Block triangular preconditioning for elliptic boundary optimal control with mixed boundary conditions

In this paper, preconditioning the saddle point problem arising from the elliptic boundary optimal control problem with mixed boundary conditions is considered. A block triangular reconditioning method is proposed based on permutations of the saddle point problem and approximations of the corresponding Schur complement. The spectral properties of the preconditioned matrix is analyzed. Numerical experiments are conducted to demonstrate the effectiveness of the proposed preconditioning method.