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


Journal Article

© 2017 Society for Industrial and Applied Mathematics. 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.

Full Text

Duke Authors

Cited Authors

  • Mycek, P; Rizzi, F; Le Maître, O; Sargsyan, K; Morris, K; Safta, C; Debusschere, B; Knio, O

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 39 / 1

Start / End Page

  • C1 - C28

Electronic International Standard Serial Number (EISSN)

  • 1095-7200

International Standard Serial Number (ISSN)

  • 1064-8275

Digital Object Identifier (DOI)

  • 10.1137/15M1051786

Citation Source

  • Scopus