Computing

, Volume 95, Issue 12, pp 1087–1119 | Cite as

Adaptive-Multilevel BDDC and its parallel implementation

Article

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.

Keywords

Parallel algorithms Domain decomposition Iterative substructuring BDDC Adaptive constraints Multilevel algorithms  

Mathematics Subject Classification (2000)

65N55 65M55 65Y05 

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Copyright information

© Springer-Verlag Wien 2013

Authors and Affiliations

  • Bedřich Sousedík
    • 1
    • 2
  • Jakub Šístek
    • 3
  • Jan Mandel
    • 4
  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Institute of ThermomechanicsAcademy of Sciences of the Czech RepublicPrague 8Czech Republic
  3. 3.Institute of MathematicsAcademy of Sciences of the Czech RepublicPrague 1Czech Republic
  4. 4.Department of Mathematical and Statistical SciencesUniversity of Colorado DenverDenverUSA

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