A new version of a preconditioning method for certain two-by-two block matrices with square blocks

摘要

Two-by-two block matrices with square matrix blocks arise in many important applications. Since the problems are of large scale, iterative solution methods must be used. Thereby the choice of an efficient and robust preconditioner is crucial. This paper presents two earlier used such preconditioners followed by a novel preconditioner based on transforming the given matrix to a proper form. Sharp eigenvalue estimates are derived. The condition numbers of each of the three methods are robust with respect to all parameters involved, including the mesh parameter. Therefore, the preconditioners are suitable for a variety of problems where such matrix structures arise. The performance of the methods are also compared numerically on a set of test problems.