Grid transfer operators for highly variable coefficient problems in two-level non-overlapping domain decomposition methods

  • Giraud L
  • Guevara Vasquez F
  • Tuminaro R
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Abstract

The authors propose a robust interpolation scheme for non-overlapping
two-level domain decomposition methods applied to two-dimensional
elliptic problems with discontinuous coefficients. The goal is to
treat efficiently the case where discontinuities are not aligned
with the boundaries of the subdomains. That interpolation is used
to design a preconditioner closely related to the BPS scheme proposed
in [J. H. Bramble, J. E. Pasciak and A. H. Schatz, Math. Comp. 47
(1986), no. 175, 103--134; MR0842125 (87m:65174)]. Through several
experiments on structured and unstructured grids the authors show
that for smooth problems the new preconditioning scheme reduces to
the BPS method but outperforms it on problems where the jumps are
not aligned with subdomain interfaces. In particular, the algorithm
also maintains good scalable convergence behaviour in that case.

Author-supplied keywords

  • Discontinuous coefficients
  • Domain decomposition
  • Elliptic partial differential equations
  • Parallel distributed computing
  • Schur complement
  • Two-level preconditioning

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Authors

  • L. Giraud

  • F. Guevara Vasquez

  • R. S. Tuminaro

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