Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids

G. Lin, A. M. Tartakovsky, D. M. Tartakovsky

Research output: Contribution to journalArticlepeer-review


Quantitative predictions of the behavior of many deterministic systems are uncertain due to ubiquitous heterogeneity and insufficient characterization by data. We present a computational approach to quantify predictive uncertainty in complex phenomena, which is modeled by (partial) differential equations with uncertain parameters exhibiting multi-scale variability. The approach is motivated by flow in random composites whose internal architecture (spatial arrangement of constitutive materials) and spatial variability of properties of each material are both uncertain. The proposed two-scale framework combines a random domain decomposition (RDD) and a probabilistic collocation method (PCM) on sparse grids to quantify these two sources of uncertainty, respectively. The use of sparse grid points significantly reduces the overall computational cost, especially for random processes with small correlation lengths. A series of one-, two-, and three-dimensional computational examples demonstrate that the combined RDD-PCM approach yields efficient, robust and non-intrusive approximations for the statistics of diffusion in random composites.

Original languageEnglish (US)
Pages (from-to)6995-7012
Number of pages18
JournalJournal of Computational Physics
Issue number19
StatePublished - 2010
Externally publishedYes


  • Polynomial chaos
  • Random composite
  • Stochastic collocation method
  • Stochastic finite element
  • 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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