Structure preserving methods based on finite difference methods with unstructured Voronoi meshes
| Project/Area Number |
23656070
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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 |
Engineering fundamentals
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| Research Institution | Osaka University |
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Principal Investigator |
FURIHATA Daisuke 大阪大学, サイバーメディアセンター, 准教授 (80242014)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 数値解析 / 偏微分方程式 / 非構造メッシュ / 構造保存数値解法 / 離散変分導関数法 / ボロノイ格子 / 構造保存解法 / Voronoi 格子 / 局所保存則 / 大域保存則 |
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| Research Abstract |
We have evaluated some mathematical features of finite difference operators with various error orders based on some Voronoi meshes in bounded domains and have studied error evaluations of them on nonsymmetric meshes. We also applied our methods to concrete partial differential equations, such as the Cahn-Hilliard equation, and obtained results that confirm our estimations. To decrease computation cost for those compromised numerical schemes, moreover, we have developed fast schemes based on predictor-corrector method with relaxed discrete variational derivative method and this attempt was a quite success.
We have also attended and given talks on some international conferences in this three years, for example, we gave a invited talk at the SciCADE 2011.
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Report
(4 results)
Research Products
(24 results)
