Fast direct solvers for the boundary element method in 3D and their applications to optimal design problems

2015 Fiscal Year Final Research Report

• Project/Area Number: 26870269
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Computational science; Design engineering/Machine functional elements/Tribology
• Research Institution: Nagoya University
• Principal Investigator: Isakari Hiroshi 名古屋大学, 工学(系)研究科(研究院), 助教 (50638773)
• Project Period (FY): 2014-04-01 – 2016-03-31
• Keywords: 境界要素法 / 高速直接解法 / トポロジー最適化 / トポロジー導関数 / 感度解析 / 随伴変数法 / 波動問題

Outline of Final Research Achievements

This study aims at developing fast direct solvers for boundary element method and efficient topology optimisations with the direct solvers. We have studied three types of the fast direct solvers; an interpolative-decomposition (ID)-based method, adaptive cross approximations with the H-matrix algebra, and the fast multipole (FMM) combined with a multifraontal solver for algebraic equations. With the proposed solvers, we have developed topology optimisations for wave devices. We have confirmed that an optimal design problem for sound-proof device, which is one of the important issues in engineering, can efficiently be solved by the proposed optimisation method.

Free Research Field

計算科学