2023 Fiscal Year Final Research Report

New solvers and strategies based on mathematical analyses to enhance parallel performance on massive computers

Research Project

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Project/Area Number	19K12008
Research Category	Grant-in-Aid for Scientific Research (C)
Allocation Type	Multi-year Fund
Section	一般
Review Section	Basic Section 60100:Computational science-related
Research Institution	Gifu Shotoku Gakuen University
Principal Investigator	Abe Kuniyoshi 岐阜聖徳学園大学, 経済情報学部, 教授 (10311086)
Co-Investigator(Kenkyū-buntansha)	生野壮一郎東京工科大学, コンピュータサイエンス学部, 教授 (70318864)
Project Period (FY)	2019-04-01 – 2024-03-31
Keywords	Krylov空間法 / 線形方程式 / 大規模計算機環境 / 通信箇所の削減 / 収束スピードの改善 / 丸め誤差解析
Outline of Final Research Achievements	In present petascale highperformance computing hardware, the main bottleneck of Krylov subspace methods for efficient parallelization is the inner products which require a global reduction. The parallel variants of BiCGSTAB such as communication avoiding and pipelined BiCGSTAB reducing the number of global communication phases and hiding the communication latency have been proposed. However, the numerical stability, specifically, the convergence speed of the parallel variants is slow, i.e., strongly affected by rounding errors. Therefore, we have designed parallel variants, which are referred to as pipelined BiCGSTAB, GPBiCG and BiCGstab(ell), and s-step CG. We have developed a stabilization strategy as well. We have examined the convergence speed between the standard and the parallel variants, and the effectiveness of the stabilization strategy by numerical experiments on the problems where the convergence has a long stagnation phase.
Free Research Field	計算科学
Academic Significance and Societal Importance of the Research Achievements	近年，大規模な計算機環境の発展が著しく，そういった大規模な計算機環境を活かす解法群の開発が始まっている．一方で，誤差に対して脆弱であるという欠点があり，大規模計算機向きアルゴリズム設計の研究と誤差の解析や制御といった研究とが，互いの長所を活かし進められていない．本研究は，アルゴリズム設計で問題となる誤差に対する脆弱性の改善と，今日の大規模な計算機環境向きアルゴリズムの設計との両面から研究を遂行するものである．同時に，これらの課題を実現すると大規模な計算機環境向き解法群が盤石なものとなり，社会に役立つ実用問題に対する緻密な解明が一層可能となる．