A new coarse space for overlapping Schwarz algorithms for H(curl) problems in three dimensions with irregular subdomains

Abstract

A new coarse space for a two-level overlapping Schwarz algorithm is presented for problems posed in three dimensions in the space H(curl, Ω). Previous studies for these methods are very restrictive about the geometry of the subdomains while this new space is well defined for general subdomains. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are used on the overlapping subdomains. The algorithm can be defined for any subdomain geometry and works for highly discontinuous coefficient distributions. Numerical experiments with irregular subdomains and different coefficient distributions are presented. The algorithm appears very promising even for random and discontinuous values of the coefficients.

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Acknowledgments

The author would like to thank his former advisor, Prof. Olof Widlund, for his valuable guidance and suggestions during the work on this article. The author gratefully acknowledges the institutional support for the project B5A28 subscribed to the Vice-Rectory for Research, University of Costa Rica.

Funding

This work was supported in part by the National Science Foundation Grant Nos. DMS-1216564 and DMS-1522736.

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Correspondence to Juan G. Calvo.

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Calvo, J.G. A new coarse space for overlapping Schwarz algorithms for H(curl) problems in three dimensions with irregular subdomains. Numer Algor 83, 885–899 (2020). https://doi.org/10.1007/s11075-019-00707-9

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Keywords

  • Domain decomposition
  • Overlapping Schwarz algorithms
  • Irregular subdomain boundaries
  • H(curl)
  • Maxwell’s equations
  • Discontinuous coefficients

Mathematics Subject Classification (2010)

  • 35Q60
  • 65F10
  • 65N30
  • 65N55