A Three-Level BDDC Algorithm for Mortar Discretizations

In this talk, three-level BDDC algorithms will be presented for the solutions of large sparse linear algebraic systems arising from the mortar discretization of elliptic boundary value problems. The mortar discretization is considered on geometrically non-conforming subdomain partitions. In the algorithms, the large coarse problems from two-level BDDC algorithms are solved approximately while a good rate of convergence is maintained. This is an extension of previous work for the three-level BDDC algorithms with standard finite element discretization by Tu [12,13]. Estimates of the condition numbers are provided for the three-level BDDC methods and numerical experiments are also discussed.