An efficient block variant of robust structured multifrontal factorization method

doi:10.1088/1674-1056/22/8/080201

中国物理B ›› 2013, Vol. 22 ›› Issue (8): 80201-080201.doi: 10.1088/1674-1056/22/8/080201

• GENERAL • 下一篇

An efficient block variant of robust structured multifrontal factorization method

左宪禹^a, 莫则尧^b, 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

收稿日期:2012-12-04 修回日期:2013-03-05 出版日期:2013-06-27 发布日期:2013-06-27
基金资助:
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).

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

Received:2012-12-04 Revised:2013-03-05 Online:2013-06-27 Published:2013-06-27
Contact: Zuo Xian-Yu, Mo Ze-Yao E-mail:xianyu_zuo@163.com; zeyao_mo@iapcm.ac.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: HSS structure, low-rank property, multifrontal method, two-dimensional three-temperature radiative diffusion equations

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.

Key words: HSS structure, low-rank property, multifrontal method, two-dimensional three-temperature radiative diffusion equations

中图分类号: (Linear algebra)

02.10.Ud

左宪禹, 莫则尧, 谷同祥. An efficient block variant of robust structured multifrontal factorization method[J]. 中国物理B, 2013, 22(8): 80201-080201.

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[J]. Chin. Phys. B, 2013, 22(8): 80201-080201.

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An efficient block variant of robust structured multifrontal factorization method

An efficient block variant of robust structured multifrontal factorization method

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