open access

https://hdl.handle.net/2115/48513

A New Acceleration Factor Decision Method for ICCG Method Based on Condition Number

英語

submatrix

2012-02

IEEE

IEEE Transactions on Magnetics

48(2)

519-522

The ICCG method is widely used to solve a sparse symmetric linear system which results from the finite element method. In order to improve the convergence property of the ICCG method, the introduction of the acceleration factor was proposed. The automatic acceleration factor decision method, using the incomplete Cholesky decomposition of a coefficient matrix, has been previously proposed. However, when employing the previously proposed automatic decision method, much more iterations of ICCG method are sometimes necessary, compared with using the optimum acceleration factor, which minimizes the number of ICCG iterations. In this paper, we propose a new acceleration factor decision method. The proposed method takes into account the condition number of the coefficient matrix. It is well known that the condition number represents the quality of the matrix, so the optimum acceleration factor should be decided to minimize the condition number of the coefficient matrix. However, the condition number of the coefficient matrix is not almost available due to requiring a large memory in computing. Therefore, we develop a new method using submatrix, that does not need a large memory. The procedure and demonstration of the proposed method are described in this paper.

学術雑誌論文

Accepted Manuscript

© 2012 IEEE. Reprinted, with permission, from Takada, A., Noguchi, S., Igarashi, H., A New Acceleration Factor Decision Method for ICCG Method Based on Condition Number, IEEE Transactions on Magnetics, Feb. 2012. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Hokkaido University products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.

0018-9464