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:
-
- 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}
}