Hierarchical-Matrix Preconditioners for Parabolic Optimal Control Problems

Authors:
Suely Oliveira;Fang Yang
Affiliations:
Department of Computer Science, The University of Iowa, Iowa City IA 52242, USA;Department of Computer Science, The University of Iowa, Iowa City IA 52242, USA
Venue:
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Year:
2007

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Abstract

Hierarchical ($\mathcal{H}$)-matrices approximate full or sparse matrices using a hierarchical data sparse format. The corresponding $\mathcal{H}$-matrix arithmetic reduces the time complexity of the approximate $\mathcal{H}$-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 $\mathcal{H}$-matrix LU-factors as preconditioners in iterative methods. The experiment shows that the $\mathcal{H}$-matrix preconditioners are effective and speed up the convergence of iterative methods.