Hierarchical-Matrix Preconditioners for Parabolic Optimal Control Problems

Abstract. Hierarchical (H)-matrices approximate full or sparse matrices using a hierarchical data sparse format. The corresponding H-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 LUfactors as preconditioners in iterative methods. The experiment shows that the H-matrix preconditioners are effective and speed up the convergence of iterative methods.

• Type: Conference
• Year: 2007
• Where: ICCS
• Authors: Suely Oliveira, Fang Yang
• Keywords: Approximate H-matrix Operators, Hierarchical Data Sparse, ICCS 2007, Iterative Methods