Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

Tipireddy, R.; Stinis, P.; Tartakovsky, A. M.

doi:10.1016/j.jcp.2017.08.067

Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

Journal Article · Mon Sep 04 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.08.067· OSTI ID:1379948

Tipireddy, R. ^[1]; Stinis, P. ^[1]; Tartakovsky, A. M. ^[1]

Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

In this paper, we present a novel approach for solving steady-state stochastic partial differential equations (PDEs) with high-dimensional random parameter space. The proposed approach combines spatial domain decomposition with basis adaptation for each subdomain. The basis adaptation is used to address the curse of dimensionality by constructing an accurate low-dimensional representation of the stochastic PDE solution (probability density function and/or its leading statistical moments) in each subdomain. Restricting the basis adaptation to a specific subdomain affords finding a locally accurate solution. Then, the solutions from all of the subdomains are stitched together to provide a global solution. We support our construction with numerical experiments for a steady-state diffusion equation with a random spatially dependent coefficient. Lastly, our results show that highly accurate global solutions can be obtained with significantly reduced computational costs.

View Accepted Manuscript (DOE)

Research Organization:: Pacific Northwest National Laboratory (PNNL), Richland, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)

Grant/Contract Number:: AC05-76RL01830

OSTI ID:: 1379948

Alternate ID(s):: OSTI ID: 1549945
OSTI ID: 22701644
OSTI ID: 1395272

Report Number(s):: PNNL-SA--115134; PII: S0021999117306484

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 351; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Stochastic basis adaptation and spatial domain decomposition for PDEs with random coefficients Tipireddy, Ramakrishna; Stinis, Panos; Tartakovsky, Alexandre arXiv https://doi.org/10.48550/arxiv.1709.02488	preprint	January 2017

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Basis adaptation and domain decomposition for steady partial differential equations with random coefficients

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