Geometric structure-preserving finite difference method for vector-valued evolution equation
| Project/Area Number |
24654026
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Shibaura Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
FURIHATA Daisuke 大阪大学, サイバーメティアセンター, 准教授 (80242014)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 数値解析 / 差分法 / 構造保存 / ベクトル値関数 / 非線形偏微分方程式 / 幾何学的構造 / 数値計算 / エネルギー構造 / 数値計算スキーム / ベクトル値 / 有限差分法 |
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| Outline of Final Research Achievements |
We propose effective numerical schemes for vector-valued partial differential equations in engineering fields and give some theoretical analyses to
these schemes. The target problem are the Landau-Lifshitz equation, Ericksen-Leslile equation, Localized Induction model and so on. We construct structure-preserving schemes for these models, that is, the proposed schemes inherit a geometric property and energy structure from the original problems and show the existence and uniqueness of the finite difference solutions and also error estimates. For the problem which exact solutions are known or constructible, we compare the numerical solutions with the exact solutions and show the effectiveness of our proposed schemes.
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Report
(4 results)
Research Products
(22 results)
