Theoretical and experimental study of the charge simulation method and the dipole simulation method

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400196
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: The University of Electro-Communications
• Principal Investigator: Ogata Hidenori 電気通信大学, 情報理工学(系)研究科, 教授 (50242037)
• Project Period (FY): 2013-04-01 – 2016-03-31
• 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

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.

Free Research Field

数値解析