Structure-preserving numerical method for partial differential equations based on Voronoi diagram
| Project/Area Number |
26610038
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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 |
Foundations of mathematics/Applied mathematics
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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) |
2014-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 構造保存数値解法 / 離散変分 / ボロノイ分割 / 非構造格子 / ボロノイ格子 / 偏微分方程式 / 局所保存則 / 大域保存則 / 離散変分導関数法 |
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| Outline of Final Research Achievements |
The discretization of the differential limiting operation is the base of the original finite difference method. We appropriately introduced it to our study via the Voronoi decomposition and derived the exact discrete Green theorem by Voronoi discretization on the arbitrary lattice in the multidimensional region, e.g., the gradient, Laplacian.Our results include mathematical proofs and mathematically rigorous.
This showed that the Voronoi-Delaunay triangulation has favorable characteristics to allow arbitrary lattice placement while inheriting excellent mathematical properties.Furthermore, we adopted this Voronoi difference as the basis of the discrete variational derivative method to design numerical schemes for some partial differential equations.This indicates that our studies strengthened both the practicality and the theoretical foundation of the numerical solution method of partial differential equations.
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Report
(4 results)
Research Products
(18 results)
