Paper Info
Title
Multispace and multilevel BDDC
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.
Year
DOI
Venue
2008
10.1007/s00607-008-0014-7
Computing
Keywords
DocType
Volume
abstract multilevel condition number,multilevel BDDC,BDDC method recursively,bdd,arbitrary fixed number,iterative substructuring,balancing domain decomposition,bddc,condition number bound,coarse problem,abstract Multispace BDDC method,multispace bddc,multilevel bddc,abstract bound,additive schwarz method,Multilevel BDDC,Multispace BDDC,abstract additive
Journal
83
Issue
ISSN
Citations 
2-3
1436-5057
9
PageRank 
References 
Authors
0.63
6
3
Name
Order
Citations
PageRank
Jan Mandel144469.36
bedřich sousedik2285.50
Clark R. Dohrmann323329.31