Computing

, Volume 83, Issue 2–3, pp 55–85 | Cite as

Multispace and multilevel BDDC

  • Jan Mandel
  • Bedřich Sousedík
  • Clark R. Dohrmann
Article
First Online:
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Accepted:

Abstract

The Balancing Domain Decomposition by Constraints (BDDC) method is the most advanced method from the Balancing family of iterative substructuring methods for the solution of large systems of linear algebraic equations arising from discretization of elliptic boundary value problems. In the case of many substructures, solving the coarse problem exactly becomes a bottleneck. Since the coarse problem in BDDC has the same structure as the original problem, it is straightforward to apply the BDDC method recursively to solve the coarse problem only approximately. In this paper, we formulate a new family of abstract Multispace BDDC methods and give condition number bounds from the abstract additive Schwarz preconditioning theory. The Multilevel BDDC is then treated as a special case of the Multispace BDDC and abstract multilevel condition number bounds are given. The abstract bounds yield polylogarithmic condition number bounds for an arbitrary fixed number of levels and scalar elliptic problems discretized by finite elements in two and three spatial dimensions. Numerical experiments confirm the theory.

Keywords

Iterative substructuring Additive Schwarz method Balancing domain decomposition BDD BDDC Multispace BDDC Multilevel BDDC 

Mathematics Subject Classification (2000)

65N55 65M55 65Y05 
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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Jan Mandel
    • 1
  • Bedřich Sousedík
    • 1
    • 2
  • Clark R. Dohrmann
    • 3
  1. 1.Department of Mathematical and Statistical SciencesUniversity of Colorado DenverDenverUSA
  2. 2.Institute of ThermomechanicsAcademy of Sciences of the Czech RepublicPrague 8Czech Republic
  3. 3.Structural Dynamics Research DepartmentSandia National LaboratoriesAlbuquerqueUSA

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