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Use of the Stochastic Collocation Method in Discrete Event Simulations
Proceedings of the 50th Computer Simulation Conference, 2018 Stochastic discrete event models commonly use continuous probability distributions to represent model parameters such as entity arrival rates or processing times.
Seck, Mamadou, Diouf, Fatou
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A Fast Collocation Method for Solving Stochastic Integral Equations
SIAM Journal on Numerical Analysis, 2009Based on sparse grid multiscale piecewise polynomial bases, we develop a fast collocation method for solving Fredholm integral equations of the second kind with stochastic loading terms. It is proved that the proposed method preserves the optimal rate of convergence and has linear (up to a logarithmic factor) computational complexity.
Yanzhao Cao, Bin Wu, Yuesheng Xu
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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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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 ...
David A. Barajas-Solano +1 more
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A Stochastic Collocation Method for Simulating Groundwater Recharge
Advanced Materials Research, 2014We propose a stochastic collocation method based on sparse tensor product spaces to efficiently estimate groundwater recharge. The spatial variability of hydraulic conductivity of soil usually leads to the uncertainty of groundwater recharge.
Yun Qing Tang +2 more
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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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Journal of Biomechanical Engineering, 2011
Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input ...
Sethuraman, Sankaran, Alison L, Marsden
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Simulations of blood flow in both healthy and diseased vascular models can be used to compute a range of hemodynamic parameters including velocities, time varying wall shear stress, pressure drops, and energy losses. The confidence in the data output from cardiovascular simulations depends directly on our level of certainty in simulation input ...
Sethuraman, Sankaran, Alison L, Marsden
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ON THE OPTIMAL POLYNOMIAL APPROXIMATION OF STOCHASTIC PDES BY GALERKIN AND COLLOCATION METHODS
Mathematical Models and Methods in Applied Sciences, 2012In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by multivariate polynomials.
Beck, Joakim +3 more
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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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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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