Dual Schur complement method for semi-definite problems

Semi-definite problems are encountered in a wide variety of engineering problems. Most domain decomposition methods efficient for parallel computing are based on iterative schemes and rarely address the problem of checking the problem’s singularity and computing the null space. In this paper we present a simple and efficient method for checking the singularity of an operator and for computing a null space when solving an elliptic structural problem with a dual Schur complement approach. The engineering community has long been reluctant to use iterative solvers mainly because of their lack of robustness. With the advent of parallel computers, domain decomposition methods received a lot of attention which resulted in some efficient, scalable and robust solvers [3, 6]. The Finite Element Tearing and Interconnecting method (FETI) has emerged as one of the most useful techniques and is making its way in structural and thermal commercial softwares [1, 4]. So far, the issue of semi-definite problems in FETI has not been fully addressed although a broad range of engineering problems are singular. For instance, the static and vibration analysis of satellites, aircrafts or multi-body structures is governed by [5]