Inexact Data-Sparse Boundary Element Tearing and Interconnecting Methods

The Boundary Element Tearing and Interconnecting (BETI) methods have recently been introduced as boundary element counterparts of the well–established Finite Element Tearing and Interconnecting (FETI) methods. In this paper we present inexact data–sparse versions of the BETI methods which avoid the elimination of the primal unknowns and dense matrices. However, instead of symmetric and positive definite systems, we finally have to solve two–fold saddle point problems. The proposed iterative solvers and preconditioners result in almost optimal solvers the complexity of which is proportional to the number of unknowns on the skeleton up to some polylogarithmical factor. Moreover, the solvers are robust with respect to large coefficient jumps.