A Numerical Study of FETI Algorithms for Mortar Finite Element Methods

The Finite Element Tearing and Interconnecting (FETI) method is an iterative substructuring method using Lagrange multipliers to enforce the continuity of the nite element solution across the subdomain interface. Mortar nite elements are nonconforming nite elements that allow for a geometrically nonconforming decomposition of the computational domain into subregions and, at the same time, for the optimal coupling of di erent variational approximations in di erent subregions. We present a numerical study of FETI algorithms for elliptic self{adjoint equations discretized by mortar nite elements. Several preconditioners which have been successful for the case of conforming nite elements are considered. We compare the performance of our algorithms when applied to classical mortar elements and to a new family of biorthogonal mortar elements and discuss the di erences between enforcing mortar conditions instead of continuity conditions for the case of matching nodes across the interface. Our experiments are carried out for both two and three dimensional problems, and include a study of the relative costs of applying di erent preconditioners for mortar elements.