Title: Three-level BDDC in Two Dimensions


Author: Xuemin Tu

BDDC methods are nonoverlapping iterative substructuring domain decomposition
methods for the solutions of large sparse linear algebraic systems arising from discretization
of elliptic boundary value problems. They are similar to the balancing Neumann-Neumann algorithm.
However, in BDDC methods, a small number of continuity constraints are enforced across the interface,
and these constraints form a new coarse, global component. An important advantage of using such
constraints is that the Schur complements that arise in the computation willa ll be strictly positive
definite. The coarse problem is generated and factored by a direct solver at the beginning of the
computation. However, this problem 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 two dimensional space, while still maintaining a good convergence rate.
Estimates of the condition numbers are provided for the two three-level BDDC methods and numerical
experiments are also discussed.