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

Abstract

Here, 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.

Authors:
 [1];  [1];  [1]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1472255
Alternate Identifier(s):
OSTI ID: 1701800
Report Number(s):
SAND2018-9779J
Journal ID: ISSN 0021-9991; 667654
Grant/Contract Number:  
AC04-94AL85000; NA0003525
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 374; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Monte Carlo; Stochastic Galerkin; Polynomial chaos; Linear elliptic partial differential equations; Uncertainty quantification; Moment estimation

Citation Formats

Chowdhary, Kenny, Safta, Cosmin, and Najm, Habib N. Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.07.004.
Chowdhary, Kenny, Safta, Cosmin, & Najm, Habib N. Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques. United States. https://doi.org/10.1016/j.jcp.2018.07.004
Chowdhary, Kenny, Safta, Cosmin, and Najm, Habib N. 2018. "Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques". United States. https://doi.org/10.1016/j.jcp.2018.07.004. https://www.osti.gov/servlets/purl/1472255.
@article{osti_1472255,
title = {Enhancing statistical moment calculations for stochastic Galerkin solutions with Monte Carlo techniques},
author = {Chowdhary, Kenny and Safta, Cosmin and Najm, Habib N.},
abstractNote = {Here, 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.},
doi = {10.1016/j.jcp.2018.07.004},
url = {https://www.osti.gov/biblio/1472255}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 374,
place = {United States},
year = {Mon Jul 23 00:00:00 EDT 2018},
month = {Mon Jul 23 00:00:00 EDT 2018}
}