Mathematical and Numerical Analysis for Variational Crack Propagation Model
| Project/Area Number |
26400195
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kanazawa University |
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Principal Investigator |
Kimura Masato 金沢大学, 数物科学系, 教授 (70263358)
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 亀裂進展モデル / 変分型モデリング / 自由境界問題 / 最適形状設計 / クリスタライン法 / 転位 / 弾性体 / バネ・ブロック系 / フェーズフィールドモデル / 移動境界問題 / バネブロックモデル |
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| Outline of Final Research Achievements |
In this research project,we considered a variational crack propagation model which the principal investigator proposed and some related moving boundary problems. We tried to establish the foundations of mathematical tools and mathematical modeling using their variational structure such as the gradient flow structure. Some efficient numerical schemes for them are also proposed. Additionally, we also studied related other topics: an elastic spring-block system, a phase field model of dislocation dynamics, a shape optimization approach to free boundary problems, a snow flake growth model by variational crystalline method, from the viewpoints of mathematical and numerical analysis and mathematical modeling based on their variational structures.
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Report
(4 results)
Research Products
(22 results)
