An alternating positive semidefinite splitting preconditioner for the three-by-three block saddle point problems

Abstract

Using the idea of dimensional splitting method we present an iteration method for solving three-by-three block saddle point problems which can appear in linear programming and finite element discretization of the Maxwell equation. We prove that  the method is convergent unconditionally. Then the induced preconditioner is used to accelerate the convergence of the GMRES method for solving the system. Numerical results are presented to compare the performance of the method with some existing ones.