Block alternating splitting implicit iteration methods for saddle-point problems from time-harmonic eddy current models

For the saddle-point problems arising from the finite element discretizations of the hybrid formulations of the time-harmonic eddy current problems, we establish a class of block alternating splitting implicit iteration methods and demonstrate its unconditional convergence. Experimental results are given to show the feasibility and effectiveness of this class of iterative methods when they are employed as preconditioners for Krylov subspace methods such as GMRES and BiCGSTAB.