On the solution of the distributed optimal control problem with time-periodic parabolic equations

We consider the system of linear equations arisen from the finite element discretization of the distributed optimal control problem with time-periodic parabolic equations. A block alternating splitting iteration (BASI) method is presented for solving the obtained system. We prove that the BASI method is unconditionally convergent. We derive the BASI preconditioner and present an estimation formula for the parameter of the BASI preconditioner. Numerical results are presented to verify the efficiency of both the BASI method and the BASI preconditioner. Comparison with some existing methods are also given.