On some new approximate factorization methods for block tridiagonal matrices suitable for vector and parallel processors

Authors:
Hou-Biao Li;Ting-Zhu Huang;Yong Zhang;Xing-Ping Liu;Hong Li
Affiliations:
School of Applied Mathematics, University of Electronic Science and Technology of China, Jianshe Road, Sichuan 610054, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Jianshe Road, Sichuan 610054, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Jianshe Road, Sichuan 610054, PR China;Lab of Comp. Phy., Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;School of Applied Mathematics, University of Electronic Science and Technology of China, Jianshe Road, Sichuan 610054, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

In this paper, to obtain an efficient parallel algorithm to solve sparse block-tridiagonal linear systems, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are suitable when the desired goal is to maximize parallelism. Moreover, some theoretical results concerning these preconditioners are presented and how to construct preconditioners effectively for any nonsingular block tridiagonal H-matrices is also described. In addition, the validity of these preconditioners is illustrated with some numerical experiments arising from the second order elliptic partial differential equations and oil reservoir simulations.