Multiple search direction conjugate gradient method II: theory and numerical experiments

Abstract

In this article, we give the convergence and consistency of the MSD-CG method [Gu, T.-X., Liu, X.-P., Mo, Z.-Y. and Chi, X.-B. (in press). Multiple search direction conjugate gradient method I: Methods and their propositions. Int. J. Comput. Math.] and estimate the convergence rate of this method. Numerical experiments on two distributed parallel computers, Dawning 3000 and P-II Cluster, show the efficiency of our method and show that it compares favorably with some domain decomposition methods.

Keywords:

• Linear systems
• Conjugate gradient-type method
• Massively parallel computing
• Inner product
• Global communication

Acknowledgements

This project is supported partly by the State Hi-Tech Research and Development Program (863), the Natural Science Fund of China (60373015) and the Foundation of National Key Laboratory of Computational Physics.