2013 Fiscal Year Final Research Report
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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| 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 |
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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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