perturbation on boundary condition Autor Pan, Jiajia, Wu, Hua

“… Firstly, the stochastic Galerkin method combined with the Legendre–Galerkin Chebyshev collocation scheme is adopted, which means that the original equation…”
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A multiscale stochastic finite element method on elliptic problems involving uncertainties Autor Xu, X. Frank

“… method and stochastic collocation method are introduced and combined with deterministic multiscale methods, i.e…”
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Performance Comparison of the SGM and the SCM in EMC Simulation Autor Jinjun Bai, Gang Zhang, Di Wang, Duffy, Alistair P., Lixin Wang

“… the reliability of simulation results. The Stochastic Galerkin Method (SGM) and the Stochastic Collocation Method (SCM…”
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Numerical comparison of three stochastic methods for nonlinear PN junction problems Autor Yao, Wenqi, Lu, Tiao

“…We apply the Monte Carlo, stochastic Galerkin, and stochastic collocation methods to solving the drift-diffusion equations coupled with the Poisson equation arising in semiconductor devices with random rough surfaces…”
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Optimal control with stochastic PDE constraints and uncertain controls Autor Rosseel, Eveline, Wells, Garth N.

“… It is shown that applying the stochastic collocation finite element method to the formulated…”
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On stability and monotonicity requirements of finite difference approximations of stochastic conservation laws with random viscosity Autor Pettersson, Per, Doostan, Alireza, Nordström, Jan

“…The stochastic Galerkin and collocation methods are used to solve an advection–diffusion equation with uncertain and spatially varying viscosity…”
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Polynomial Chaos Based Statistical Analysis of the Shielding Effectiveness of an Enclosure With Apertures Under Multiple Uncertainties Autor Wang, Jinping, Nie, Bao-Lin, Yang, Yanfu, Zhang, Wei, Wang, Jiabao, Du, Pingan

“…This article presents an efficient statistical analysis of the shielding effectiveness (SE) of an enclosure with apertures under multiple uncertainties. It…”
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Explicit cost bounds of stochastic Galerkin approximations for parameterized PDEs with random coefficients Autor Dexter, Nick C., Webster, Clayton G., Zhang, Guannan

“…This work analyzes the overall computational complexity of the stochastic Galerkin finite element method (SGFEM…”
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Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs Autor Nobile, F., Tamellini, L., Tempone, R.

“…: “On the optimal polynomial approximation of stochastic PDEs by Galerkin and collocation methods…”
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Uncertainty Quantification of Crosstalk Using Stochastic Reduced Order Models Autor Fei, Zhouxiang, Huang, Yi, Zhou, Jiafeng, Xu, Qian

“… It is nonintrusive, accurate, efficient, and stable, thus could be a promising alternative to some well-established methods, such as the Stochastic Galerkin and stochastic collocation (SC) methods…”
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Entropy Stable Galerkin Methods with Suitable Quadrature Rules for Hyperbolic Systems with Random Inputs Autor Zhong, Xinghui, Shu, Chi-Wang

“…) approximations, which is one of the most popular methods for uncertainty quantification (UQ) and can be implemented with either the stochastic Galerkin (SG…”
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