Primal and Dual Interface Concentrated Iterative Substructuring Methods

Abstract

This paper is devoted to the fast solution of interface concentrated finite element equations. The interface concentrated finite element schemes are constructed on the basis of a nonoverlapping domain decomposition where a conforming boundary concentrated finite element approximation is used in every subdomain. Similar to boundary element domain decomposition methods, the total number of unknowns per subdomain behaves like $O((H/h)^{(d-1)})$, where H, h, and d denote the usual scaling parameter of the subdomains, the average discretization parameter of the subdomain boundaries, and the spatial dimension, respectively. We propose and analyze primal and dual substructuring iterative methods which asymptotically exhibit the same or at least almost the same complexity as the number of unknowns. In particular, the so-called all-floating finite element tearing and interconnecting solvers are highly parallel and very robust with respect to large coefficient jumps.