(A) FETI formulation with mortar methods using locally nonconforming elements

Abstract

The FETI method is a domain decomposition method, for which Lagrange multipliers are introduced at the substructure interfaces to enforce the continuity of the displacement field. It is especially efficient for large-scale problems occurring in solid and fluid mechanics. Although the original FETI method was developed for conforming finite elements, it can be extended for nonconforming finite elements using mortar methods. Mortar methods allow for nonconforming finite elements in which independent discretizations in each subdomain as well as nonmatching grids at the interfaces are possible. In this thesis, we apply the FETI method for two dimensional linear elliptic boundary value problems discretized by locally nonconforming elements(Crouzeix-Raviart elements) with mortar methods. We also show the superiority of the FETI operator with the Neumann-Dirichlet preconditioner proposed by Kim and Lee.