Title: Three-Level BDDC in Three Dimensions

(NYU-CS-TR862)

Author:  Xuemin Tu

Abstract:
BDDC methods are nonoverlapping iterative substructuring domain decomposition 
methods for the solution of large sparse linear algebraic systems arising from 
discretization of elliptic boundary value problems. Its coarse problem is 
given by a  small number of continuity constraints which are enforced across 
the interface. The coarse problem matrix is generated and factored  by direct 
solvers at the beginning of the computation and it can ultimately become a 
bottleneck, if the number of subdomains is very large.   

In this paper, two three-level BDDC methods  are introduced for solving 
the coarse problem approximately in three dimensions. This is an extension 
of previous work for the two dimensional case and since vertex constraints 
alone do not suffice to obtain polylogarithmic condition number bound, edge 
constraints are considered in this paper. Some new technical tools are then 
needed in the analysis and this  makes the three dimensional case  more 
complicated than the two dimensional case.

Estimates of the condition numbers are provided for two three-level BDDC 
methods and numerical experiments are also discussed.