Algebraic Multigrid method with minimized communication

2018 Fiscal Year Final Research Report

• Project/Area Number: 15K15998
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: High performance computing
• Research Institution: Kogakuin University
• Principal Investigator: Fujii Akihiro 工学院大学, 情報学部(情報工学部), 准教授 (10383986)
• Project Period (FY): 2015-04-01 – 2019-03-31
• Keywords: 代数的多重格子法 / 粗格子集約 / ニアカーネルベクトル / 時間積分並列化

Outline of Final Research Achievements

Algebraic multigrid method is a linear solver, which calculates the smaller sized problem from the original large sized problem. It solves those large and small matrix equations alternatively, and makes the solution reach convergent very fast. From the view point of computing environment, supercomputers offer huge parallelism these days. In such an environment, small sized problems of the multigrid method tend to be too much distributed all over the processes, which leads to large communication time. In this case, it becomes the bottle neck of execution time, and higher parallel execution degrades the performance more. This research proposes an original method that balances the paralelism and communication amount of the distributed smaller sized problems in algebraic multigrid method. It was effective in our numerical experimetns, and our solver is published as an example implementation.

Free Research Field

高性能計算

Academic Significance and Societal Importance of the Research Achievements

線形問題の解法として多重格子法は流体解析も含めて，広い範囲のアプリケーションで利用されている．本研究では主に，高並列時に課題になるサイズの小さい問題の生成方法についてと，問題に応じて収束性をあげるためのニアカーネルベクトルの設定手法について新規手法を提案し，発表をしてきた．今後，本研究の考察の対象としているような超高並列な計算環境や，問題に応じて収束しにくい成分を設定して代数的多重格子法を適用する場面において，本研究の成果が取り込まれていくことを期待している．