Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques

JOURNAL OF COMPUTATIONAL PHYSICS

卷:374

Article

Chowdhary, Kenny¹  Safta, Cosmin¹  Najm, Habib N.¹ 

[1] Sandia Natl Labs, Livermore, CA 94550 USA

关键词: Monte Carlo;    Stochastic Galerkin;    Polynomial chaos;    Linear elliptic partial differential equations;    Uncertainty quantification;    Moment estimation;   

DOI  :  10.1016/j.jcp.2018.07.004

来源: Elsevier

【 摘 要 】

In this work, we provide a method for enhancing stochastic Galerkin moment calculations to the linear elliptic equation with random diffusivity using an ensemble of Monte Carlo solutions. This hybrid approach combines the accuracy of low-order stochastic Galerkin and the computational efficiency of Monte Carlo methods to provide statistical moment estimates which are significantly more accurate than performing each method individually. The hybrid approach involves computing a low-order stochastic Galerkin solution, after which Monte Carlo techniques are used to estimate the residual. We show that the combined stochastic Galerkin solution and residual is superior in both time and accuracy for a one-dimensional test problem and a more computational intensive two-dimensional linear elliptic problem for both the mean and variance quantities. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free