A dual iterative substructuring method with a penalty term

An iterative substructuring method with Lagrange multipliers is considered for the second order elliptic problem, which is a variant of the FETI-DP method. The standard FETI-DP formulation is associated with the saddle-point problem which is induced from the minimization problem with a constraint for imposing the continuity across the interface. Starting from the slightly changed saddle-point problem by addition of a penalty term with a positive penalization parameter η, we propose a dual substructuring method which is implemented iteratively by the conjugate gradient method. Performance of such a dual iterative substructuring method is directly connected with the condition number of a relevant dual system. For η = 0, the proposed method is reduced to the FETI-DP method. For the preconditioned FETI-DP with the optimal Dirichlet preconditioner, it is well-known that the condition number is bounded by a polylogarithmic factor: (1+ log(H/h)) in two dimensions and (H/h)(1+ log(H/h)) in three dimensions. To the contrary, in spite of the absence of any preconditioners, it is shown that the proposed method is numerically scalable in the sense that for a large value of η, the condition number of the resultant dual problem is bounded by a constant independent of both the subdomain size H and the mesh size h. We deal with a computational issue and present numerical results. Furthermore, we extend the proposed method to the three dimensional problem.