A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

Paul Mycek*, Andres Contreras, Olivier Le Maître, Khachik Sargsyan, Francesco Rizzi, Karla Morris, Cosmin Safta, Bert Debusschere, Omar Knio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

Original languageEnglish (US)
Pages (from-to)18-34
Number of pages17
JournalComputer Physics Communications
StatePublished - Jul 2017


  • Exascale computing
  • Polynomial chaos
  • Resilience
  • Uncertainty quantification

ASJC Scopus subject areas

  • Hardware and Architecture
  • General Physics and Astronomy


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