2011 Fiscal Year Final Research Report
New development of discrete differential geometry by discrete integrable systems
| Project/Area Number |
21656027
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Engineering fundamentals
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| Research Institution | Kyushu University |
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Principal Investigator |
KAJIWARA Kenji 九州大学, マス・フォア・インダストリ研究所, 教授 (40268115)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 離散可積分系 / 離散微分幾何 |
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| Research Abstract |
Discrete differential geometry has been considered, which is a mathematical framework describing the dynamics of geometric objects on computers. Theory of discrete integrable systems has been developed, which was successfully applied to discretize the planar curve dynamics on Eucledian plane and to construct explicit formulas in terms of the z functions. As by-products, highaccuracy stable numerical schemes for curve dynamics with adaptive step size control, and seeds of new development to the theory of discrete conformal mappings have been obtained.
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