| Project/Area Number |
09440081
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehima University |
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Principal Investigator |
AMANO Kaname Faculty of Engineering, Ehime University, Professor, 工学部, 教授 (80113512)
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| Co-Investigator(Kenkyū-buntansha) |
OGATA Hidenori Faculty of Engineering, Ehime University, Lecturer, 工学部, 講師 (50242037)
TSUDA Koichi Faculty of Engineering, Ehime University, Professor, 工学部, 教授 (20112253)
IGARI Katsuju Faculty of Engineering, Ehime University, Professor, 工学部, 教授 (90025487)
SUGIHARA Masaaki Department f Computational Science and Engineering, Nagoya University, Professor, 大学院・工学研究科, 教授 (80154483)
OKANO Dai Faculty of Engineering, Ehime University, Assistant, 工学部, 助手 (90294785)
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| Project Period (FY) |
1997 – 1999
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| Keywords | numerical analysis / conformal mappings / charge simulation method / multiply-connected domains / potential problems / appoximation / fundamental solutions |
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| Research Abstract |
Conformal mappings are familiar in science and engineering. But, exact mapping functions are not known except for special domains. Particularly, conformal mappings of unbounded multiply-connected domains are well known as a method of two-dimensional potential flow analysis. The mappings of a domain exterior to closed Jordan curves onto parallel, circular and radial slit domains are directly related to the problems of uniform, vortex and point-souce flows around obstacles, respectively.
We presented a simple method of numerical conformal mappings of the multiply-connected domains onto the parallel, circular and radial slit domains. We reduced the mapping problems to the Dirichlet problem with a pair of conjugate harmonic functions and employed the charge simulation method, where the pair of conjugate harmonic functions are appoximated by a linear combination of complex logarithmic potentials. The method has the following features :
1. Conformal mappings onto the parallel slit domains with slits parallel to the imaginary axis and parallel to the real axis constitute a dual problem and can be computed in a dual way.
2. Conformal mappings onto the circular and radial slit domains constitute a dual problem and can be computed in a dual way.
3. They are reformulated into a more integrated form in which the linear equations to be solved have the same coefficient matrix.
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