Discrete a priori bounds for the detection of corrupted PDE solutions in exascale computations

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

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A priori bounds are derived for the discrete solution of second-order elliptic partial differential equations (PDEs). The bounds have two contributions. First, the influence of boundary conditions is taken into account through a discrete maximum principle. Second, the contribution of the source field is evaluated in a fashion similar to that used in the treatment of the continuous a priori operators. Closed form expressions are, in particular, obtained for the case of a conservative, second-order finite difference approximation of the diffusion equation with variable scalar diffusivity. The bounds are then incorporated into a resilient domain decomposition framework, in order to verify the admissibility of local PDE solutions. The computations demonstrate that the bounds are able to detect most system faults, and thus considerably enhance the resilience and the overall performance of the solver.

Original languageEnglish (US)
Pages (from-to)C1-C28
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Society for Industrial and Applied Mathematics.


  • Discrete bounds
  • Domain decomposition
  • Elliptic PDE
  • Exascale computing
  • Maximum principle
  • Resilience

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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