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

Journal Article · Mon Jul 23 00:00:00 EDT 2018 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2018.07.004· OSTI ID:1472255

Chowdhary, Kenny ^[1]; Safta, Cosmin ^[1]; Najm, Habib N. ^[1]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)

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.

• Research Organization: Sandia National Laboratories (SNL-CA), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21). Scientific Discovery through Advanced Computing (SciDAC)
• Grant/Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1472255
• Alternate ID(s): OSTI ID: 1701800; OSTI ID: 23078089
• Report Number(s): SAND2018--9779J; 667654
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 374; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Linear elliptic partial differential equations
Moment estimation
Monte Carlo
Polynomial chaos
Stochastic Galerkin
Uncertainty quantification