Fast solution for ultra-large scale systems as a basis of computational materials science

2014 Fiscal Year Final Research Report

• Project Area: Materials Design through Computics: Complex Correlation and Non-equilibrium Dynamics
• Project/Area Number: 22104004
• Research Category: Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Nagoya University
• Principal Investigator: ZHANG Shao-Liang 名古屋大学, 工学(系)研究科(研究院), 教授 (20252273)
• Co-Investigator(Kenkyū-buntansha): ABE Kuniyoshi 岐阜聖徳学園大学, 経済情報学部, 教授 (10311086) ; YAMAMOTO Yusaku 電気通信大学, 情報理工学研究科, 教授 (20362288) ; SOGABE Tomohiro 愛知県立大学, 情報科学部, 准教授 (30420368) ; IMAHORI Shinji 名古屋大学, 大学院工学研究科, 准教授 (90396789) ; MIYATA Takahumi 名古屋大学, 大学院工学研究科, 助教 (90581645)
• Co-Investigator(Renkei-kenkyūsha): SUGIHARA Masaaki 青山学院大学, 理工学部, 教授 (80154483)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 計算物理 / 数理物理 / 数理工学 / シミュレーション工学 / 応用数学

Outline of Final Research Achievements

Finding novel complex correlation phenomena and clarifying the non-equilibrium dynamics are of prime importance in the field of materials design. This research group tackles the challenging problems from the viewpoints of numerical linear algebra, optimization and high-performance computing. The major purpose of the researches is to develop robust and efficient numerical algorithms for solving large linear systems and eigenvalue problems in order to shed light on a breakthrough toward the challenging problems. Some of numrical algrotihms for solving linear systems we developed are as follows: the shifted COCR method for solving shifted complex symmetric linear systems; the look back GMRES(m) method for nonsymmetric linear systems; a variand of the IDR(s) method for nonsymmetric linear systems. Some of numrical algrotihms for solving eigenvalue problems we developed are as follows: the Arnoldi(M,W,G) method; an extension of the SS method;

Free Research Field

数値解析学