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Sparse grid

About: Sparse grid is a research topic. Over the lifetime, 1013 publications have been published within this topic receiving 20664 citations.


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Proceedings ArticleDOI
16 Apr 2007
TL;DR: A Spectral Stochastic Collocation Method is proposed for the capacitance extraction of interconnects with stochastic geometric variations for nanometer process technology and can achieve higher accuracy and faster convergence rate compared with the perturbation method.
Abstract: In this paper, a Spectral Stochastic Collocation Method (SSCM) is proposed for the capacitance extraction of interconnects with stochastic geometric variations for nanometer process technology. The proposed SSCM has several advantages over the existing methods. Firstly, compared with the PFA (Principal Factor Analysis) modeling of geometric variations, the K-L (Karhunen-Loeve) expansion involved in SSCM can be independent of the discretization of conductors, thus significantly reduces the computation cost. Secondly, compared with the perturbation method, the stochastic spectral method based on Homogeneous Chaos expansion has optimal (exponential) convergence rate, which makes SSCM applicable to most geometric variation cases. Furthermore, Sparse Grid combined with a MST (Minimum Spanning Tree) representation is proposed to reduce the number of sampling points and the computation time for capacitance extraction at each sampling point. Numerical experiments have demonstrated that SSCM can achieve higher accuracy and faster convergence rate compared with the perturbation method.

51 citations

Journal ArticleDOI
TL;DR: A new computational method to evaluate comprehensively the positional accuracy reliability for single coordinate, single point, multipoint and trajectory accuracy of industrial robots is proposed using the sparse grid numerical integration method and the saddlepoint approximation method.

51 citations

Journal ArticleDOI
TL;DR: A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme and the conditional mathematical expectations derived from the original equation are approximated using sparse-Grid Gauss-Hermite quadrature rule and (adaptive) hierarchical sparse- grid interpolation.
Abstract: A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and (adaptive) hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our s

51 citations

Journal ArticleDOI
TL;DR: In this article, the Galerkin finite-element method with bilinear trial functions was used to solve the linear reaction-diffusion problem on the unit square with homogeneous Dirichlet boundary conditions, where e is a small positive parameter and the problem is in general singularly perturbed.
Abstract: The linear reaction-diffusion problem -e 2 Δu + bu = f is considered on the unit square with homogeneous Dirichlet boundary conditions. Here e is a small positive parameter and the problem is in general singularly perturbed. The numerical solution of this problem is analysed on a Shishkin mesh that has N intervals in each coordinate direction, using the Galerkin finite-element method with bilinear trial functions. The accuracy of this method, measured in the associated energy norm, is shown to be O(N -2 + e 1/2 N -1 lnN). It is proved that a two-scale sparse grid method achieves the same order of accuracy while reducing the number of degrees of freedom from O(N 2 ) to O(N 3/2 ). These results are then generalized to systems of reaction-diffusion equations.

50 citations

Journal ArticleDOI
TL;DR: Based on a hierarchical structure of parameter, model, and scenario uncertainties and on recently developed techniques of model and scenario-averaging, this article derived new global sensitivity indices for multiple models and multiple scenarios.

50 citations

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202314
202242
202157
202040
201960
201872