A hybrid domain decomposition method based on one-level FETI and BDDC algorithms

A three-level domain decomposition is considered. Bodies in contact with each other are divided into subdomains, which in turn are the union of elements. Using an approach based purely on FETI (finite element tearing and interconnecting) algorithms with only Lagrange multipliers as unknowns, which has been developed by the engineering community, does not lead to a scalable algorithm with respect to the number of subdomains in each body. Instead, we consider a new method based on the saddle point formulation of the FETI methods with both displacement vectors and Lagrange multipliers as unknowns. The resulting system is solved with a block-diagonal preconditioner which combines the one-level FETI and the BDDC (balancing domain decomposition by constraints) methods. We show that this new method is scalable with respect to the number of subdomains. A model contact problem is solved by a nonlinear algorithm which combines the new method and a primal-dual active set method.