Extended preconditioners for the FETI method applied to constrained problems

An e cient and simple approach for handling linear multipoint constraints in a class of substructurebased solvers, namely the nite element tearing and interconnecting (FETI) method, is proposed. Previously, it was argued that multipoint constraints should be handled in FETI by adding a second level iteration on a coarse grid such that the FETI iterates satisfy the multipoint constraints exactly. The procedure presented here does not require an additional coarse grid but instead takes account of the multipoint constraints in the preconditioning step. The preconditioning strategy is shown to be mechanically consistent and to incur only a small additional computational cost. This strategy is simpler and computationally less expensive than the two-level FETI procedure. Its numerical scalability even for highly heterogeneous problems is demonstrated in several test examples