Resilient asynchronous primal Schur method

Guillaume Gbikpi-Benissan; Frédéric Magoulès

Applications of Mathematics (2022)

  • Volume: 67, Issue: 6, page 679-704
  • ISSN: 0862-7940

Abstract

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This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.

How to cite

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Gbikpi-Benissan, Guillaume, and Magoulès, Frédéric. "Resilient asynchronous primal Schur method." Applications of Mathematics 67.6 (2022): 679-704. <http://eudml.org/doc/298529>.

@article{Gbikpi2022,
abstract = {This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.},
author = {Gbikpi-Benissan, Guillaume, Magoulès, Frédéric},
journal = {Applications of Mathematics},
keywords = {asynchronous iterations; Schur complement method; domain decomposition method; parallel computing},
language = {eng},
number = {6},
pages = {679-704},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Resilient asynchronous primal Schur method},
url = {http://eudml.org/doc/298529},
volume = {67},
year = {2022},
}

TY - JOUR
AU - Gbikpi-Benissan, Guillaume
AU - Magoulès, Frédéric
TI - Resilient asynchronous primal Schur method
JO - Applications of Mathematics
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 6
SP - 679
EP - 704
AB - This paper introduces the application of asynchronous iterations theory within the framework of the primal Schur domain decomposition method. A suitable relaxation scheme is designed, whose asynchronous convergence is established under classical spectral radius conditions. For the usual case where local Schur complement matrices are not constructed, suitable splittings based only on explicitly generated matrices are provided. Numerical experiments are conducted on a supercomputer for both Poisson's and linear elasticity problems. The asynchronous Schur solver outperformed the classical conjugate-gradient-based one in case of computing node failures.
LA - eng
KW - asynchronous iterations; Schur complement method; domain decomposition method; parallel computing
UR - http://eudml.org/doc/298529
ER -

References

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