All-floating coupled data-sparse boundary and interface-concentrated finite element tearing and interconnecting methods

Abstract

Efficient and robust tearing and interconnecting solvers for large scale systems of coupled boundary and finite element domain decomposition equations are the main topic of this paper. In order to reduce the complexity of the finite element part from $${\mathcal{O}}((H/h)^{d})$$ to $${\mathcal{O}}((H/h)^{d-1})$$ , we use an interface-concentrated hp finite element approximation. The complexity of the boundary element part is reduced by data-sparse approximations of the boundary element matrices. Finally, we arrive at a parallel solver whose complexity behaves like $${\mathcal{O}}((H/h)^{d-1})$$ up to some polylogarithmic factor, where H, h, and d denote the usual scaling parameters of the subdomains, the minimal discretization parameter of the subdomain boundaries, and the spatial dimension, respectively.