scholarly journals The Exact Exponent of Sparse Grid Quadratures in the Weighted Case

2001 ◽  
Vol 17 (4) ◽  
pp. 840-849 ◽  
Author(s):  
Leszek Plaskota ◽  
Grzegorz W. Wasilkowski
Keyword(s):  
Sparse Grid ◽  
Weighted Case

Weighted higher order exponential type inequalities in metric spaces and applications

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huiju Wang ◽  
Pengcheng Niu
Keyword(s):  
Homogeneous Space ◽  
Lie Groups ◽  
Sobolev Spaces ◽  
Exponential Type ◽  
Metric Spaces ◽  
Type Inequality ◽  
Higher Order ◽  
Geodesic Space ◽  
Stratified Lie Groups ◽  
Weighted Case

AbstractIn this paper, we establish weighted higher order exponential type inequalities in the geodesic space {({X,d,\mu})} by proposing an abstract higher order Poincaré inequality. These are also new in the non-weighted case. As applications, we obtain a weighted Trudinger’s theorem in the geodesic setting and weighted higher order exponential type estimates for functions in Folland–Stein type Sobolev spaces defined on stratified Lie groups. A higher order exponential type inequality in a connected homogeneous space is also given.

scholarly journals Sparse grid-based adaptive noise reduction strategy for particle-in-cell schemes

2021 ◽  
pp. 100094
Author(s):  
Sriramkrishnan Muralikrishnan ◽  
Antoine J. Cerfon ◽  
Matthias Frey ◽  
Lee F. Ricketson ◽  
Andreas Adelmann
Keyword(s):  
Noise Reduction ◽  
Sparse Grid ◽  
Reduction Strategy ◽  
Particle In Cell ◽  
Adaptive Noise ◽  
Grid Based

scholarly journals Reliability-Based Topology Optimization Using Stochastic Response Surface Method with Sparse Grid Design

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Qinghai Zhao ◽  
Xiaokai Chen ◽  
Zheng-Dong Ma ◽  
Yi Lin
Keyword(s):  
Topology Optimization ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Computational Efficiency ◽  
Sparse Grid ◽  
Stochastic Response ◽  
Stochastic Response Surface Method ◽  
Surface Method ◽  
Grid Design

A mathematical framework is developed which integrates the reliability concept into topology optimization to solve reliability-based topology optimization (RBTO) problems under uncertainty. Two typical methodologies have been presented and implemented, including the performance measure approach (PMA) and the sequential optimization and reliability assessment (SORA). To enhance the computational efficiency of reliability analysis, stochastic response surface method (SRSM) is applied to approximate the true limit state function with respect to the normalized random variables, combined with the reasonable design of experiments generated by sparse grid design, which was proven to be an effective and special discretization technique. The uncertainties such as material property and external loads are considered on three numerical examples: a cantilever beam, a loaded knee structure, and a heat conduction problem. Monte-Carlo simulations are also performed to verify the accuracy of the failure probabilities computed by the proposed approach. Based on the results, it is demonstrated that application of SRSM with SGD can produce an efficient reliability analysis in RBTO which enables a more reliable design than that obtained by DTO. It is also found that, under identical accuracy, SORA is superior to PMA in view of computational efficiency.

Comparison of sparse-grid geometric and random sampling methods in nonlinear inverse solution uncertainty estimation

2012 ◽  
Vol 61 (1) ◽  
pp. 28-41 ◽  
Author(s):  
Michael J. Tompkins ◽  
Juan Luis Fernández Martínez ◽  
Zulima Fernández Muñiz
Keyword(s):  
Random Sampling ◽  
Sampling Methods ◽  
Uncertainty Estimation ◽  
Inverse Solution ◽  
Sparse Grid

Weighted renewal functions: a hierarchical approach

2002 ◽  
Vol 34 (02) ◽  
pp. 394-415 ◽  
Author(s):  
Edward Omey ◽  
Jef L. Teugels
Keyword(s):  
Hierarchical Approach ◽  
Weighting Coefficients ◽  
Weighted Case

We extend classical renewal theorems to the weighted case. A hierarchical chain of successive sharpenings of asymptotic statements on the weighted renewal functions is obtained by imposing stronger conditions on the weighting coefficients.

Propagation of Parametric Uncertainties in a Nonlinear Aeroelastic System Using an Improved Adaptive Sparse Grid Quadrature Routine

2018 ◽  
Vol 4 (4) ◽  
Author(s):  
Harshini Devathi ◽  
Sunetra Sarkar
Keyword(s):  
Basis Functions ◽  
Sparse Grid ◽  
Parametric Uncertainties ◽  
Relative Importance ◽  
Stochastic Response ◽  
Aeroelastic System ◽  
Accelerated Convergence ◽  
Aerodynamic Parameters ◽  
Stall Flutter ◽  
Sparse Grid Quadrature

A novel uncertainty quantification routine in the genre of adaptive sparse grid stochastic collocation (SC) has been proposed in this study to investigate the propagation of parametric uncertainties in a stall flutter aeroelastic system. In a hypercube stochastic domain, presence of strong nonlinearities can give way to steep solution gradients that can adversely affect the convergence of nonadaptive sparse grid collocation schemes. A new adaptive scheme is proposed here that allows for accelerated convergence by clustering more discretization points in regimes characterized by steep fronts, using hat-like basis functions with nonequidistant nodes. The proposed technique has been applied on a nonlinear stall flutter aeroelastic system to quantify the propagation of multiparametric uncertainty from both structural and aerodynamic parameters. Their relative importance on the stochastic response is presented through a sensitivity analysis.

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