A dual iterative substructuring method with a penalty term in three dimensions

The FETI-DP method is one of the most advanced dual substructuring methods, which introduces Lagrange multipliers to enforce the pointwise matching condition on the interface. In our previous work for two dimensional problems, a dual iterative substructuring method was proposed, which is a variant of the FETI-DP method based on the way to deal with the continuity constraint on the interface. The proposed method imposes the continuity not only by the pointwise matching condition on the interface but also by using a penalty term which measures the jump across the interface. In this paper, a dual substructuring method with a penalty term is extended to three dimensional problems. A penalty term with a penalization parameter ηη is constructed by focusing on the geometric complexity of an interface in three dimensions caused by the coupling among adjacent subdomains. For a large ηη, it is shown that the condition number of the resultant dual problem is bounded by a constant independent of both subdomain size HH and mesh size hh. From the implementational viewpoint of the proposed method, the difference from the FETI-DP method is to solve subdomain problems which contain a penalty term with a penalization parameter ηη. To prevent a large penalization parameter from making subdomain problems ill-conditioned, special attention is paid to establish an optimal preconditioner with respect to a penalization parameter ηη. Finally, numerical results are presented.