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

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

Research output: Contribution to journalArticlepeer-review

Abstract

We present a novel approach for solving steady-state stochastic partial differential equations in 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. Our results show that accurate global solutions can be obtained with significantly reduced computational costs.

Original languageEnglish (US)
Pages (from-to)203-215
Number of pages13
JournalJournal of Computational Physics
Volume351
DOIs
StatePublished - Dec 15 2017
Externally publishedYes

Keywords

  • Basis adaptation
  • Dimension reduction
  • Domain decomposition
  • Polynomial chaos
  • Uncertainty quantification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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