2021 Fiscal Year Final Research Report
Development of eigenvalue analysis methods using a quadrature-type eigensolver with nonlinear transformations
| Project/Area Number |
18H03250
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Review Section |
Basic Section 60100:Computational science-related
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
二村 保徳 筑波大学, システム情報系, 助教 (30736210)
今倉 暁 筑波大学, システム情報系, 准教授 (60610045)
保國 惠一 筑波大学, システム情報系, 助教 (90765934)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Keywords | 固有値解析 / 積分型固有値解法 / 非線形変換 |
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| Outline of Final Research Achievements |
In this research, we developed a method for improving the performance of the quadrature-type parallel eigenvalue solver through nonlinear variable transformation. Compared to conventional sequential eigenvalue solvers, quadrature-eigenvalue solvers have high parallelism and can solve nonlinear eigenvalue problems with the same algorithm as linear eigenvalue problems. On the other hand, its performance is affected by the distribution of eigenvalues in the neighborhood of the target domain. We proposed a method to transform the linear eigenvalue problems to the corresponding nonlinear eigenvalue problems by using nonlinear variable transformations. The obtained nonlinear eigenvalue problem is solved using the nonlinear version of the quadrature-type eigenvalue solver. The performance of the proposed method is theoretically analyzed, and the effectiveness of the proposed method is confirmed by applying the developed method to several applications.
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| Free Research Field |
数値解析学
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| Academic Significance and Societal Importance of the Research Achievements |
本研究課題において、線形固有値問題を非線形固有値問題に帰着させて解くこれまでにない新規の方法論を提案し、その手法の構築と評価を行ったことが学術的な意義である。大規模な固有値解析は、素粒子や原子核などの基礎物理分野、ナノマテリアルやフォトニック結晶の応用物理分野、自動車・建築物の設計、新素材・デバイスの開発、流体・振動解析、創薬、ネットワーク・データ解析など、幅広いシミュレーションでの応用がある。本課題で開発・拡張を進めた超並列な固有値解法が活用されることで、幅広い分野の科学技術シミュレーション・データ解析応用の発展に寄与する。
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