2017 Fiscal Year Final Research Report
Visualizaion of exteremal quasiconformal mappings
| Project/Area Number |
16K16061
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
High performance computing
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| Research Institution | Yamanashi Eiwa College |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2018-03-31
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| Keywords | 極値的擬等角写像 / 数値擬等角写像 / 擬等角写像 / 可視化 / 高性能計算 |
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| Outline of Final Research Achievements |
In this project, the visualization method of extremal quasiconformal mappings was studied. We constructed an approximant as a piecewise linear mapping, which is obtained by the least squares solution of an overdetermined linear system. The Beltrami coefficients and boundary correspondence was used for our linear system. Numerical experiments show high accuracy of approximants.
Furthermore, we studied the numerical construction of the Loewner flow in view of application for quasiconformal mappings. The approximant was constructed as a family of polynomials. We proved the convergence of the coefficients of polynomial. The results were published in a mathematical journal and presented on international conferences.
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| Free Research Field |
情報学
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