A note on preconditioning for the 3 × 3 block saddle point problem

Abstract

In this paper, we mainly propose some new preconditioners for a special class of 3 × 3 block saddle point problems, which can arise from the time-dependent Maxwell equations and some other practical problems. Firstly, the solvability of this kind of problem is investigated under suitable assumptions. Then, we analyze the corresponding eigenvalues of the new preconditioned matrices presented in this work. Furthermore, we show that proposed preconditioned matrices only have at most three distinct eigenvalues. Finally, two numerical examples are also carried to verify the effectiveness of proposed preconditioners.