Hierarchical-matrix preconditioners for parabolic optimal control problems

Hierarchical (H)-matrices approximate full or sparse matrices using a hierarchical data sparse format. The corresponding R-matrix arithmetic reduces the time complexity of the approximate H-matrix operators to almost optimal while maintains certain accuracy. In this paper, we represent a scheme to solve the saddle point system arising from the control of parabolic partial differential equations by using H-matrix LU-factors as preconditioners in iterative methods. The experiment shows that the H-matrix preconditioners are effective and speed up the convergence of iterative methods.