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

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 nonmatching 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 of literatures 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 [6] for noncomparably nonmatching grids, while the superiority of the preconditioner by Dryja and Widlund [2] is confirmed for matching grids and comparably nonmatching grids.