Abstract
BDDC (Balancing Domain Decomposition by Constraints) methods, so far developed for two levels [3, 7, 8], are similar to the balancing Neumann-Neumann algorithms. However, the BDDC coarse problem is given in terms of a set of primal constraints and the matrix of the coarse problem is generated and factored by direct solvers at the beginning of the computation. The coarse component of the preconditioner 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 and three dimensions, 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.
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