|
|
An efficient block variant of robust structured multifrontal factorization method |
Zuo Xian-Yu (左宪禹)a, Mo Ze-Yao (莫则尧)b, Gu Tong-Xiang (谷同祥)b |
a School of Computer and Information Engineering, Henan University, Kaifeng 475004, China;
b Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China |
|
|
Abstract Based on the two-dimensional three-temperature (2D3T) radiation diffusion equations and its discrete system, using the block diagonal structure of the three-temperature matrix, the reordering and symbolic decomposition parts of the RSMF method are replaced with corresponding block operation in order to improve the solution efficiency. We call this block form method block RSMF (in brief, BRSMF) method. The new BRSMF method not only makes the reordering and symbolic decomposition become more effective, but also keeps the cost of numerical factorization from increasing and ensures the precision of solution very well. The theoretical analysis of the computation complexity about the new BRSMF method shows that the solution efficiency about the BRSMF method is higher than the original RSMF method. The numerical experiments also show that the new BRSMF method is more effective than the original RSMF method.
|
Received: 04 December 2012
Revised: 05 March 2013
Accepted manuscript online:
|
PACS:
|
02.10.Ud
|
(Linear algebra)
|
|
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 61202098, 61033009, 61170309, 91130024, and 11171039) and the China Tianyuan Mathematics Youth Fund (Grant No. 11226337). |
Corresponding Authors:
Zuo Xian-Yu, Mo Ze-Yao
E-mail: xianyu_zuo@163.com; zeyao_mo@iapcm.ac.cn
|
Cite this article:
Zuo Xian-Yu (左宪禹), Mo Ze-Yao (莫则尧), Gu Tong-Xiang (谷同祥) An efficient block variant of robust structured multifrontal factorization method 2013 Chin. Phys. B 22 080201
|
[1] |
George J A 1973 SIAM J. Numer. Anal. 10 345
|
[2] |
Hoffman A J, Martin M S and Rose D J 1973 SIAM J. Numer. Anal. 10 364
|
[3] |
Bebendorf M and Hackbusch W 2003 Numer. Math. 95 1
|
[4] |
Bebendorf M 2005 Math. Comp. 74 1179
|
[5] |
Chandrasekaran S, Dewilde P and Gu M 2010 SIAM J. Matrix Anal. Appl. 31 2261
|
[6] |
Grasedyck L, Kriemann R and Le Borne S 2006 Springer LNCSE 55 661
|
[7] |
Xia J L, Chandrasekaran S, Gu M and Li X 2009 SIAM J. Matrix Anal. Appl. 31 1382
|
[8] |
Börm S, Grasedyck L and Hackbusch W 2002 Computing 69 1
|
[9] |
Eidelman Y and Gohberg If 1999 Integral Equations Operator Theory 34 293
|
[10] |
Hackbusch W 1999 Computing 62 89
|
[11] |
Vandebril R, Van Barel M, Golub G and Mastronardi N 2005 A Bibliography on Semiseparable Matrices Calcolo 42 249
|
[12] |
Polizzi E and Sameh A 2006 Parallel Comput. 32 177
|
[13] |
Sambavarama S R, Sarin V, Sameh A and Grama A 2003 Parallel Comput. 29 1261
|
[14] |
Wang S, Li X S, Xia J L, Situ Y and de Hoop M V 2012 Revised SIAM J. Sci. Comput.
|
[15] |
Xia J L 2012 High-Perform. Sci. Comput. (Berlin: Springer) p. 199
|
[16] |
Duff I S and Reid J K 1983 ACM Bans. Math. Software 9 302
|
[17] |
Liu J W H 1992 SIAM Rev. 34 82
|
[18] |
Xia J L and Gu M 2010 SIAM J. Matrix Anal. Appl. 31 2899
|
[19] |
Pei W B 2007 J. Comm. Comput. Phys. 2 255
|
[20] |
An H B, Mo Z Y, Xu X W and Liu X 2009 J. Comput. Phys. 228 3268
|
[21] |
Baldwin C, Brown P N, Falgout R D, Graziani F and Jones J 1999 J. Comput. Phys. 154 1
|
[22] |
Fu S W, Fu H Q, Shen L J, Huang S K and Chen G N 1998 Chin. J. Comput. Phys. 15 489 (in Chinese)
|
[23] |
Gu T X, Dai Z H, Hang X D, Fu S W and Liu X P 2005 Chin. J. Comput. Phys. 22 471 (in Chinese)
|
[24] |
Mo Z Y, Fu S W and Shen L J 2000 Chin. J. Comput. Phys. 17 625 (in Chinese)
|
[25] |
Mo Z Y, Shen L J and Wittum G 2004 Int. J. Comp. Math. 81 361
|
[26] |
Zhang R P, Yu X J and Zhu J 2012 Chin. Phys. Lett. 29 110201
|
[27] |
Zhao G Z, Yu X J and Zhang R P 2013 Chin. Phys. B 22 020202
|
[28] |
Wu G C 2012 Chin. Phys. B 21 120504
|
[29] |
METIS http://glaros.dtc.umn.edu/gkhome/views/metis
|
[30] |
Parter S V 1961 SIAM Rev. 3 119
|
[31] |
Tewarson R P 1967 SIAM Rev. 9 91
|
[32] |
Schmitz P and Ying L 2012http://www.ma.utexas.edu/users/lexing/publications/direct2d.pdf
|
[33] |
Mo Z Y, Zhang A Q, Cao X L, Liu Q K, Xu X W, An H B, Pei W B and Zhu S P 2010 Front. Comp. Sci. China 4 480
|
No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|