Preconditioners for the dual-primal FETI methods on nonmatching grids: Numerical study

The FETI-DP method is a substructuring method that uses Lagrange multipliers to match the continuity condition on the subdomain boundaries. For the FETI-DP method on non-matching grids, two different formulations are known with respect to how to employ the mortar matching condition. Keeping step with the developments of the FETI-DP methods, a variety of preconditioners for the FETI-DP operator have been developed. However, there has not been any numerical study for the FETI-DP method, which compares those preconditioners on nonmatching grids while there have been a few papers for numerical study on the comparison of FETI preconditioners. Therefore, we present the numerical study of four different preconditioners for two-dimensional elliptic problems. The numerical results confirm the superiority of the preconditioner by Kim and Lee [1] for noncomparably nonmatching grids, while the superiority of the preconditioner by Dryja and Widlund [2] is confirmed for matching grids and comparably nonmatching grids.