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Adaptive-Multilevel BDDC and its parallel implementation

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Abstract

We combine the adaptive and multilevel approaches to the BDDC and formulate a method which allows an adaptive selection of constraints on each decomposition level. We also present a strategy for the solution of local eigenvalue problems in the adaptive algorithm using the LOBPCG method with a preconditioner based on standard components of the BDDC. The effectiveness of the method is illustrated on several engineering problems. It appears that the Adaptive-Multilevel BDDC algorithm is able to effectively detect troublesome parts on each decomposition level and improve convergence of the method. The developed open-source parallel implementation shows a good scalability as well as applicability to very large problems and core counts.

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Notes

  1. http://www.math.cas.cz/~sistek/software/bddcml.html.

  2. http://code.google.com/p/blopex.

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Acknowledgments

We would like to thank to Jaroslav Novotný, Jan Leština, Radim Blaheta, and Jiří Starý for providing data of real engineering problems. This work was supported in part by National Science Foundation under grant DMS-1216481, by Czech Science Foundation under grant GA ČR 106/08/0403, and by the Academy of Sciences of the Czech Republic through RVO:67985840. B. Sousedík acknowledges support from the DOE/ASCR and the NSF PetaApps award number 0904754. J. Šístek acknowledges the computing time on Hector supercomputer provided by the PRACE-DECI initiative. A part of the work was done at the University of Colorado Denver when B. Sousedík was a graduate student and during visits of J. Šístek, partly supported by the Czech-American Cooperation program of the Ministry of Education, Youth and Sports of the Czech Republic under research project LH11004.

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Authors and Affiliations

  1. Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA, 90089-2531, USA

    Bedřich Sousedík

  2. Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Dolejškova 1402/5, CZ, 182 00 , Prague 8, Czech Republic

    Bedřich Sousedík

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 , Prague 1, Czech Republic

    Jakub Šístek

  4. Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO, 80217-3364, USA

    Jan Mandel

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  1. Bedřich Sousedík
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  2. Jakub Šístek
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  3. Jan Mandel
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Correspondence to Jakub Šístek.

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Dedicated to Professor Ivo Marek on the occasion of his 80th birthday.

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Sousedík, B., Šístek, J. & Mandel, J. Adaptive-Multilevel BDDC and its parallel implementation. Computing 95, 1087–1119 (2013). https://doi.org/10.1007/s00607-013-0293-5

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