Synthetical development of fast numerical methods for solving large-scale linear systems which arise g from the field of computational science and engineerin

计算科学与工程领域兴起的用于求解大规模线性系统的快速数值方法的综合发展

• 批准号: 15360042
• 负责人: ZHANG Shao-liang
• 金额: $ 9.73万
• 依托单位: Nagoya University (2005-2006)The University of Tokyo (2003-2004)
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-15360042/
• 关键词: large-scale 1inear systems; fast numerical method; Krylov-subspace method; preconditioning technique; super computer; parallel computer; singular matrix; library; 大規模線形方程式; 可変的前処理; 電子構造計算; Toeplitz行列; Bi-CR法; COCR法

The target of this project is synthetically to develop fast numerical methods for solving large-scale linear systems which arise from the field of computational science and engineering. Throughout the whole of this project, we completed almost the target.The research results of this project are concluded as follows.1. The circumstance of applications which lead large linear systems was investigated by all of numbers.2. The coefficient matrix of linear systems was classified from size, structure and algebra.3. The convergent property of new methods GPBi-CG(ω) and GPBi-CG was evaluated through many test problems.4. The convergence theory for singular linear systems was studied.5. Several kinds of preconditioning technique was studied.6. A new fast and basic method, so-called Bi-CR, was proposed.7. A new systems of parallel computer was built for this project.8. A new web server system for large linear system was built almost.

该项目的目标是综合开发快速数值方法来求解计算科学和工程领域产生的大规模线性系统。纵观整个项目，我们基本完成了预期目标。本项目的研究成果如下： 1．对大型线性系统的应用情况进行了全面的调查。 2．从大小、结构和代数方面对线性系统的系数矩阵进行了分类。 3．通过大量的测试问题评估了新方法GPBi-CG(ω)和GPBi-CG的收敛性。 4．研究了奇异线性系统的收敛理论； 5．对几种预处理技术进行了研究。 6．提出了一种新的快速且基本的方法，即Bi-CR。7．为该项目搭建了一套新的并行计算机系统。 8．一个新的大型线性系统Web服务器系统基本建成。

项目成果

CGS法の改良について

关于CGS方法的改进

• 发表时间: 2004
• 期刊: 日本応用数理学会論文誌 14・1
• 作者: 曽我部知広;金成海;阿部邦美;張紹良
• 通讯作者: 張紹良

Application of the GMRES method to singular systems and least squares Problems

GMRES 方法在奇异系统和最小二乘问题中的应用

• 发表时间: 2006
• 期刊: Proceedings of the Seventh China-Japan Seminar on Numerical Mathematics(in Z. -C. Shi and H. Okamoto eds. ) (Science Press)
• 作者: K.Hayami;T.Ito
• 通讯作者: T.Ito

A Variant of the Orthamin (2) Method for Singular Linear Systems

奇异线性系统的 Orthamin (2) 方法的变体

• 发表时间: 2004
• 期刊: Numerical Algorithms Vol.36
• 作者: K.Abe;S.-L.Zhang;曽我部知広;K.Abe;T.Sogabe;K.Abe
• 通讯作者: K.Abe

K.Abe, S.-L.Zhang: "A strategy of fast solvers for elliptic boundary value problems"the proceedings of the 4th International Workshop on Shock Wave/Vortex Interaction. 169-177 (2003)

K.Abe、S.-L.Zhang：“椭圆边值问题的快速求解器策略”第四届冲击波/涡相互作用国际研讨会论文集。

非対称Toeplitz行列のための置換行列による前処理

使用不对称 Toeplitz 矩阵的置换矩阵进行预处理

• 发表时间: 2005
• 期刊: 日本応用数理学会論文誌 Vol.15, No.2
• 作者: 曽我部知広;鄭波;橋本康;張紹良
• 通讯作者: 張紹良