Theoretical and experimental study of the charge simulation method and the dipole simulation method
| Project/Area Number |
25400196
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
Ogata Hidenori 電気通信大学, 情報理工学(系)研究科, 教授 (50242037)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 代用電荷法 / 双極子法 / ポテンシャル / 複素関数論 / 解析関数 / 数値積分 / 超函数 / 調和関数 / 周期関数 / ラプラス方程式 / 境界値問題 / 等角写像 |
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| Outline of Final Research Achievements |
In this study, we examined the charge simulation method and the dipole simulation method for potential problems. In the charge simulation method, we approximate the solution by the superposition of fictitious point charges. We obtain the dipole simulation method as an approximation by the superposition of fictitious electric dipoles in stead of point charges. We are especially interested in the positioning of the dipoles and found from numerical experiments that it is good to use the points obtained by a conformal mapping of equally distributed points on a circle.
We also applied these methods to the approximation of complex analytic functions. We find that these approximations achieve good accuracy by theoretical error estimates and numerical experiments.
Besides, as a related research, we studied numerical integration methods based on the hyperfunction theory.
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Report
(4 results)
Research Products
(14 results)
