On the Moore-Penrose inverse in solving saddle-point systems with singular diagonal blocks

The paper deals with the role of the generalized inverses in solving saddle-point systems arising naturally in the solution of many scientific and engineering problems when FETI based domain decomposition methods are used to their numerical solution. It is shown that the Moore-Penrose inverse may be obtained in this case at negligible cost by projecting an arbitrary generalized inverse using orthogonal projectors. Applying an eigenvalue analysis based on the Moore-Penrose inverse, it is proved for simple model problems that the number of conjugate gradient iterations required for the solution of associate dual systems does not depend on discretization norms. The theoretical results are confirmed by numerical experiments with linear elasticity problems. Copyright c © 2011 John Wiley & Sons, Ltd.