Title: BDDC Domain Decomposition Algorithms: Methods with Three Levels  and for Flow in Porous Media


Authors:  Xuemin Tu


Two inexact coarse solvers for Balancing Domain Decomposition by Constraints (BDDC) algorithms are introduced and analyzed. These solvers help remove a bottleneck for the two-level BDDC algorithms related to the cost of the coarse problem when the number of subdomains is large. At the same time, a good convergence rate is maintained.
BDDC algorithms are also developed for the linear systems arising from flow in porous media discretized with mixed and hybrid finite elements. Our methods are proven to be scalable and the condition numbers of the operators with our BDDC preconditioners grow only polylogarithmically with the size of the subdomain problems.