Direct Schur complement method by domain decomposition based on H-matrix approximation

The goal of this paper is the construction of a data-sparse approximation to the Schur complement on the interface corresponding to FEM and BEM approximations of an elliptic equation by domain decomposition. Using the hierarchical (H-matrix) formats we elaborate the approximate Schur complement inverse in an explicit form. The required cost O(N-Gamma log(q) N-Gamma) is almost linear in N-Gamma -the number of degrees of freedom on the interface. As input, we require the Schur complement matrices corresponding to subdomains and represented in the H-matrix format. In the case of piecewise constant coefficients these matrices can be computed via the BEM representation with the cost O(N-Gamma log(q) N-Gamma), while in the general case the FEM discretisation leads to the complexity O(N-Omega log(q) N-Omega), where N-Omega is the number of degrees of freedom in the domain.