(A) numerical study of dual-primal FETI methods for two dimensional elliptic problems

Abstract

FETI-DP method is an iterative substructuring method that uses Lagrange multipliers to match the continuity condition on the subdomain boundaries. It was developed on matching grids first, and was developed on nonmatching grids recently. For the FETI-DP methods developed on nonmatching grids, two different formulations are known. Especially, for the FETI-DP formulation on nonmatching grids, mortar matching condition has been employed. Keeping step with the developments of the FETI-DP methods, a variety of preconditioners for the FETI-DP method have been developed. However, there has not been any the numerical study which compares those preconditioners while there have been a few of literatures for numerical study on the comparison of FETI preconditioners. Therefore, we would compare those preconditioners in this thesis and 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 for noncomparably nonmatching grids, while the superiority of the preconditioner by Dryja and Widlund is confirmed for matching and comparably nonmatching grids.