2022 Fiscal Year Final Research Report
A study on a space-time boundary element method for the wave equation
Project/Area Number |
20K11849
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 60100:Computational science-related
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Research Institution | Kyoto University |
Principal Investigator |
Niino Kazuki 京都大学, 情報学研究科, 助教 (10728182)
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Project Period (FY) |
2020-04-01 – 2023-03-31
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Keywords | space-time法 / 境界要素法 / 波動方程式 |
Outline of Final Research Achievements |
For numerical analysis of time-domain partial differential equations (PDEs), marching-on-in-time numerical methods, which independently discretises time and spacial axes, have been widely studied. The space-time method, which is another discretisation method for time-domain PDEs, discretises a space-time domain by regarding the time axis as an additional axis of the space. This method has advantages such as more flexible mesh decomposition, better efficiency of parallel computations, easy application to problems with deformation depending on time, etc. In this study we have worked on stability analyses and flexible mesh decomposition on a space-time domain for 2D and 3D wave equations, as a fundamental study of the space-time method to be used for analysing complex problems in applications.
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Free Research Field |
計算力学
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Academic Significance and Societal Importance of the Research Achievements |
space-time法の研究は有限要素法との組み合わせの研究が多く、本研究で提案した、波動散乱問題の解析に有効な境界要素法とspace-time法とを組み合わせた数値解法は、時間域の波動散乱問題に対する有力な数値解法と成り得ると考えられる。また我々の知る限り、本研究の他にSpace-time境界要素法の安定性解析に関する研究や、3次元の問題に対するspace-time境界要素法の研究はほとんど行われていないため、今後様々な応用上現れる大規模な問題に適用可能なspace-time境界要素法の開発に向けた基礎的研究として、本研究の意義は大きいものと考える。
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