On the stability of boundary integral methods in wave problems
| Project/Area Number |
18H03251
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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 | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
高橋 徹 名古屋大学, 工学研究科, 准教授 (90360578)
新納 和樹 京都大学, 情報学研究科, 助教 (10728182)
吉川 仁 京都大学, 情報学研究科, 准教授 (90359836)
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| Project Period (FY) |
2018-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2020: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2019: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2018: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
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| Keywords | 波動方程式 / 境界積分法 / 安定性 / 櫻井杉浦法 / 波動問題 / 時間域境界積分法 / 時間域 / Sakurai Sugiura法 |
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| Outline of Final Research Achievements |
Stability of time domain boundary integral methods for wave problems using collocation is a long standing tough problem which still remains open in spite of many efforts to solve it. This study proposes a method to investigate the stability of boundary integral methods in time domain using a solver of non-linear eigenvalue problems called the Sakurai Sugiura method. We test the proposed method via numerical experiments. It is found that the proposed method is effective not only in assessing the stability but in studying the accuracy of boundary integral formulations. We also proposed a stable fast method in 3D as well as a space-time method for variable domains, both of which turned out to be effective.
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| Academic Significance and Societal Importance of the Research Achievements |
選点法を用いた時間域の境界積分法は，数値計算上の種々の利点を有する魅力的な解法でありながら，安定性に関する確実な知見が得られていないために広く用いられるには至っていない．本研究は安定性の問題を研究するための新しい方法を提供するものであり，今後，時間域解法を実問題に適用してゆく上で有用なツールとなることが期待される．特に，本手法は安定性の問題を周波数域の積分方程式の固有値問題に帰着させることから直感が効きやすく，安定性の高い積分方程式の定式化を得る上で有用であると考えられる．更に高精度の境界積分法を得る上で有用であることも提案手法の大きな利点である．
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Report
(4 results)
Research Products
(19 results)
